Habilitationsschriftzur

Erlangung der Venia legendifur das Fach Physik

derRuprecht-Karls-Universitat

Heidelberg

vorgelegt von

Alban Kellerbauergeb. in Munchen

2008

Dynamics of Antihydrogen Production in Penning Trapsand Indirect Laser Cooling of Antiprotons

If there is negative electricity, why not negative gold, as yellow and valuable asour own, with the same boiling point and identical spectral lines; different only inso far that if brought down to us it would rise up into space with an accelerationof 981 [cm/s2].

Arthur Schuster (1851–1934), German-born British physicistIn: “Potential matter.—A holiday dream,” Nature 58 (1898) 367.

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Table of Contents

1 Introduction: Antihydrogen for tests of CPT symmetry and general relativity 11.1 CPT symmetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Antimatter gravity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51.3 The need for ultracold antihydrogen . . . . . . . . . . . . . . . . . . . . . . . 7

2 Dynamics of antihydrogen production in Penning traps 92.1 Antihydrogen recombination and detection . . . . . . . . . . . . . . . . . . . . 92.2 Temperature dependence of antihydrogen production . . . . . . . . . . . . . . 122.3 Laser-induced formation of antihydrogen . . . . . . . . . . . . . . . . . . . . 172.4 Antihydrogen temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

3 Indirect laser cooling of antiprotons 253.1 Towards ultracold antihydrogen . . . . . . . . . . . . . . . . . . . . . . . . . 253.2 Laser cooling of negative ions . . . . . . . . . . . . . . . . . . . . . . . . . . 273.3 High-resolution laser spectroscopy on the negative osmium ion . . . . . . . . . 31

A Complete list of publications 35A.1 Journal and review articles . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35A.2 Conference papers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38A.3 Popular-science articles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44A.4 Invited talks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

B Selection of most important publications 47

1. M. Amoretti et al., “Antihydrogen production temperature dependence,” Phys. Lett. B583 (2004) 59 [A9].

2. M. Amoretti et al., “Dynamics of antiproton cooling in a positron plasma during antihy-drogen formation,” Phys. Lett. B 590 (2004) 133 [A11].

3. N. Madsen et al., “Spatial distribution of cold antihydrogen formation,” Phys. Rev. Lett.94 (2005) 033403 [A17].

4. A. Kellerbauer and J. Walz, “A novel cooling scheme for antiprotons,” New J. Phys. 8(2006) 45 [A22].

5. A. Kellerbauer et al., “Sideband cooling of ions in a non-neutral buffer gas,” Phys. Rev.A 73 (2006) 062508 [A25].

6. M. Amoretti et al., “Search for laser-induced formation of antihydrogen atoms,” Phys.Rev. Lett. 97 (2006) 213401 [A28].

7. M. C. Fujiwara et al., “Temporally controlled modulation of antihydrogen productionand the temperature scaling of antiproton-positron recombination,” Phys. Rev. Lett. 101(2008) 053401 [A39].

8. U. Warring et al., “High-resolution spectroscopy on the negative osmium ion,” submittedfor publication in Phys. Rev. Lett. (2008).

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1

1 Introduction: Antihydrogen for tests of CPT symmetryand general relativity

1.1 CPT symmetry

Almost fifteen years ago, a group of physicists at the European Organization for Nuclear Re-search (CERN) in Geneva first managed to synthesize antihydrogen (H), an atom composedentirely of antimatter, at the low-energy antiproton ring (LEAR).1 In 2002, the ATHENA col-laboration working at LEAR’s successor at CERN, the antiproton decelerator (AD), achievedthe first production of cold antihydrogen from antiproton and positron plasmas confined in Pen-ning traps,2 a result that was reproduced shortly afterward by the competing ATRAP group.3

These spectacular achievements were the first steps toward probing one of the great unsolvedquestions in physics today: Why is there no primary antimatter in the observable universe?

The concept of antimatter first arose in the context of Paul Dirac’s equation describing theproperties of particles with half-integer spin, such as the electron.4 Dirac himself realized soonafterward that the equation had a corresponding negative-energy solution for every ordinarypositive solution. After initially dismissing them as “unphysical,” he later interpreted thesenegative solutions as representing the antimatter counterparts to ordinary particles.5 Galvanizedby this prediction, experimentalists began looking for the unique signatures of antiparticles inthe naturally occurring cosmic radiation. Less than two years later, the anti-electron, dubbed thepositron, was discovered and unambiguously identified in cloud chamber photographs.6 Withthe successful synthesis of the antiparticles of the proton and the neutron during the 1950’sat the Bevatron accelerator at Berkeley,7,8 the possibility that all elementary particles had anantimatter counterpart was being seriously considered. It was formally expressed as the CPTtheorem by W. Pauli, who postulated that all physical laws continue to hold when the combinedCPT operator – charge conjugation, parity, and time reversal – is applied to any system.9

In particular, it follows from the CPT theorem that any particle is transformed into its an-tiparticle when the CPT operations are applied to the its wavefunction (see Fig. 1), and thatfurthermore the particle and antiparticle have identical properties, such as lifetime, inertialmass, electric charge and magnetic moment. Some properties (those which correspond to ad-ditive quantum numbers) have the identical magnitude, but the inverse sign. The most strikingconsequence of the existence of antimatter, which results from the equivalence of mass and en-ergy10 on the one hand and the observed conservation of the abovementioned quantum numbers

1G. Baur et al., “Production of antihydrogen,” Phys. Lett. B 368 (1996) 251.2M. Amoretti et al., “Production and detection of cold antihydrogen atoms,” Nature 419 (2002) 456.3G. Gabrielse et al., “Background-free observation of cold antihydrogen with field-ionization analysis of its

states,” Phys. Rev. Lett. 89 (2002) 213401.4P. A. M. Dirac, “The quantum theory of the electron,” Proc. Roy. Soc. A 117 (1928) 610.5P. A. M. Dirac, “Quantised singularities in the electromagnetic field,” Proc. Roy. Soc. A 133 (1931) 60.6C. D. Anderson, “The positive electron,” Phys. Rev. 43 (1933) 491.7O. Chamberlain et al., “Observation of antiprotons,” Phys. Rev. 100 (1955) 947.8B. Cork et al., “Antineutrons produced from antiprotons in charge-exchange collisions,” Phys. Rev. 104

(1956) 1193.9W. Pauli, in: Niels Bohr and the development of physics, New York: Pergamon (1955), p. 30.

10A. Einstein, “Ist die Tragheit eines Korpers von seinem Energieinhalt abhangig?” Ann. Physik 18 (1905)639.

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Figure 1: (From left to right) The combined operations charge conjugation, parity and timereversal transform a particle into its antiparticle.

Figure 2: Second-order Feynman diagrams for (a) pair production and (b) annihilation.Antiparticles are represented with arrows pointing in the direction of decreasing time.

on the other, is the fact that pairs of particles and antiparticles can be created out of vacuum,provided that a total energy of at least 2mc2 is supplied, where m is the rest mass of the particleand c is the speed of light. Conversely, the collision of a particle with its antiparticle leads tothe annihilation of both and the release of the same amount of energy in the form of photons orlighter particles. The Feynman diagrams for some of these processes are shown in Fig. 2. In theframework of modern quantum field theories (and hence, within the standard model of particlephysics), CPT symmetry arises automatically as long as the theories meet certain fundamentalrequirements, such as a flat space-time structure and the point-like nature of elementary par-ticles. However, in light of recent developments in theoretical particle physics, such as stringtheory,11 such seemingly self-evident conditions are being increasingly challenged. At verysmall length scales, some of these theories introduce additional spatial dimensions, thus open-ing the possibility for CPT violations, which would express themselves as minute deviationsbetween the properties of matter and antimatter particles.

According to our current understanding of the formation of the universe, all matter – alongwith an equal amount of antimatter – was created in the big bang approximately 13.7 billionyears ago. Among the created particles, the baryons constitute an important subgroup. They

11J. Polchinski, String theory, Cambridge (England): Cambridge University Press (1998).

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are massive particles which consist exclusively of quarks. Their antiparticles consisting of an-tiquarks are called antibaryons. Surprisingly, all celestial objects observable today, such asgalaxies and individual stars, are made of ordinary matter.12 If they weren’t, the nucleosynthe-sis process in stars, by which the heavier elements are formed, would invariably lead to theemission of such atoms, some of which should also arrive at earth. Experiments have shownthat antihydrogen nuclei [i.e., antiprotons ( p)] do arrive at the earth’s outer atmosphere in ap-preciable numbers, with an antimatter–matter ratio of about 1/10,000. However, their energydistribution suggests that they are secondary particles created by the passage of primary cos-mic radiation through our milky way. In contrast, the hypothetical presence of antiparticles ofheavier elements could not be explained by interactions with the interstellar medium; they canonly be formed in nuclear processes in antistars. Thus, in 1998 the AMS-01 experiment wasconducted on board the space shuttle Discovery. It orbited earth for 10 days at an altitude of400 km and registered the signals of heavy atomic nuclei. In the course of that experiment,several million helium nuclei were detected, but not a single antihelium nucleus.13

This observation can only be explained by one of the following mechanisms: First, morematter than antimatter was created in the big bang; second, the imbalance emerged in the courseof evolution of the early universe; third, the antimatter originally created still exists but is segre-gated in a different domain or “bubble” of the universe by anomalous gravitational interactionwith ordinary matter. The first possibility is generally discounted due to the singular (and hence,fundamentally symmetric) nature of the big bang. The third will be discussed in Sec. 1.2. Letus now consider the second hypothesis. Roughly 380,000 years after the big bang, the universehad expanded and cooled off sufficiently to permit the formation of atomic hydrogen. Evenbefore, however, the vast majority of the particles and antiparticles initially created had annihi-lated into photons. The photons from this process are a likely origin of the cosmic microwavebackground (CMB). We can then define an asymmetry parameter η = [n(B)−n(B)]/n(γ), wheren(B) and n(B) are the densities of baryons and antibaryons, and n(γ) is the photon density inthe universe. The asymmetry parameter can be extracted from the primordial abundances oflight elements14 or from the CMB anisotropy.15 Both methods yield a result of η ≈ 6 × 10−10.We can therefore surmise that out of every 10 billion baryons created in the big bang, all buta few have annihilated with a corresponding antibaryon partner. All of the 100 billion knowngalaxies – and hence also our own solar system – have developed from the remaining tinyfraction of ordinary matter. In 1967 a first set of conditions which could explain the observedbaryon asymmetry was proposed.16 According to this model, both C and CP symmetry as wellas baryon number conservation would have to have been violated at some stage of the evolutionof the universe. Furthermore, an epoch of thermal equilibrium must have occurred at one time.Some years ago, it was recognized that an excess of baryons can also arise from a simpler setof circumstances involving only CPT violation and baryon number non-conservation, without

12E. W. Kolb and M. S. Turner, The early universe, Reading (Massachussetts): Addison-Wesley (1990).13M. Aguilar, “The Alpha Magnetic Spectrometer (AMS) on the International Space Station: Part I - results

from the test flight on the space shuttle,” Phys. Rep. 366 (2002) 354.14R .H. Cyburt, “Primordial nucleosynthesis for the new cosmology: Determining uncertainties and examining

concordance,” Phys. Rev. D 70 (2004) 023505.15W. Hu and S. Dodelson, “Cosmic microwave background anisotropies,” Annu. Rev. Astron. Astrophys. 40

(2002) 171.16A. D. Sakharov, “Violation of CP invariance, C asymmetry, and baryon asymmetry of the universe,” Sov.

Phys. – JETP 5 (1967) 24.

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the added requirement of thermal non-equilibrium.17

Just over 50 years ago, it was assumed that the parity and charge–parity symmetries alsoheld separately, but P and CP violations have since been discovered in nuclear beta decay andthe disintegration of neutral kaons, respectively.18,19 The experimentally established CP viola-tion, however, is too weak to explain the observed baryon asymmetry according to the Sakharovconditions. Consequently, CPT symmetry has been tested very thoroughly by comparing manydifferent properties of a variety of antimatter–matter particle pairs. For instance, the mass-to-charge ratios of the electron/positron and proton/antiproton pairs have been compared to highprecision in Penning traps.20,21 Using vastly different techniques – ion traps on the one handand a particle accelerator on the other – comparisons of the g factors of the electron/positronand muon/antimuon pairs have also been carried out.22,23 None of these or any other CPT testsperformed to this day have revealed a deviation from perfect CPT symmetry. Hence, the CPTtheorem remains an integral part of the standard model. It must be emphasized, however, thatthe absence of a deviation in one characteristic of a particle–antiparticle pair, such as the mass,does not rule out differences in other properties.

Therefore, further high-precision comparisons of particles and their antiparticle counter-parts continue to garner significant interest, especially if they hold the prospect of improvingupon the experimental precision of earlier studies. In this context, the frequency of the atomic1S–2S transition in (anti-)hydrogen is a promising candidate. The metastable 2S state – witha comparatively long lifetime of 122 ms and the correspondingly narrow natural linewidth– is particularly suited for high-precision measurements. Using the well-established methodof two-photon spectroscopy, this transition in hydrogen has been determined with a relativeprecision of 2 × 10−14, making the Rydberg constant, which is derived from this transition fre-quency, the most precisely determined of all fundamental constants.24 For obvious reasons, itwould be desirable to perform the same experiment on antihydrogen atoms, provided they canbe created, cooled and stored in the laboratory in sufficient numbers. Currently, the ATRAPand ALPHA collaborations at CERN/AD are attempting to capture neutral antihydrogen intoa neutral-atom trap, with the goal of subsequently performing 1S–2S spectroscopy on the con-fined antiatoms.25,26 Like the experiments performed with ordinary hydrogen, these will requirea cryogenic antihydrogen sample at liquid-helium temperature or below.

17O. Bertolami et al., “CPT violation and baryogenesis,” Phys. Lett. B 395 (1997) 178.18C. S. Wu et al., “Experimental test of parity conservation in beta decay,” Phys. Rev. 105 (1957) 1413.19J. H. Christenson et al., “Evidence for the 2π decay of the K0

2 meson,” Phys. Rev. Lett. 13 (1964) 138.20P. B. Schwinberg et al., “Trapping and thermalization of positrons for geonium spectroscopy,” Phys. Lett. A

81 (1981) 119.21G. Gabrielse et al., “Precision mass spectroscopy of the antiproton and proton using simultaneously trapped

particles,” Phys. Rev. Lett. 82 (1999) 3198.22R. S. Van Dyck, Jr. et al., “New high-precision comparison of electron and positron g factors,” Phys. Rev.

Lett. 59 (1987) 26.23G. W. Bennett et al., “Measurement of the negative muon anomalous magnetic moment to 0.7 ppm,” Phys.

Rev. Lett. 92 (2004) 161802.24M. Niering et al., “Measurement of the hydrogen 1S -2S transition frequency by phase coherent comparison

with a microwave cesium fountain clock,” Phys. Rev. Lett. 84 (2000) 5496.25G. Gabrielse et al., “Antiproton confinement in a Penning-Ioffe trap for antihydrogen,” Phys. Rev. Lett. 98

(2007) 113002.26G. Andresen et al., “Antimatter plasmas in a multipole trap for antihydrogen,” Phys. Rev. Lett. 98 (2007)

023402.

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1.2 Antimatter gravity

As was mentioned above, the apparent disappearance of antimatter by segregation in remoteregions of the universe could be caused by an anomalous behavior with respect to the gravi-tational force. Among the four fundamental interactions, gravity plays a special role. Whereasthe electromagnetic force as well as the weak and strong nuclear forces can be described asbeing due to the exchange of virtual particles, the general theory of relativity defines gravity asa purely geometric phenomenon: Massive particles (via their stress–energy tensor) distort four-dimensional spacetime, and all objects travel on geodesics, i.e., locally straight lines, throughthe curved 4-dimensional geometry. Therefore, gravity has until now resisted all efforts to com-bine it with the other forces into a “theory of everything.” Notwithstanding the fundamental ob-stacles, quantum theories of gravity are being developed, in which the interaction is mediatedby hypothetical exchange particles, the so-called gravitons. They can be repulsive or attractive,depending on the spins of these exchange bosons as well as the signs of the mass “charges”to which they couple. Hence, the formulation of a quantum theory of gravitation automaticallybrings about the possibility of different types of exchange particles as well as negative masscharge. Efforts to formulate a renormalizable quantum field theory of gravitation have so farbeen unsuccessful, but may prove feasible within the framework of an effective field theory.27

Within such a theory, the infinite-range, attractive ordinary “Newtonian” gravity is associ-ated with a massless tensor (spin-2) exchange particle. In addition to this tensor part, gravitycould also include contributions from scalar (spin-0) and vector (spin-1) components. As a gen-eral rule, even-spin exchange particles create an attractive force between all types of charges,whereas the exchange of odd-spin particles leads to a repulsive force between like charges.Therefore, it is possible that hypothetical scalar and vector parts of gravity cancel out when ap-plied to ordinary matter, but they would produce dramatic effects when studying the interactionbetween ordinary matter and antimatter. Such a deviating behavior of antimatter in the earth’sgravitational field, for instance, would therefore constitute a violation of the weak equivalenceprinciple (also called the universality of free fall) and thus directly contradict the general theoryof relativity.

Many arguments against “anti-gravity” – i.e., a tensor-type gravitational interaction withopposite sign for antimatter – have been put forward,28 the simplest and most elegant of themdemonstrating that such a phenomenon would violate conservation of energy.29 All of thesearguments, however, do not apply to more elaborate models involving scalar and vector gravi-tons. While the behavior of ordinary matter under the influence of gravity has been thoroughlytested over a large range of distance scales,30 the same is not true for antimatter. In fact, noexperimental study on the behavior of antimatter particles in a gravitational field has ever beensuccessfully carried out. The only two previous attempts, at Stanford31 and CERN’s LEAR32

27J. F. Donoghue, “General relativity as an effective field theory: The leading quantum corrections,” Phys. Rev.D 50 (1994) 3874.

28M. M. Nieto and T. Goldman, “The arguments against ‘antigravity’ and the gravitational acceleration ofantimatter,” Phys. Rep. 205 (1991) 221.

29P. Morrison, “Approximate nature of physical symmetries,” Am. J. Phys. 26 (1958) 358.30B. Heckel et al., “Results on the strong equivalence principle, dark matter, and new forces,” Adv. Space Res.

25 (2000) 1225.31W. M. Fairbank et al., “Experiments to determine the force of gravity on single electrons and positrons,” in:

B. Bertotti (ed.), Proc. Int. School Phys. Enrico Fermi, New York: Academic Press (1974), p. 310.32M. H. Holzscheiter et al., “Trapping of antiprotons in a large Penning trap – progress towards a measurement

6

Figure 3: Overview sketch of the proposed AEGIS experiment. Antihydrogen is created viaa positronium charge exchange reaction from antiprotons at rest. The recombined antiatomsare formed into a beam by Stark acceleration with an inhomogeneous electric field. Thegravity measurement is performed with a Moire deflectometer. For details see Ref. [C58].

were foiled by the overwhelming effect of stray electric and magnetic fields on the electricallycharged test particles.

Evidently, neutral atomic antimatter such as antihydrogen can overcome this fundamentallimitation of charged elementary antiparticles. A first direct observation of the gravitationalinteraction between matter and antimatter has therefore come within reach. Based in part on anearlier suggestion,33 we have recently proposed an antimatter experiment to study the deflectionof an antihydrogen beam in the earth’s gravitational field [C58]. An overview of the plannedAEGIS experiment (Antimatter Experiment: Gravity, Interferometry, Spectroscopy) is shownin Fig. 3. It is intended to create antihydrogen by a charge exchange reaction of positronium (Ps)with a cold antiproton plasma, which will be discussed in more detail in Sec. 3.1. Positronium iscreated very efficiently by bombarding a nano-porous material with a pulse of cold positrons.34

The antihydrogen atoms thus created from antiprotons at rest expand thermally from the centraltrap region. They will then quickly be formed into a beam using Stark acceleration, due to theforce exerted on an atom’s electric dipole moment by an external electric-field gradient.35 Sincethe dipole moment scales approximately with the square of the principal quantum number,Rydberg atoms are especially amenable to being manipulated in this way.

of the gravitational acceleration of the antiproton,” Nucl. Phys. A 558 (1993) 709c.33T. J. Phillips, “Antimatter gravity studies with interferometry.” In: International Workshop on Antimatter

Gravity and Antihydrogen Spectroscopy, Sepino, Italy, 19–25 May 1996 / Ed. by M. H. Holzscheiter – Hyperf.Interact. 109 (1997) 357.

34D. W. Gidley, H.-G. Peng and R. S. Vallery, “Positron annihilation as a method to characterize porous mate-rials,” Annu. Rev. Mater. Res. 36 (2006) 49.

35E. Vliegen et al., “Stark deceleration and trapping of hydrogen Rydberg atoms,” Phys. Rev. A 76 (2007)023405.

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The actual gravity measurement will be carried out by passing the horizontal antihydrogenbeam through a so-called Moire deflectometer,36,37 the classical counterpart of a Mach–Zehndermatter wave interferometer. The device consists of two material gratings (grating period d) anda position-sensitive detector, placed at equal distances L from each other. The gratings create ashadow pattern at the location of the detector, whose vertical position is displaced by a distanceδx = −gT 2, where g is the local gravitational acceleration and T is the time of flight betweenthe gratings. Unlike atomic fountain interferometers, this principle does not rely on trappedantiatoms, and neither spatial nor temporal coherence of the incoming particle beam are re-quired. Some years ago, a Moire deflectometer was first used to measure the local gravitationalacceleration on an argon beam.38 Simulations of the AEGIS apparatus, assuming experimentalparameters feasible with current technology, have shown shown that a measurement of g to 1%relative precision can be achieved within a few weeks of beam time at the AD.

1.3 The need for ultracold antihydrogen

Precision atomic-physics experiments are typically carried out either on a beam of atoms orions or on a ensemble confined in a particle trap. In either case, the temperature of the sam-ple determines the achievable resolution (and hence, ultimately, the uncertainty) of precisionexperiments. Temperature is, by definition, an expression of the random residual motion of acollection of particles. This impacts the experimental resolution in the following two ways:First, rapid particle motion reduces the observation time of a measurement. This leads to so-called time-of-flight broadening, where the width of a resonance is increased in accordancewith the Heisenberg uncertainty principle. Second, the random particle motions translate into aDoppler broadening of a resonance. The proposed AEGIS experiment, for instance, is mainlysensitive to Doppler broadening: Subsequent to antihydrogen production, the vertical compo-nent of the sample temperature will increase the beam divergence and thus reduce the numberof particles that traverse the entire apparatus and are recorded on the detector. Furthermore,the horizontal temperature component will introduce an uncertainty in the determination of theentire time of flight, thus making the determination of g less precise.

The confinement of antihydrogen in a magnetic trap poses additional challenges with re-spect to the required particle temperature. The principle of a magnetic trap39 is shown inFig. 4(a). An (anti-)atom with a magnetic moment �μ in an inhomogeneous magnetic field ex-periences a force �F = ±μ (∇B) in the direction of the magnetic-field gradient (or opposite toit, depending on the orientation of the magnetic moment with respect to the B field direction).The inhomogeneous field is achieved by multipole magnets with a radial field profile of theform Brad(r) = ksr(s−1), where s is the order of the multipole and ks is a constant that dependson s. For a given magnetic solenoid field B and radial trapping field Brad, the trap depth is givenby δB = (B2 + B2

rad)1/2 − B. If a large fraction of antiatoms is to become trapped, their temper-ature must satisfy the condition kBT ≤ μB δB (assuming they are in the quantum-mechanicalground state), where μB is the Bohr magneton and δB is the trap depth. Atoms in higher internalstates will initially be more strongly confined, but may leave the trap as they de-excite and the

36L. Zehnder, “Ein neuer Interferenzrefraktor,” Z. Instrumentenkunde 11 (1891) 275.37L. Mach, “Ueber einen Interferenzrefraktor,” Z. Instrumentenkunde 12 (1892) 89.38M. K. Oberthaler et al., Phys. Rev. A 54 (1996) 3165.39H. Friedberg and W. Paul, “Optische Abbildungen mit neutralen Atomen,” Naturwiss. 38 (1951) 159.

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Figure 4: (a) Principle of atom confinement in a magnetic-multipole trap. The magnetic-field gradient exerts a restoring force on the magnetic moment of the atom. (b) Fraction ofatoms captured in a magnetic multipole trap as a function of the trap depth, for different Htemperatures.

confining potential is reduced. Figure 4(b) illustrates that the trapping efficiency of magneticmultipole traps strongly depends on the sample temperature and that the fraction of trappedparticles is exceedingly low for typical trap depths of a few tenths of T, unless the antihydrogencan be produced at temperatures well below 4 K.

Hence, we have seen that the temperature and to a lesser degree the internal quantum stateof antihydrogen are crucial parameters that impact the ability to trap the antiatoms and to carryout precision measurements on them. As will be discussed in Sec. 2.1, these parameters are,in turn, intimately tied to the H recombination process. The main goal of the ATHENA col-laboration after the initial breakthrough of the first cold-antihydrogen production was thereforeto understand which was the dominant process for antihydrogen recombination. Those studiesare presented in Secs. 2.2 and 2.3. Furthermore, the antihydrogen temperature was also mea-sured directly by analyzing the spatial characteristics of H emission from the Penning trap, aswill be discussed in Sec. 2.4. As one of the main results of the aforementioned experiments,it was found that antihydrogen produced by mixing antiprotons with positrons is created atmany times the temperature of the surrounding trap, too hot for precision experiments on abeam and for capture in a magnetic trap. In Sec. 3.2 a novel technique is introduced which– if demonstrated to work – holds the potential of cooling antiprotons to temperatures wellbelow the surrounding environment. This scheme relies on a precise knowledge of the bound–bound electric-dipole transition in the negative osmium ion. The results of high-resolution spec-troscopy on Os− are presented in Sec. 3.3

9

Figure 5: Principle of three antihydrogen recombination processes: (a) Spontaneous ra-diative recombination (SRR); (b) Three-body recombination (TBR); (c) Laser-stimulatedrecombination (LSR). The ionic energy continuum is displayed as shaded in the diagrams.

2 Dynamics of antihydrogen production in Penning traps

2.1 Antihydrogen recombination and detection

The antihydrogen atom is the bound system of an antiproton and a positron. As is the casefor hydrogen, the atomic binding energy is 13.6 eV. Its formation, also called recombination,occurs spontaneously when cold antiprotons and positrons are brought together. Since recom-bination is balanced by electron impact ionization processes, it sets in below kBT = 13.6 eVand is enhanced at lower temperatures, when excited bound states can also withstand ionizationand contribute to the recombination rate. It is evident that an isolated recombination processcannot simultaneously satisfy energy and momentum conservation. Therefore, spontaneous re-combination proceeds only via the two competing reactions

p + e+ −→ H + hν (1)

andp + 2e+ −→ H + e+, (2)

called (spontaneous) radiative recombination (SRR) and three-body recombination (TBR), re-spectively.40 The principle of these two processes is illustrated in Fig. 5(a) and (b). In eachcase, the excess energy of the reaction is carried off by an additional reaction partner. Thecorresponding processes of hydrogen formation from protons and electrons have been studiedsince the 1930s and are well understood in terms of cross-sections and recombination rates, atleast in the absence of strong electric or magnetic fields.41

40M. H. Holzscheiter, M. Charlton and M. M. Nieto, “The route to ultra-low energy antihydrogen,” Phys. Rep.402 (2004) 1.

41A. Muller and A. Wolf, “Production of antihydrogen by recombination of p with e+: What can we learnfrom electron–ion collision studies?” In: International Workshop on Antimatter Gravity and Antihydrogen Spec-troscopy, Sepino, Italy, 19–25 May 1996 / Ed. by M. H. Holzscheiter – Hyperf. Interact. 109 (1997) 233.

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While positrons occur naturally in the β+ decay of radioactive nuclides, the production ofantiprotons is much more involved and requires major accelerator infrastructure. Currently theonly facility worldwide which can supply large quantities of antiprotons is the AD at CERN,also called the “antimatter factory.”42 At the AD, antiprotons are produced by bombarding athick iridium target with a pulse of 1013 protons which have been accelerated to a kinetic energyof 26 GeV in the proton synchrotron. In the collisions of protons with target nuclei, about 107

protons and antiprotons are created by pair production with a kinetic energy of ≈ 3.5 GeV. Aftermass separation in a magnetic filter, which removes other secondary particles such as pions andmuons, the antiprotons are injected into a storage ring of about 190 m circumference. As theycirculate in the ring, they are slowed in radiofrequency quadrupole decelerators. At the sametime, the antiproton bunch is centered azimuthally by stochastic (v ≈ c) and electron cooling(v ≈ 0.3–0.1c). At the end of the deceleration cycle, which lasts about 100 s, the antiprotonshave attained a kinetic energy of 5 MeV and are ejected to the AD experiments installed withinthe storage ring.

The main components of the ATHENA apparatus43 are a Surko-type positron source andaccumulator,44 a cryogenic cylindrical Penning trap45 (temperature ≈ 15 K, diameter 25 mm,total length ≈ 1 m) in the 3-T field of a superconducting magnet, and a combined silicon stripand CsI crystal detector for the detection of antihydrogen annihilations.46 At a kinetic energyof 5 MeV, the antiprotons delivered from the AD are still much too energetic to be captured in aPenning trap. Therefore, they are passed through a thin (5 μm) degrader foil whose thickness ischosen such that a maximum of the emerging antiprotons have an energy below 5 keV. In thisway, typically 104 antiprotons per AD spill can be captured, while the remaining 99.9% are lostin the degrading process. The antiprotons are then cooled by bringing them into overlap with aplasma of about 108 electrons which were previously prepared in the trap and allowed to cool.At the same time, positrons are produced from a strong (1.4 GBq) source of radioactive 22Na,which emits highly energetic β radiation as it decays to 22Ne. The positrons are moderated ina layer of solid neon and cooled and accumulated in the axial potential minimum of a buffer-gas-filled 0.14-T Penning trap [A19]. After each accumulation cycle, about 108 positrons areavailable for recombination. Their number, density, aspect ratio, and relative temperature canbe measured non-destructively with a diagnostics system that resonantly excites and detects thefirst and second axial plasma modes.47,48

The mixing of antiprotons and positrons takes place in the central section of the cylin-drical Penning trap. This so-called mixing trap is shown schematically in Fig. 6. In order tosimultaneously confine the oppositely charged positrons and antiprotons, the axial electrostatic

42J. Y. Hemery and S. Maury, “The antiproton decelerator: Overview,” Nucl. Phys. A 655 (1999) 345c.43M. Amoretti et al., “The ATHENA antihydrogen apparatus,” Nucl. Instrum. Methods A 518 (2004) 679.44C. M. Surko, M. Leventhal and A. Passner, “Positron plasma in the laboratory,” Phys. Rev. Lett. 62 (1989)

901.45L. S. Brown and G. Gabrielse, “Geonium theory: Physics of a single electron or ion in a Penning trap,” Rev.

Mod. Phys. 58 (1986) 233.46C. Regenfus, “A cryogenic silicon micro-strip and pure-CsI detector for detection of antihydrogen annihila-

tions,” Nucl. Instrum. Methods 501 (2003) 65.47M. Amoretti et al., “Complete nondestructive diagnostic of nonneutral plasmas based on the detection of

electrostatic modes,” Phys. Plasmas 10 (2003) 3056.48M. Amoretti et al., “Positron plasma diagnostics and temperature control for antihydrogen production,” Phys.

Rev. Lett. 91 (2003) 055001.

11

Figure 6: Detailed sketch of the mixing trap, which is operated in a nested-trap configu-ration. The graph shows the axial trap potential before (dashed) and after (solid line) theantiproton injection.

potential in the recombination region is operated in a so-called nested-trap configuration.49

The nested trap is achieved by applying an electric potential in the form of the letter “M,” asshown in the graph of Fig. 6. First, the central well of the trap is loaded with the positrons.Like electrons, they rapidly cool to the temperature of the surrounding trap (≈ 15 K) by emis-sion of synchrotron radiation due to their high-frequency (≈ 85 GHz) cyclotron motion inthe strong magnetic field.50 The 104 antiprotons are initially transferred to a small lateral well(dashed line in the figure) before being launched into the positron plasma with a kinetic en-ergy of about 10 . . . 30 eV. By Coulomb collisions with the positrons, they are cooled to thesame temperature with a cooling time constant which we have experimentally determined tobe τp ≈ 10 ms [A11]. After about 20–30 ms, H production begins spontaneously. As soon asneutral antihydrogen atoms are formed, they are no longer confined in the charged-particle trapbut are ejected from the mixing region with a momentum essentially equal to that of the an-tiproton just prior to recombination. After a few μs, the H atoms hit one of the trap electrodes,where their constituents annihilate with electrons and protons.

The spatially and temporally correlated signal of these two annihilation events serves asthe unambiguous indication that the formation of antiatoms has, in fact, occurred. The antihy-drogen detector consists of a granular array of 8192 silicon strips in two layers and 192 CsIcrystals read out by avalanche photo diodes. The Si detectors record the signal of the chargedpions produced in the p–p annihilations, which are used to reconstruct the vertex of the an-nihilation. The resolution of this reconstruction, about 4 mm, is limited by the fact that thecurvature of the charged-particle tracks cannot be reconstructed from only two detector hits

49G. Gabrielse et al., “Antihydrogen production using trapped plasmas,” Phys. Lett. A 129 (1988) 38.50G. Gabrielse et al., “Cooling and slowing of trapped antiprotons below 100 meV,” Phys. Rev. Lett. 63 (1989)

1360.

12

Figure 7: Signal of the production of cold antihydrogen with ATHENA. (a) Charged-pionvertex distribution (azimuthal projection); (b) Opening angle distribution of the photonsrecorded in coincidence with the charged-particle hits, as seen from the charged-particlevertex.

per track. The array of crystals detects the photons from the e+–e− annihilation, most of which(> 95%) have a multiplicity of two and are hence emitted back-to-back, i.e., with an open-ing angle of 180◦ as seen from the reconstructed vertices from the charged particles. Figure 7shows a typical annihilation signal recorded during standard mixing cycles.2 In the left panel,the number of events recorded by the silicon detector is graphed as a function of the azimuthalcoordinates. The highest number of events, shown in red, is recorded at the trap electrodes atr = 12.5 mm. The right panel of Fig. 7 shows the number of 511-keV γ events recorded in thecrystal detector as a function of the opening angle θγγ. As expected, the data displays a clearpeak for an opening angle of 180◦ (cos θγγ = −1). For the purpose of quantitative analysis, theopening angle excess is defined as the number of events with cos θγγ ≤ −0.95 which exceed theaverage number of events at all other angles. Monte Carlo simulations indicate that the detectorsolid angle coverage for H emerging isotropically from the mixing region is ≈ 98%.

2.2 Temperature dependence of antihydrogen production

Prior to recombination, the positrons occupy a narrow band of states (corresponding to theirtemperature) in the ionic continuum of the yet-to-be-formed atom, whereas the antiprotons,due to their much larger mass, can be considered at rest in the positron gas. In a cryogenic trapenvironment, the positrons’ kinetic energy Ee is typically much smaller than the binding energyE0 of the atomic ground state. Under these circumstances, the SRR cross-section for capture toa state with principal quantum number nH can be expressed in analytic form as51

σSRR(nH, Ee) =32√

39

πα3a20E0

nHEe(1 + n2HEe/E0)

, (3)

where α is the fine structure constant and a0 is the Bohr radius. The total cross-section σSRR(Ee)is the sum over all nH states up to some cutoff, which is usually given by collisional or field

51H. A. Bethe and E. E. Salpeter, Quantum mechanics of one- and two-electron atoms, New York: Plenum(1977).

13

re-ionization of weakly bound states. It follows directly from Eq. (3) that capture into low-nH

states is favored by the SRR process. The recombination rate is obtained by integrating overthe phase space overlap between the positrons and antiprotons:40

RSRR =

∫σSRR(v) f (v) v dv

∫ne(�r) np(�r) d3r (4)

where f (v) is the distribution of the positrons’ and antiprotons’ relative velocity v, and ne andnp are their respective spatial densities. The first integral is called the recombination rate coef-ficient αSRR(v) and has been calculated for a spherically symmetric Maxwell–Boltzmann dis-tribution, as well as for a so-called flattened distribution where the relative velocities in onedimension greatly exceed those in the perpendicular plane.52 In the case of a spherically sym-metric velocity distribution, the temperature dependence has a leading T−1/2 term. When acorrection for the aforementioned cutoff in nH is applied,41 an overall dependence of the ratecoefficient (and hence, the total rate) on the temperature of αSRR(v) ∝ T−0.63 is found. The de-pendence of the recombination rate on the positron density of RSRR(v) ∝ ne is due to the spatialintegral in Eq. (4).

In the case of three-body recombination, Eq. (4) applies accordingly, but the recombinationcross-section cannot be determined analytically. However, using a classical-trajectory MonteCarlo simulation, the TBR rate coefficient was numerically calculated to be53

αTBR = 2 × 10−27cm6 s−1 ne

(1 eVkBT

)9/2

, (5)

again assuming a spherically symmetric velocity distribution. The inclusion of an external mag-netic field reduces the rate by roughly an order of magnitude.54 Three-body recombination pro-duces Rydberg atoms with principal quantum numbers nH 10. These excited states rapidlydecay to the ground state, but can also be re-ionized by collision or by the strong electric fieldspresent in the mixing region. Under real experimental conditions, an equilibrium between de-excitation and re-ionization is expected to set in. Below a “bottleneck” threshold binding energyof ≈ 4kBT , atoms become resilient to collisional ionization. The temperature dependence of theTBR rate coefficient, αTBR ∝ T−9/2, is due to the fact that the rate is proportional to the square ofthe characteristic length scale of the reaction, the Thomson radius RT = 2e2/3kBT , which is thedistance between two elementary charges at which the potential of their Coulomb interaction isequal to the thermal energy.55 The quadratic dependence on the positron density, RTBR(v) ∝ n2

e ,arises from the fact that each recombination event requires the participation of two positrons.

The main characteristics of the two recombination processes, including total rates calcu-lated for the operating parameters of the ATHENA apparatus, are summarized in Tab. 1. Aswas discussed in Sec. 1.3, the H temperature final quantum state are crucial for precision ex-periments on an antihydrogen beam and for the prospect of confining H in a magnetic trap.

52M. Bell and J. S. Bell, “Capture of cooling electrons by cool protons,” Part. Accel. 12 (1982) 49.53P. Mansbach and J. Keck, “Monte Carlo trajectory calculations of atomic excitation and ionization by thermal

electrons,” Phys. Rev. 181 (1969) 275.54M. E. Glinsky and T. M. O’Neil, “Guiding center atoms: Three-body recombination in a strongly magnetized

plasma,” Phys. Fluids B 3 (1991) 1279.55G. Gabrielse, S. L. Rolston and L. Haarsma, “Antihydrogen production using trapped plasmas,” Phys. Lett.

A 129 (1988) 38.

14

Table 1: Comparison of some characteristics of spontaneous radiative and three-body re-combination, calculated for the operating parameters of the ATHENA experiment.

Radiative Three-bodyrecombination recombination

Temperature dependence ∝ T−0.63 ∝ T−9/2

Positron density dependence ∝ ne ∝ n2e

Cross-section at 1 K 10−16 cm2 10−7 cm2

Final quantum states n < 10 n 10Expected recombination rate several 10 Hz several 100 Hz

The temperature at which H formation sets in – and hence, the temperature of the producedantihydrogen – depends on the ratio of cooling rate of antiprotons in the positron plasma on theone hand and the recombination rate on the other. As we have seen, the recombination rates,as well as their dependence on the experimental conditions, vary greatly between the differentrecombination processes. Therefore, the question of which of the two spontaneous recombi-nation reactions (1) and (2) is the dominant antihydrogen formation process is of the utmostimportance. The table shows that the recombination mechanisms can be clearly distinguishedby means of their different positron temperature scaling. We therefore undertook two separatemeasurement campaigns to elucidate this important question.

In the first, we performed antiproton–positron mixing under otherwise standard conditionsas described in Sec. 2.1, but with varying positron temperature [A9]. For the present study,typically 0.7×108 positrons and 104 antiprotons were brought together in the interaction region.The plasma parameters were determined with the non-destructive plasma diagnostics system.48

The temperature of the plasma was varied by applying a radiofrequency (RF) excitation at theplasma dipole mode (around 20 MHz) to the electrode adjacent to the central ring electrode.Temperature change, as well, was measured with the plasma diagnostics system, which candetect an increase as low as 175 K. Four data samples with sufficient data for a detailed analysiswere accumulated at the following temperatures: kBΔT = 0 meV, 15 meV, 43 meV, 306 meV,corresponding to T ≈ 15 K (“cold”), 190 K, 500 K, 3500 K (“hot”). Qualitatively, it wasfound that the opening angle excess and the number of total triggers decrease with increasingtemperature, but antihydrogen is unexpectedly still produced even at room temperature. At“hot” mixing conditions, however, both are completely suppressed.

For a quantitative analysis, the following parameters were examined as possible proxiesfor antihydrogen production: 1) The opening angle excess, as defined in Sec. 2.1; 2) The totalnumber of triggers recorded in the first 3 s; 3) The total number of triggers recorded in over180 s (the entire mixing cycle); and 4) The peak trigger rate (excluding first 20 ms of mixing,where p can be lost immediately following injection). The fraction of silicon strip trigger eventswhich is due to antihydrogen annihilations increases with the event rate and was shown toaverage about 85% during the first second of mixing.56 Therefore, it was concluded that thepeak trigger rate constitutes the cleanest proxy for antihydrogen production, with as many as

56M. Amoretti et al., “High rate production of antihydrogen,” Phys. Lett. B 578 (2004) 23.

15

Figure 8: Temperature dependence of antihydrogen production (peak trigger rate) as a func-tion of temperature, for the four data points with the highest statistics [A9]. The best fit tothe data with a simple power law [scaling with T−0.7(2)] is indicated by the solid and dashedred lines.

95% of the counts representing actual H annihilation events. These data points are shown inFig. 8 in a double-logarithmic plot, in which simple power functions should take on the form ofstraight lines. It is evident that the rates do not scale as any simple power law; rather, there is anunexpected turnover of the rate at low temperature. The scaling with T−9/2 as expected for TBRis clearly inconsistent with data; in particular the behavior at low temperatures is not compatiblewith the three-body reaction. Furthermore, attempts to fit the data with a combination of twopower laws also failed. If the data are nevertheless fitted with a simple power function, thebest fit is obtained for a scaling that behaves as T−0.7(2), shown as red lines in Fig. 8. Thisresult would be compatible with the SRR mechanism, however, the observed rates are roughlya factor 10 too high.

The second study on the temperature dependence of antihydrogen production involved aslightly different approach: Rather than maintaining the positron plasma at a constant temper-ature over the entire duration of the mixing cycle, a periodic positron heating was applied,thereby modulating H production in regular intervals [A39]. In addition, a larger temperaturerange up to kBT = 1.5 eV (corresponding to almost 20,000 K) was explored. A similar tech-nique has previously been applied for the studies on the recombination of highly charged atomicions in storage rings57,58 Again, some 104 antiprotons were brought into overlap with 5 × 107

positrons in the mixing region of the ATHENA apparatus. The e+ plasma properties were alsocomparable, with a plasma length of 30 mm and a density of a few 108 cm−3. As was discussedabove, the H formation can be suppressed by heating the e+ plasma with an RF excitation at thedipole plasma modes. Now, instead of constant RF excitation, a periodical square-wave modu-lated RF heating was applied to the positron plasma, with an ON/OFF period ranging from 8 sto 30 s.

57G. Kilgus et al., “High-resolution measurement of dielectronic recombination of lithiumlike Cu26+,” Phys.Rev. A 46 (1992) 5730.

58H. Gao et al., “Energy and charge dependence of the rate of electron–ion recombination in cold magnetizedplasmas,” J. Phys. B 30 (1997) 113002.

16

Figure 9: (a) Temporal and (b) spatial distributions of p annihilations (longitudinal pro-jection at trap diameter) during modulated heating of the positron plasma by RF excita-tion [A39].

With such an excitation, antihydrogen production is suppressed after less than 100 ms.After the heating is turned off, H production sets in again as the positron plasma cools byemission of synchrotron radiation, with a cooling time constant of ≈ 0.5 s. Figure 9(a) showshow the production is interrupted by heating, only to resume at a similar rate when the heating isdiscontinued. The spatial distribution of annihilation events, shown in Figure 9(b), is consistentwith H production during heating ON and consistent with background events from residualgas (or possibly trapped ions) which may annihilate with antiprotons at the trap center. As theplasma cools, the instantaneous annihilation rate can be recorded quasi-continuously over abroad energy range, until the base temperature T0 (believed to be 15 K) is reached. Hence, thetemperature dependence of H production can be determined from the temperature evolution ofthe positron plasma.

However, since the positron plasma temperature decreases asymptotically with time ratherthan linearly, and since furthermore the initial p reservoir is gradually depleted, the evolutionof the observed recombination rate with time cannot be fitted to a simple power law of the formRH ∝ T−P, but is instead given by the function

RH = A[ΔT e−t/τ + T0

]P+ Rbg, (6)

where A is a normalization factor and Rbg is the background rate. We see from Eq. (6) that themodel relies on a precise knowledge of the cooling time constant, which can be calculated tobe τ = 0.43 s for the ATHENA e+ plasma parameters from a cold-fluid model of the positronplasma.59 The cooling time constant was also determined experimentally in off-line measure-ments with positrons only, yielding the compatible value τ = 0.48(5) s.

For a quantitative analysis, a heating cycle with alternating intervals of 5 s OFF, 3 s ON wasapplied at five different RF amplitudes (and hence, temperatures). The initial temperatures justprior to turning the heating offwere measured with the modes diagnostics system to be kB ΔT =270 meV, 400 meV, 870 meV, 1150 meV and 1470 meV. The evolution of the annihilation rates

59B. R. Beck, J. Fajans and J. H. Malmberg, “Temperature and anisotropic-temperature relaxation measure-ments in cold, pure-electron plasmas,” Phys. Plasmas 3 (1996) 1250.

17

Figure 10: Onset of H production after heating OFF at t = 0 [A39]. The annihilation rates(histograms) are shown along with fits according to Eq. (6).

for a time interval of 7 s, starting 2 s prior to turning the heating off, is shown in Fig. 10. Becausethe fits according to Eq. (6) yielded a value for the base temperature which was much higherthan the expected 15 K, an alternative fit over a shorter fit time window and using a slightlymodified function, where T0 was constrained to zero, was also performed. In either case thepower dependence of H production was found to be compatible, with a combined result ofRH ∝ T−1.1(5). This outcome is consistent with that of the previous study, but is based on datathat cover a much larger temperature range. Again, the power scaling was found to be in fairagreement with the one expected for SRR, but the observed rates were indicative of TBR.

2.3 Laser-induced formation of antihydrogen

In addition to the spontaneous recombination processes detailed in the previous section, an-tihydrogen formation can also be accomplished by laser-stimulated recombination (LSR), ac-cording to the reaction40

p + e+ + hν −→ H + 2hν, (7)

whose principle is illustrated in Fig. 5(c). It was first suggested as a possible mechanism forpositronium formation60 and later proposed as an alternative technique for antihydrogen pro-duction.61 In addition to enhancing the total spontaneous H formation rate, this process is attrac-tive because it affords a selectivity of the populated quantum state and allows a time-resolvedproduction in case a pulsed (or chopped) laser is employed. LSR has been used to enhance therecombination of hydrogen into a wide range of quantum levels in merged-beam experiments

60L. A. Rivlin, “Stimulated formation of relativistic positronium atoms,” Sov. J. Quantum Electron. 9 (1979)353.

61A. Wolf, “Laser-stimulated formation and stabilization of antihydrogen atoms.” In: Antihydrogen Workshop,Munich, Germany, 30–31 July 1992 / Ed. by D. Klepner – Hyperf. Interact. 76 (1993) 189.

18

Figure 11: Energy level diagram of (anti-)hydrogen, illustrating the principle of two-steplaser-stimulated recombination via the 11d and 2p states.61 Levels are not to scale.

with protons and electrons.62,63 In the latter, an enhancement of hydrogen recombination by afactor 4 was observed with a 15-W cw CO2 laser.

In thermal equilibrium, the partial laser-mediated recombination rate into a bound state withprincipal and angular momentum quantum numbers (n,l) is given by61

RnlH = NpN(E)wnl

rnlabs(E)γnl

rnlabs(E) + γnl

, (8)

where E is the electron energy, N(E) is the level population function of the continuum Coulombstate, wnl is the statistical weight of the bound state, Np is the number of protons, rnl

abs is theinduced absorption rate, and γnl is the spontaneous radiative decay rate of the (n,l) state. Incalculating the total recombination rate, one must sum over all possible final states, taking intoaccount the Doppler width and the laser bandwidth, as well as the Zeeman splitting of theatomic levels in an external magnetic field. It follows from Eq. (8) that large rates are achievedwith high power densities and small photon energies (i.e., when high Rydberg states are pop-ulated). Therefore, a multi-step process in which a highly excited state is initially populatedwill be advantageous in terms of the required laser power.61 Figure 11 shows the principle of atwo-step stimulated recombination involving a non-resonant transition from the continuum intothe 11d state and a resonant transition from the 11d to the 2p state, which rapidly de-excitesto the ground state of the atom. The 11d state was chosen primarily because high-power CO2

gas lasers in the relevant infrared wavelength range at λ ≈ 11 μm are commercially available.For the same reason, the driven transition into the 11d state was also chosen as a test case forlaser-stimulated antihydrogen with ATHENA [A28]. However, for reasons of simplicity onlythe first stimulated recombination step was carried out, relying on spontaneous radiative decayfor the further de-excitation to the ground state.

62U. Schramm et al., “Observation of laser-induced recombination in merged electron and proton beams,”Phys. Rev. Lett. 67 (1991) 22.

63F. B. Yousif et al., “Experimental observation of laser-stimulated radiative recombination,” Phys. Rev. Lett.67 (1991) 26.

19

The ATHENA apparatus was slightly modified to allow access of the laser beam (diame-ter ≈ 2 mm) to the mixing region and to bring it into overlap with the e+ plasma (diameter≈ 1 mm). For this purpose, laser windows were installed at both ends of the vacuum chamberwhich holds the main Penning trap. The path of the laser beam was mechanically well con-strained by diaphragms at the laser windows and the large distance from the diaphragms to theinteraction region, given by the mechanical size of the superconducting magnet. The tunableCO2 laser was operated at a wavelength of λ = 10.96 μm and supplied a power of 10 W anda peak intensity of I ≈ 160 W cm−1. Its bandwidth was Γlas ≈ 100 MHz. For the ATHENAexperimental conditions (and assuming thermal equilibrium at T0 = 15 K), Eq. (8) yields atotal stimulated H production rate of 60 Hz, whereas the spontaneous radiative rate was esti-mated at 24 Hz; hence, a sizable enhancement factor of roughly 3.5 was expected. However,as mentioned in Sec. 2.2, the collisional recombination rates should be much higher, at leastpartially masking the enhancement effect. Since the intermediate 2p state was not depletedby stimulated emission, its re-ionization while the H atom is still within the laser beam mustalso be considered. Furthermore, the highly excited states formed by three-body recombinationare also subject to re-ionization by the 11-μm laser. It was calculated, however, that the ra-diative decay rate exceeded the re-ionization rate for all states with principal quantum number11 < n < 60, with ionization probabilities generally below 60%. A comparison of laser ONand OFF events was achieved bu pulsing the laser light with a chopper at a frequency of 25 Hzand recording the state of the laser along with each annihilation event.

The antihydrogen production was performed by standard “cold mixing,” and a total of≈ 156,000 annihilation events were recorded during 345 mixing cycles of 50 s each. To de-termine the impact of laser stimulation on antihydrogen formation, the following parameterswere studied: 1) The time evolution of the event rate; 2) The radial p annihilation vertex dis-tribution; 3) The opening angle distribution of 511-keV photon events in coincidence with thep annihilation events, as in Fig. 7(b). The latter two parameters are shown in Fig. 12. In orderto suppress background events, which mainly originate at the trap center, radial cuts limitingthe active region radially to 7 < r < 25 mm were applied, as indicated in the figure. The datadisplay no significant deviations between the laser ON/OFF signals. Rather, when taking intoaccount the measured signal fraction of 87%, a slight but statistically insignificant reduction inH production of −0.4(1.1) events per mixing cycle of 50 s is obtained. This observation alsoholds when different time sub-intervals during the mixing cycle are considered. The presentmeasurements therefore yielded a clear null result, which suggests that radiative recombina-tion makes a negligible contribution to H formation under the experimental conditions of theATHENA apparatus.

The two sets of experimental results presented in this section strongly indicate that the the-oretical models that describe antihydrogen formation in thermal equilibrium and in the absenceof external electric and magnetic fields cannot adequately describe the more complex situa-tion of H production with the nested-trap technique. In addition to the influence by the externalfields, also a modified temperature scaling due to collisional relaxation and finite transit time ofthe antiprotons through the positron plasma must be considered.64,65 Recently a very detailed

64J. Stevefelt, J. Boulmer and J.-F. Delpech, “Collisional-radiative recombination in cold plasmas,” Phys. Rev.A 12 (1975) 1246.

65P. O. Fedichev, “Formation of antihydrogen atoms in an ultra-cold positron–antiproton plasma,” Phys. Lett.A 226 (1997) 289.

20

Figure 12: (a) Radial distribution of p annihilation vertices (longitudinal projection) and(b) opening angle distribution of coincident 511-keV events for laser OFF (black histro-gram) and laser ON (red crosses) [A28]. The gray histogram is the background from “hotmixing” cycles, and the vertical arrows indicate the radial cuts applied to reduce the back-ground.

Monte Carlo simulation was performed, in which great care was taken to reproduce the actualexperimental conditions of the ATHENA and ATRAP experiments66 These simulations alsotake into account the brief interaction time between antiprotons and positrons due to the finitesize of the e+ plasma and reproduce the ATHENA and ATRAP data very well, including thefact that H production is observed at several 100 K with ATHENA. The author concludes thatTBR is the main process for antihydrogen production with the nested-trap technique, but thatthe mechanism is modified to an “arrested three-body capture” due to the fact that the reactionpartners can separate before collisional re-ionization can take place.

2.4 Antihydrogen temperature

As was discussed in Sec. 2.2, the temperature of the produced antiatoms strongly depends onthe ratio of the antiproton cooling rate in the positron plasma to the antihydrogen formationrate, which is expected to differ significantly between the SRR and TBR processes. Since theexperimental investigations described in the previous section yielded contradictory results asto which is the dominant mechanism for H production, we performed a measurement of thetemperature of the produced H in order to obtain this important information directly, withoutresorting to theoretical models of recombination processes [A17].

Antihydrogen was produced in standard “cold mixing” mode, with typically 0.7 × 108

positrons, 104 antiprotons and mixing cycle durations of 180 s. The e+ plasma parameters wereradius 2.5 mm, length 32 mm and density 1.7 × 108 cm−3. Signals of antiproton annihilationson the trap walls were recorded with the silicon strip detector and the reconstructed annihila-tion vertices plotted as a function of the axial distance from the trap center. The complete axialvertex distribution exhibited lateral peaks to either side of the central maximum, which are due

66F. Robicheaux, “Simulations of antihydrogen formation,” Phys. Rev. A 70 (2004) 022510.

21

Figure 13: Comparison of the axial vertex distribution from “cold mixing” (filled circleswith error bars) to distributions from Monte Carlo simulations for longitudinal temperaturesT‖ = 15 K (solid blue line) and T‖ = 150 K (solid green line) [A17].

to antiproton annihilations on the trap walls. As was previously shown, these antiproton-onlyevents are confined to a few very sharply delimited “hot spots” on the cylindrical surface ofthe trap.67 Therefore, it was possible to eliminate these background signals by considering onlyevents from an azimuthal quadrant in which no hot spots were present. The detector responsefunction (which varies with the axial distance from the trap center) was calculated by means ofa Monte Carlo simulation and corrected for. The filled circles in Fig. 13 represent the correctedvertex distribution used in the following analysis.

In order to correctly interpret the vertex data, we must take into account the dynamics ofthe positron plasma in the trap. A non-neutral one-component plasma confined in a Penningtrap generates an internal electric field which counteracts the external field, causing the ions toevolve in a regime of laminar flow. The entire ellipsoidal plasma rigidly rotates about the trapaxis, as shown in Fig. 14, with a rotational frequency68

ωrot =ωc

2

⎛⎜⎜⎜⎜⎜⎜⎜⎝1 −√

1 − 2ω2p

ω2c

⎞⎟⎟⎟⎟⎟⎟⎟⎠ , (9)

where ωc = eB/me is the cyclotron frequency of the positrons and ωp = (nee2/meε0)1/2 is theplasma frequency (ε0 is the permittivity of free space, me is the electron mass, and e is theelementary charge). Under the ATHENA experimental conditions, the rotational frequency isωrot ≈ 80 kHz, corresponding to a surface velocity of only ≈ 1.3 × 103 m s−1. The antiprotonstraverse the rotating plasma axially with an oscillation frequency of ≈ 100 kHz. During theirpassage, they thermalize azimuthally with the plasma and are dragged along with the positronsin their rotation. Centrifugal separation may occur in two-component plasmas when the compo-

67M. C. Fujiwara et al., “Three-dimensional annihilation imaging of trapped antiprotons,” Phys. Rev. Lett. 92(2004) 065005.

68R. C. Davidson, An introduction to the physics of non-neutral plasmas. Redwood City: Addison-Wesley(1990).

22

Figure 14: A non-neutral one-component plasma confined in a Penning trap performs arigid rotation about the trap axis.

nents have different masses,69 but is not an issue here because it takes place on long timescalesof hundreds of seconds. In the following, temperature is understood to be within the rotatingreference frame; thermal equilibrium refers to the state where Tp = Te within that frame. Be-cause the positrons’ thermal velocity is much larger than the rotational velocity in the plasma,the effect of the latter on the recombination rate can be neglected; hence, H can be consideredto be formed homogeneously throughout the e+ plasma.

For a Monte Carlo model of the vertex distribution, a three-dimensional Gaussian veloc-ity distribution with different azimuthal and longitudinal temperatures T⊥ and T‖ was chosento allow for recombination under non-equilibrium conditions. Antihydrogen atoms were thenrandomly distributed in the formation region (the entire plasma volume) and their undisturbedpaths to the electrodes were calculated. The resulting axial coordinates were folded with thedetector resolution (σ ≈ 4 mm) and response function. The temperature of the positrons was ne-glected because the final H momentum is dominated by the initial p momentum. The solid linesin Fig. 13 are the simulated distributions for different ratios of longitudinal to azimuthal tem-peratures, assuming T⊥ = 15 K: Full thermalization with T‖ = T⊥ (blue) and non-equilibriumconditions with T‖ ≈ 10 T⊥ (green). The best agreement with the experimental data was foundfor T‖ = 10(2) T⊥, suggesting a lower limit of the longitudinal temperature of T ≥ 150 K.A similar distribution for fully thermalized antiprotons can only be achieved when assuminga much longer e+ plasma (≈ 60 mm) or a higher base temperature. In the latter case, the ra-tio between T‖ and T⊥ asymptotically decreases to 2.3, but the temperature of the producedantihydrogen would by far exceed the lower bound of 150 K in that scenario.

We therefore find an axial enhancement of H production due to the fact that the antiprotonswhich form antihydrogen are not in full thermal equilibrium with the positron plasma. Thisobservation further supports the result obtained in Sec. 2.2 that the H recombination rate mustby far exceed the cooling rate of antiprotons in the positron plasma. Like the temperaturedependence of antihydrogen production found there, the present result also agrees with themost recent detailed Monte Carlo simulations which fully model the ATHENA experimentalconditions. Furthermore, our data corroborate an earlier study by the ATRAP collaboration.70

In that work, a potential well in the axial electric potential was rapidly oscillated, thereby

69M. Amoretti et al., “Centrifugal separation of ions and an oppositely charged non-neutral plasma,” Phys.Plasmas 13 (2006) 012308.

70G. Gabrielse et al., “First measurement of the velocity of slow antihydrogen atoms,” Phys. Rev. Lett. 93(2004) 073401.

23

allowing a determination of the H axial velocity in a way analogous to the measurement of thespeed of light with a mechanical cogwheel.71 The ATRAP group also found that H was emittedat high axial velocities, corresponding to a temperature of ≈ 2000 K.

71H. Fizeau, “Sur une experience relative a la vitesse de propagation de la lumiere,” C. R. Acad. Sci. 29 (1849)90.

25

Figure 15: Principle of laser cooling: (a) and (b) The atom or ion absorbs a red-shifted pho-ton propagating in the direction opposite to the motion of the atom or ion and is decelerated;(b) The atom or ion spontaneously emits a photon in a random direction. On average, themomentum �p of the atom or ion is reduced with each absorption and emission cycle.

3 Indirect laser cooling of antiprotons

3.1 Towards ultracold antihydrogen

The experimental investigations presented in the previous chapter have shown that the nested-trap scheme is inadequate for producing H that may be magnetically trapped or used directly forprecision spectroscopy. While the anti-atoms produced by ATHENA and ATRAP are certainly“cold” compared to those created at relativistic velocities in the first in-beam experiment atLEAR,1 they are most probably far from the temperatures required for precision tests. In thefollowing we will discuss two alternative ways in which even colder antihydrogen may beproduced.

1. Laser cooling of antihydrogen atoms after production

Laser cooling is a well-established technique72 which employs light to cool atoms or ions tovery low temperatures. Its simplest form is the so-called optical molasses or Doppler cooling.The principle is based on the directional absorption of a photon by excitation of an atomic orionic system, followed by the spontaneous emission of a photon in a random direction at somelater time (see Fig. 15). The laser light is red-detuned with respect to the natural transitionfrequency, such that resonant absorption can only occur when the atom/ion momentum and thephoton momentum are opposed. After a large number of such scattering processes, the samplereaches an equilibrium between the laser cooling by directed absorption and heating by randomemission. The corresponding temperature is called the Doppler temperature

TD =�γ

2kB, (10)

72H. J. Metcalf and P. van der Straten, Laser cooling and trapping, corr. 2nd printing, New York: Springer(2001).

26

where � is the reduced Planck constant and γ is the linewidth of the transition. The laser coolingtechnique was initially envisaged73 in 1975 and demonstrated shortly after in positive ions.74,75

Several years later, the cooling of neutral atoms confined in a magnetic trap was also achieved.76

Laser cooling of antihydrogen has been discussed by several authors,77,78,79 based on theexcitation of the 1S–2P transition (Lyman-α) at 121.56 nm. The laser cooling of ordinary hy-drogen via this transition to a temperature of 8 mK, near the Doppler temperature TD = 2.4 mKfor this transition, was accomplished around the same time.80 Narrow-band continuous-waveLyman-α light sources based on four-wave mixing in a mercury vapor are now available;81

however, the achievable laser power is only sufficient to cool (anti-)hydrogen already con-fined in a magnetic trap, but not to create a much more strongly confining optical dipole trapnecessary to trap and cool antihydrogen created under the ATHENA or ATRAP experimentalconditions. Hence, this option cannot (at least not yet) alleviate the problems associated withthe high temperature of H created with the nested-well technique.

2. Use of a different recombination mechanism

In addition to the recombination processes discussed in Secs. 2.1 and 2.3, antihydrogen forma-tion can also be achieved by other reactions. One mechanism that has garnered considerableinterest is the charge exchange reaction of positronium with antiprotons, according to the reac-tion82

Ps∗ + p −→ H∗+ e−. (11)

It was soon realized83 that the reaction rate can be strongly increased by exciting the Ps toRydberg states prior to bringing them into overlap with the antiprotons, because the cross-section scales with the fourth power of the positronium’s principal quantum number. Highlyexcited states are denoted by a star in Eq. (11). Due to the resonant nature of the reaction,only a narrow band of final quantum states is populated in the H atom. These can either beallowed to decay spontaneously or be rapidly de-excited by stimulated emission. The process

73T. Hansch and A. Schawlow, “Cooling of gases by laser radiation,” Opt. Commun. 13 (1975) 68.74D. J. Wineland, R. E. Drullinger and F. L. Walls, “Radiation-pressure cooling of bound resonant absorbers,”

Phys. Rev. Lett. 40 (1978) 1639.75W. Neuhauser et al., “Optical-sideband cooling of visible atom cloud confined in parabolic well,” Phys. Rev.

Lett. 41 (1978) 233.76S. Chu et al., “Three-dimensional viscous confinement and cooling of atoms by resonance radiation pres-

sure,” Phys. Rev. Lett. 55 (1985) 48.77W. Ertmer and H. Wallis, “Laser cooling of antihydrogen.” In: Symposium on the Production and Investiga-

tion of Atomic Antimatter, Karlsruhe, Germany, 30 November – 2 December 1987 / Ed. by H. Poth and A. Wolf– Hyperf. Interact. 44 (1988) 319.

78P. D. Lett, P. L. Gould and W. D. Phillips, “Propects for electromagnetic manipulation and trapping ofantihydrogen.” Ibid. – Hyperf. Interact. 44 (1988) 335.

79W. D. Phillips et al., “Laser manipulation and cooling of (anti)hydrogen.” In: Antihydrogen Workshop, Mu-nich, Germany, 30–31 July 1992 / Ed. by D. Klepner – Hyperf. Interact. 76 (1993) 265.

80I. D. Setija, et al., “Optical cooling of atomic hydrogen in a magnetic trap,” Phys. Rev. Lett. 70 (1993) 2257.81K. S. E. Eikema, J. Walz and T. W. Haansch, “Continuous coherent Lyman-α excitation of atomic hydrogen,”

Phys. Rev. Lett. 86 (2001) 5679.82J. W. Humberston et al., “On antihydrogen formation in collisions of antiprotons with positronium,” J. Phys.

B 20 (1987) L25.83M. Charlton, “Antihydrogen production in collisions of antiprotons with excited states of positronium,” Phys.

Lett. A 143 (1990) 143.

27

Figure 16: Principle sketches of the formation of antihydrogen by positronium charge ex-change in (a) the ATRAP experiment85 and (b) the proposed AEGIS experiment [C58].

is technologically challenging because it necessitates both the availability of large numbers ofpositronium atoms and the capability to excite them to Rydberg states.

Both requirements can be simultaneously addressed under the experimental conditions ofan antihydrogen experiment by a technique that involves an additional charge exchange reactionbetween Rydberg cesium atoms and positrons,84 illustrated in Fig. 16(a). Cesium atoms froman oven are brought into Rydberg states by a two-step laser excitation before they interact withcool e+ in a Penning trap and form positronium, also in a highly excited state. Antihydrogenformation takes place in a second charge exchange reaction, between the Ps and antiprotonswhich have been cooled to the trap temperature by electron cooling. This technique has beendemonstrated by the ATRAP collaboration, who reported the detection of 14 H atoms formedin this way.85 The small number of events mainly results from the small solid angle betweenthe multiple interaction regions. As was already mentioned in Sec. 1.2, it is planned to alsouse this H formation mechanism as part of the proposed AEGIS experiment. In AEGIS, Pswill be produced by the bombardment of a nano-porous positronium converter material witha positron pulse, as shown in Fig. 16(b). Due to the large p/e+ mass ratio, the antihydrogenproduced with any variation of this technique should have the temperature of the antiprotonsprior to recombination, usually ≈ 4 . . . 15 K. In the next section, we will discuss a methodwhich may allow the pre-cooling of antiprotons to sub-K temperatures and thus, the creationof ultracold antihydrogen.

3.2 Laser cooling of negative ions

We have seen that when the Ps charge exchange technique is used to form antihydrogen, anyreduction in the antiproton temperature will directly translate into a corresponding decrease inthe temperature of the produced antihydrogen atoms. Therefore, a mechanism is required bywhich antiprotons can be cooled to cryogenic temperatures well below that of the surrounding

84E. A. Hessels, D. M. Homan and M. J. Cavagnero, “Two-stage Rydberg charge exchange: An efficient methodfor production of antihydrogen,” Phys. Rev. A 57 (1998) 1668.

85C. H. Storry et al., “First laser-controlled antihydrogen production,” Phys. Rev. Lett. 93 (2004) 263401.

28

Figure 17: Principle of negative-ion formation, illustrated by means of the fluorine atom.(a) and (b) The electric field of the electron polarizes the neutral atom, such that an attrac-tive force arises. (c) The Z + 1 electrons rearrange into the energetically most favorableconfiguration.

environment. Unfortunately, the antiproton, being a subatomic particle without an atomic struc-ture, does not lend itself to laser cooling. It can only be cooled by collisions with other particles,a process that is called sympathetic cooling. Additionally, resonant excitation of the p’s charac-teristic motions may be used to compress or expand the antiproton cloud as it evolves within thecooling plasma of electrons or positrons. Along these lines, the techniques of sideband coolingand rotating-wall compression have been thoroughly investigated by ATHENA [A25, A31].

However, as the antiprotons cool, their temperature asymptotically approaches that of thecooling medium, which is at best in thermal equilibrium with the cryogenic environment. Thisrestriction can only be overcome if the ion which is used for sympathetic cooling is itselfactively cooled. In this context, laser cooling immediately comes to mind. Atomic ions thatare confined in the same trap region as the antiprotons could be laser-cooled and would thensuccessively remove thermal energy from the p cloud until the Doppler temperature is reached.Such an indirect cooling scheme has been demonstrated to work86 with 198Hg+ ions whichwere sympathetically cooled by the much lighter species 9Be+. However, since antiprotonsare negatively charged, only negative ions can be employed in cooling them. This is becausepositive ions would rapidly annihilate with the antiprotons, to which they are attracted by anelectrostatic force. As was mentioned in Sec. 3.1, the laser cooling of positive ions and ofneutral atoms was accomplished more than 20 years ago. In contrast, the same is not the casefor negative ions. This is because until recently, no negative ion was known which exhibits abound–bound transition that is appropriate for laser cooling.

The structure of negative atomic ions is fundamentally different from neutral atoms or pos-itive ions because of the nature of the potential experienced by the valence electron.87 Classi-cally, negative ions should not exist, as it is not energetically favorable for a negatively chargedelectron to attach itself to a neutral core. Most elements, however, nevertheless form negativeions. They are created by polarization of the neutral atom, as shown schematically in Fig. 17,and are stable due to quantum-mechanical correlation effects. The so-called correlation en-ergy, the energy gained when all Z + 1 electrons adjust their wavefunctions in accordance withthe Pauli exclusion principle and electrostatic repulsion, is typically about an order of magni-

86D. J. Larson et al., “Sympathetic cooling of trapped ions: A laser-cooled two-species nonneutral ion plasma,”Phys. Rev. Lett. 57 (1986) 70.

87D. J. Pegg, “Structure and dynamics of negative ions,” Rep. Prog. Phys. 67 (2004) 857.

29

tude smaller than the binding energies in atoms or positive ions. The potential is both shallowand short-ranged; therefore, only a limited number of bound states (if any) exist. Bound ex-cited states are known to exist in only a small fraction of elements that form negative ions.88

Most of these states have the same parity as the ground state, such that no strong optical tran-sitions can be observed. Electric-dipole transitions, which can only occur between states ofopposite parity, are of particular interest because in addition to being accessible to investiga-tions with spectroscopic techniques, they could in principle be used to laser-cool the negativeion. Opposite-parity bound states have been predicted for the anions of some lanthanides andactinides89,90,91,92 and for cesium93,94 on the basis of theoretical calculations. While some ofthese candidates have not yet been investigated experimentally, the existence of such states incesium and lanthanum has already been ruled out.95,96 Recently, a strong resonant transitionjust below the photodetachment threshold was fortuitously discovered in the negative osmiumion and investigated by infrared laser photodetachment spectroscopy.97 Figure 18 shows theenergy level diagram for Os− which results from these measurements and from calculations onthe ground state configuration.98 In this detailed experimental study of Os−, performed usingphotodetachment spectroscopy with a pulsed dye laser, the transition frequency (in the nearinfrared, wavelength λ ≈ 1162.7 nm) was determined with an uncertainty of ≈ 5 Ghz. It wasfound that the bound excited state is very weakly bound (binding energy ≈ 11.5 eV) and that itsEinstein coefficient is A ≈ 104. The narrow linewidth of only 10 kHz means that the Dopplertemperature achievable by laser cooling is TD = 0.24 μK, four orders of magnitude lower thanthat of (anti-)hydrogen when using the Lyman-α transition.

On the basis of this experimental information, we undertook a theoretical investigationinto the suitability of Os− for laser cooling [A22]. Quantitative estimates were derived forstandard operating parameters similar to those used in the ATHENA Penning traps (magneticfield magnitude B = 6 T, electric potential U0 = 10 V, characteristic trap dimension d0 =

14 mm). Assuming that 106 Os− ions can be simultaneously confined in the trap, this resultsin an ion plasma with a density of 2.4 × 107 cm−3, an azimuthal plasma area of πr2

0 = 10 mm2

88T. Andersen, H. K. Haugen and H. Hotop, “Binding energies in atomic negative ions: III,” J. Phys. Chem.Ref. Data 28 (1999) 1511.

89S. H. Vosko et al., “Theoretical study of even- and odd-parity states in La− and Ac−: Evidence for theuniqueness of La−,” Phys. Rev. A 43 (1991) 6389.

90D. Datta and D. R. Beck, “Electron affinities of opposite-parity bound states in Th−: Relativistic-configuration-interaction studies,” Phys. Rev. A 50 (1994) 1107.

91K. Dinov, D. R. Beck and D. Datta, “Electron affinities of six bound states of Ce− formed by attachment of6p and 5d electrons to Ce,” Phys. Rev. A 50 (1994) 1144.

92S. M. O’Malley and D. R. Beck, “Valence calculations of lanthanide anion binding energies: 6p attachmentsto 4 f n6s2 thresholds,” Phys. Rev. A 78 (2008) 012510.

93C. Froese Fischer and D. Chen, “Numerical multiconfiguration Hartree-Fock calculations for nsnp3P statesof Rb and Cs negative ions,” J. Mol. Struct. (Theochem) 199 (1989) 61.

94C. H. Greene, “Photoabsorption spectra of the heavy alkali-metal negative ions,” Phys. Rev. A 42 (1990)1405.

95A. M. Covington et al., “Measurement of the electron affinity of lanthanum,” J. Phys. B 31 (1988) L855.96M. Scheer et al., “Experimental evidence that the 6s6p 3PJ states of Cs− are shape resonances,” Phys. Rev.

Lett. 80 (1998) 684.97R. C. Bilodeau and H. K. Haugen, “Experimental studies of Os−: Observation of a bound-bound electric

dipole transition in an atomic negative ion,” Phys. Rev. Lett. 85 (2000) 534.98P. L. Norquist and D. R. Beck, “Binding energies, hyperfine structure, and magnetic dipole decay rates for

Os− 5d76s2 4F levels,” Phys. Rev. A 61 (2000) 014501.

30

Figure 18: Energy level diagram of the negative osmium ion. The red arrow indicates therelevant transition for laser cooling.

and a half-length of z0 = 10 mm2. The extremely small binding energy of the valence electronin the excited state means that the excited ion is fragile and may easily be neutralized when itis exposed to strong electric fields. While the trapping field is too small to cause breakup, theions encounter high electric fields in Coulomb collisions with each other. The probability perunit time W for the breakup of atoms in static electric fields99 exhibits a sharp cutoff for fieldsbelow ≈ 2 kV cm−1, corresponding to ion collisions at a tepmerature of ≈ 100 K. Therefore, theosmium ions must be pre-cooled at least to liquid-nitrogen temperature before laser excitationcan begin.

Laser cooling from 80 K to the Doppler temperature requires the scattering of some 105

photons, which takes about 5 minutes when the laser is operated at the saturation intensity ofthe transition. Due to the rather small spontaneous decay rate of the excited state, the ions mayabsorb additional photons before they decay back to the ground state, resulting in photodetach-ment and hence, neutralization. Neutralized ions will leave the trap and are no longer availablefor laser cooling. At the saturation intensity, the branching ratio into the detachment channel isonly of the order of 10−6, but over the course of the entire laser cooling cycle a sizable fractionof the ions may nevertheless be lost. An estimate of the branching ratios towards the interme-diate states was also performed, which was based on theoretical calculations of their energiesand lifetimes98 in the absence of experimental data for these parameters. It was concluded thatthe repumping of those states which can be populated by allowed transitions from the Je statewould likely be necessary. In summary, we established that based on the available experimen-tal data, the laser cooling of Os− should be technically feasible. However, many aspects of thetechnique, ranging from the scattering rate (and hence, the cooling time) to the fraction of ionslost by photodetachment, depend heavily on the cross-section of the cooling transition as wellas the configuration of the bound state. Therefore, it became clear that a deeper understandingof the properties of the opposite-parity bound state must be reached before laser cooling of Os−

can be attempted.

99B. M. Smirnov and M. I. Chibisov, “The breaking up of atomic particles by an electric field and by electroncollisions,” Sov. Phys. – JETP 22 (1966) 585.

31

Figure 19: Mass spectrum obtained by scanning the current in the coil of the mass separatormagnet. Assignments of the peaks were made on the basis of isotopic abundances.

3.3 High-resolution laser spectroscopy on the negative osmium ion

In order to further investigate the prospect of ultracold antiprotons, the UNIC project (Ultra-cold Negative Ions by indirect laser Cooling) was established at the Max Planck Institute forNuclear Physics (MPIK) in Heidelberg. The apparatus, whose construction began in 2007,consists of a negative ion source, a mass separator, a cylindrical Penning trap contained inthe magnetic field of a superconducting magnet, and a laser system. As was concluded in theprevious section, a more detailed knowledge of the relevant bound–bound transition in Os−

was required before laser cooling could be attempted. Therefore, a spectroscopy section wasadded to the UNIC apparatus, in which collinear laser spectroscopy can be carried out on theion beam. The first milestone of the project was to confirm the existence of the electric-dipoletransition, improve the experimental uncertainty on the transition frequency and perform a di-rect measurement of the scattering cross-section [A40sub]. This was achieved by performinghigh-resolution collinear laser spectroscopy on a beam of 192Os− ions.

In the UNIC apparatus, negative Os ions are produced in a Middleton-type sputter ionsource.100 They are extracted from the source and accelerated to E = 2.5 . . . 6.5 keV by electro-static potentials. The primary ion beam consists mainly of the most abundant isotope 192Os−, butcontains other atomic and molecular contaminant ions. The beam is therefore passed througha large dipole magnet for mass separation, which has a resolving power of ≈ 180. A massspectrum obtained by scanning the magnet current is shown in Fig. 19. After mass separation,the resulting 50-nA beam consists of more than 90% 192Os−. The ion beam is then electrostat-ically deflected into the spectroscopy arm of the apparatus [see Fig. 20(a)], which consists ofentrance and exit diaphragms (diameter 7.5 mm, length of interaction region 520 mm), an ion-izer, a deflector, a micro-channel-plate detector (MCP) and a Faraday cup. The ion beam andthe laser beam are passed collinearly through the entire interaction region. In this way, the ef-fect of velocity bunching101 reduces the Doppler width of the resonance by up to a factor of 10for our experimental conditions (ion temperature ≈ 1500 K, beam energy 5 kV). In the ionizer,the beam passes through three parallel meshes placed in a plane perpendicular to the beam, at

100R. Middleton, Nucl. Instrum. Methods 214, 139 (1983).101W. Demtroder, Laser spectroscopy. Berlin: Springer, 3rd ed. (2002).

32

Figure 20: (a) Sketch of the spectroscopy arm of the UNIC apparatus showing entrance andexit diaphragms, ionizer, deflector, MCP detector and Faraday cup. (b) Typical resonanceof the bound–bound electric-dipole transition, at an ion beam energy of 5 keV. The figureillustrates the efficiency gain of about two orders of magnitude due to the field-detachmentproces.

which a voltage of up to 6.5 keV can be applied, corresponding to a longitudinal electric fieldof up to 2 × 106 V m−1. A deflector leads the ions into a Faraday cup, whereas the MCP countsneutralized particles which are not deflected.

The laser used in the present experiment is a commercial optical parametric oscillator sys-tem custom-built for this application. It is built around a periodically poled lithium niobate(PPLN) crystal placed in a bow-tie cavity, pumped by a frequency-doubled Nd:YAG laser. Thenon-linear crystal produces signal and idler waves at 980 nm and 1163 nm, respectively, thelatter being sustained by the resonator mode. When pumped at a power of 2 W, the OPO pro-duces close to 200 mW; its frequency can be swept continuously over a range of 1.5 GHz. Thelaser bandwidth was measured to be smaller than 5 MHz with a Fabry–Perot interferometer.The wavelength is recorded and regulated with a wavemeter, which in turn is calibrated by astabilized diode laser. Ions which have been excited to the Je state in the interaction regioncan be neutralized in one of two ways: Either the ion absorbs a second photon leading to pho-todetachment of its excess electron, or the electron will be field-detached by the electric fieldin the ionizer. In both cases, the neutral atoms are detected by the MCP placed in the forwarddirection. A typical excitation resonance is shown in Fig. 20(b). A corresponding resonanceobtained without the ionizing potential is also shown, illustrating the dramatic enhancement ef-fect due to the field detachment. The width of the (mainly Gaussian) resonance, Γres ≈ 45 MHz,is dominated by the Doppler width; its slight asymmetry is due to a corresponding asymmetryin the velocity distribution of the ions.

In collinear laser spectroscopy, the measured transition frequency must be corrected for theDoppler effect. In order to also take into account a possible slight offset in the beam energy,we performed a number of measurements at different beam energies, fitting the data points tothe well-known function for the Doppler shift. The result of these measurements and the fit isshown in Fig. 21(a). From the fit, we obtained a transition frequency of 257.831190(30) THz[corresponding to a wavelength of 1162.74706(14) nm], in good agreement with the only prior

33

Figure 21: (a) Blue-shifted resonance frequencies as a function of the ion beam energy. Thesolid line is the result of the fit for the Doppler shift, its extrapolation to zero beam energyis shown in the inset. The lower pane shows the residuals of the fit. (b) Number of detectedatoms as a function of the laser intensity, recorded in resonance and for a fixed beam energy.The solid fit is a fit to the data according to the rate equation model.

measurement,97 but more than two orders of magnitude more precise, making this the mostprecise measurement of any feature in an atomic negative ion to date.

The resonant cross-section can be determined by considering the time evolution of theground and excited state populations in the beam, as well as the number of neutralized atoms.Neglecting decay to intermediate levels, a set of differential rate equations102 can be analyticallysolved to yield the number of excited and detached ions as a function of the time of flight t inthe interaction region:

Ne(t) = C−12 e−t (2σ0τφ+C1+C2)

2τ

(e

tC2τ − 1

)σ0τφ (12)

and

Nd(t) = − 1

2C22

e−t((2σ0+σd)φ+ 1τ ) ×

(−2C2

2et((2σ0+σd)φ+ 1τ )

+et (2σ0τφ+C1−C2)2τ

(4σ02τ2φ2 − 2σ0τ (C2 − 2) φ +C2

1 −C1C2

)+et (2σ0τφ+C1+C2)

2τ

(4σ02τ2φ2 + 2σ0τ (C2 + 2) φ +C2

1 +C1C2

)), (13)

where τ is the total lifetime of the excited state and φ is the photon flux. The factors C1 and C2

are given byC1 = σdτφ + 1 (14)

and

C2 =

√C2

1 + 4σ02τ2φ2 + 4σ0τφ. (15)

102R. Loudon, The quantum theory of light. New York: Oxford Science Publications, 2nd ed. (1983).

34

The total number of neutralized particles Nneut is obtained by numerical integration of the sumof Eqs. (12) and (13) over time and the radial extent of the overlapping beams. It is a function ofthe average laser power and has four independent parameters: The resonant and non-resonantcross-sections σ0 and σd, the number of ions within the overlap region N0 and the lifetime τ ofthe excited state. The latter is of course related to the cross-section via

τ =c2

4π2σ0ν20Γres, (16)

but was nevertheless treated as an independent parameter of the function for the purpose of thisanalysis.

The number of neutralized atoms detected on the MCP was recorded as a function of thelaser power, which was varied via a polarizing beam splitter, leaving all other beam charac-teristics unchanged. A typical measurement with its corresponding fit according to the rateequation model is shown in Fig. 21(b). Taking into account a simulated ion beam divergenceof 1.5◦ in the interaction region, effectively reducing the interaction region by about 30%, weobtained a resonant cross-section of σ0 = 2.5(7) × 10−15 cm2 from 10 such measurements.The fit function is not sufficiently sensitive to the parameter τ to extract a definite value forthe lifetime of the excited state; however, that value can be determined from the cross-sectionvia Eq. (16). In this way, a value of τ = 3(1) ms is obtained. The measured observed cross-section yields an Einstein coefficient of A = 330 s−1, confirming that the resonance is due toan electric-dipole transition. Our measurements indicate that the natural linewidth is even nar-rower than suggested by the result of the prior measurement,97 which yielded A ≈ 104 s−1.Given this small Einstein A coefficient, the Doppler temperature achievable by laser coolingof Os− will in the foreseeable future be limited by the laser bandwidth. With our laser and adetuning of δ = Γlas/2, the cooling rate may be as low as 50 Hz and cooling times from 80 Kto the Doppler temperature prohibitively long. Therefore, it may be necessary to pre-cool theions to liquid-helium temperature or even below, using electrons. The cooling from 4 K to theDoppler temperature would then take roughly 5 minutes.

Given the high sensitivity of our apparatus, the study of the corresponding transition in theanions of some of the less abundant isotopes of Os should be feasible. In this way, the iso-tope shift could be extracted. Furthermore, the isotopes 187Os and 189Os have a non-vanishingnuclear spin, and the expected hyperfine structure of the transition may allow a direct determi-nation of the total angular momentum Je of the excited state, which in turn conveys informationof the relevant decay channels to intermediate states.

35

A Complete list of publications

A.1 Journal and review articles

2008

[A39] M. C. Fujiwara et al., “Temporally controlled modulation of antihydrogen productionand the temperature scaling of antiproton-positron recombination,” Phys. Rev. Lett. 101(2008) 053401.

[A38] S. George et al., “Time-separated oscillatory fields for high-precision mass measure-ments on short-lived Al and Ca nuclides,” Europhys. Lett. 82 (2008) 50005.

[A37] M. Mukherjee et al., “Mass measurements and evaluation around A = 22,” Eur. Phys. J.A 35 (2008) 31.

[A36] M. Mukherjee et al., “ISOLTRAP: An on-line Penning trap for mass spectrometry onshort-lived nuclides,” Eur. Phys. J. A 35 (2008) 1.

[A35] M. Dworschak et al., “Restoration of the N = 82 shell gap from direct mass measure-ments of 132,134Sn,” Phys. Rev. Lett. 100 (2008) 072501.

[A34] C. Weber et al., “Atomic mass measurements of short-lived nuclides around the doubly-magic 208Pb,” Nucl. Phys. A 803 (2008) 1.

2007

[A33] A. Kellerbauer et al., “High-precision masses of neutron-deficient rubidium isotopesusing a Penning trap mass spectrometer,” Phys. Rev. C 76 (2007) 045504.

[A32] C. Yazidjian et al., “Evidence for a breakdown of the Isobaric Multiplet Mass Equation:A study of the A = 35, T = 3/2 isospin quartet,” Phys. Rev. C 76 (2007) 024308.

[A31] R. Funakoshi et al., “Positron plasma control techniques for the production of coldantihydrogen,” Phys. Rev. A 76 (2007) 012713.

[A30] S. George et al., “Ramsey method of separated oscillatory fields for high-precision Pen-ning trap mass spectrometry,” Phys. Rev. Lett. 98 (2007) 162501.

[A29] C. Guenaut et al., “High-precision mass measurements of nickel, copper, and galliumisotopes and the purported shell closure at N = 40,” Phys. Rev. C 75 (2007) 044303.

2006

[A28] M. Amoretti et al., “Search for laser-induced formation of antihydrogen atoms,” Phys.Rev. Lett. 97 (2006) 213401.

36

[A27] N. Zurlo et al., “Evidence for the production of slow antiprotonic hydrogen in vacuum,”Phys. Rev. Lett. 97 (2006) 153401.

[A26] P. Delahaye et al., “High-accuracy mass measurements of neutron-rich Kr isotopes,”Phys. Rev. C 74 (2006) 034331.

[A25] A. Kellerbauer et al., “Sideband cooling of ions in a non-neutral buffer gas,” Phys. Rev.A 73 (2006) 062508.

[A24] D. Rodrıguez et al., “Accurate mass measurements on neutron-deficient krypton iso-topes,” Nucl. Phys. A 769 (2006) 1.

[A23] A. Herlert et al., “Towards high-accuracy mass spectrometry of highly charged short-lived ions at ISOLTRAP,” Int. J. Mass Spectrom. 251 (2006) 131.

[A22] A. Kellerbauer and J. Walz, “A novel cooling scheme for antiprotons,” New J. Phys. 8(2006) 45.

2005

[A21] G. Sikler et al., “Mass measurements on neutron-deficient Sr and neutron-rich Sn iso-topes with the ISOLTRAP mass spectrometer,” Nucl. Phys. A 763 (2005) 45.

[A20] C. Weber et al., “Weighing excited nuclear states with a Penning trap mass spectrome-ter,” Phys. Lett. A 347 (2005) 81.

[A19] L. V. Jørgensen et al., “New source of dense, cryogenic positron plasmas,” Phys. Rev.Lett. 95 (2005) 025002.

[A18] A. Herlert et al., “Mass spectrometry of atomic ions produced by in-trap decay of short-lived nuclides,” New J. Phys. 7 (2005) 44.

[A17] N. Madsen et al., “Spatial distribution of cold antihydrogen formation,” Phys. Rev. Lett.94 (2005) 033403.

2004

[A16] J. Dilling et al., “Direct mass measurements of neutron-deficient xenon isotopes usingthe ISOLTRAP mass spectrometer,” Eur. Phys. J. A 22 (2004) 163.

[A15] D. Rodrıguez et al., “Mass measurement on the rp-process waiting point 72Kr,” Phys.Rev. Lett. 93 (2004) 161104.

[A14] M. Mukherjee et al., “The mass of 22Mg,” Phys. Rev. Lett. 93 (2004) 150801.

[A13] K. Blaum et al., “Population inversion of nuclear states by a Penning trap mass spectro-meter,” Europhys. Lett. 67 (2004) 586.

37

[A12] A. Kellerbauer et al., “Direct mass measurements on the superallowed emitter 74Rband its daughter 74Kr: Isospin-symmetry-breaking correction for standard-model tests,”Phys. Rev. Lett. 93 (2004) 072502.

[A11] M. Amoretti et al., “Dynamics of antiproton cooling in a positron plasma during anti-hydrogen formation,” Phys. Lett. B 590 (2004) 133.

[A10] J. Van Roosbroeck et al., “Unambiguous identification of three β-decaying isomers in70Cu,” Phys. Rev. Lett. 92 (2004) 112501.

[A9] M. Amoretti et al., “Antihydrogen production temperature dependence,” Phys. Lett. B583 (2004) 59.

[A8] G. Ban et al., “Transport and cooling of singly charged noble gas ion beams,” Nucl.Instrum. Methods A 518 (2004) 712.

2003

[A7] K. Blaum et al., “Masses of 32Ar and 33Ar for fundamental tests,” Phys. Rev. Lett. 91(2003) 260801.

[A6] A. Kellerbauer, “Recent improvements of ISOLTRAP: absolute mass measurements ofexotic nuclides at 108 precision,” Int. J. Mass Spectrom. 229 (2003) 107.

[A5] A. Kellerbauer et al., “From direct to absolute mass measurements: A study of the ac-curacy of ISOLTRAP,” Eur. Phys. J. D 22 (2003) 53.

2001

[A4] S. Schwarz et al., “Accurate masses of neutron-deficient nuclides close to Z = 82,”Nucl. Phys. A 693 (2001) 533.

[A3] F. Herfurth et al., “Breakdown of the isobaric multiplet mass equation at A = 33, T =3/2,” Phys. Rev. Lett. 87 (2001) 142501.

[A2] A. Kellerbauer et al., “Buffer gas cooling of ion beams,” Nucl. Instrum. Methods A 469(2001) 276.

[A1] F. Herfurth et al., “A linear radiofrequency ion trap for accumulation, bunching, andemittance improvement of radioactive ion beams,” Nucl. Instrum. Methods A 469(2001) 254.

38

A.2 Conference papers

2008

[C59] G. Testera et al., “Formation of a cold antihydrogen beam in AEGIS for gravity mea-surements.” In: 1st International Workshop on Cold Antimatter Plasmas and Applicationto Fundamental Physics, Okinawa, Japan, 20–22 February 2008. / Ed. by Y. Kanai andY. Yamazaki – AIP Conf. Proc. 1037 (2008) 5.

[C58] A. Kellerbauer et al., “Proposed antimatter gravity measurement with an antihydro-gen beam.” In: 14th International Workshop on Low Energy Positron and PositroniumPhysics, Reading, UK, 1–4 August 2007. / Ed. by G. F. Gribakin and H. R. J. Walters –Nucl. Instrum. Methods B 266 (2008) 351.

2007

[C57] L. Venturelli et al., “Protonium production in ATHENA.” In: 19th International Confer-ence on the Application of Accelerators in Research and Industry, Fort Worth (Texas),USA, 20–25 August 2006 / Ed. by F. D. McDaniel et al. – Nucl. Instrum. Methods B261 (2007) 40.

2006

[C56] N. Zurlo et al., “Production of slow protonium in vacuum.” In: 4th International Con-ference on Trapped Charged Particles and Fundamental Physics, Parksville (BritishColumbia), Canada, 3–8 September 2006 / Ed. by J. Dilling and G. Gwinner – Hyperf.Interact. 172 (2006) 97.

[C55] A. Herlert et al., “Spin-related aspects of mass determination of radionuclides.” In:Symmetries and Spin, Prague, Czech Republic, 19–26 July 2006 / Ed. by M. Finger,A. V. Efremov and G. Mitselmakher – Czech. J. Phys. 56 (2006) F277.

[C54] A. Herlert et al., “High-accuracy mass measurements for a test of the Standard Model.”In: 13th General Conference of the European Physical Society, Bern, Switzerland, 11–15 July 2005 / Ed. by A. M. Cruise and L. Ouwehand – Noordwijk: European SpaceAgency (2006), ESA SP-637.

[C53] P. Genova et al., “Production and study of antihydrogen in the ATHENA experi-ment.” In: NATO Advanced Research Workshop on Nuclear Science and Safety in Eu-rope, Yalta, Ukraine, 10–16 September 2005 / Ed. by T. Cechak, L. Jenkovszky andIu. Karpenko – Berlin/Heidelberg: Springer (2006), p. 41.

[C52] A. Herlert et al., “High-precision mass measurements for reliable nuclear astrophysicscalculations.” In: 9th International Symposium on Nuclei in the Cosmos, Geneva,Switzerland, 25–30 June 2006 / Ed. by A. Mengoni et al. – Proc. Science NIC-IX (2006)051.

39

[C51] K. Blaum et al., “Penning trap mass spectrometry for nuclear structure studies.” In:7th International Workshop on Nuclear Ground and Isomeric State Properties, Poznan,Poland, 29 May – 1 June 2006 / Ed. by Z. Błaszczak, B. Markov, and K. Marinova –Hyperf. Interact. 171 (2006) 83.

[C50] A. Herlert et al., “High-accuracy mass measurements on neutron deficient neon iso-topes.” In: International Conference on Frontiers in Nuclear Structure, Astrophysics,and Reactions, Kos, Greece, 12–17 September 2005 / Ed. by S. V. Harissopulos,P. Demetriou, and R. Julin – AIP Conf. Proc. 831 (2006) 152.

[C49] A. Kellerbauer et al., “ISOLTRAP mass measurements for weak-interaction studies.”In: International Conference on Frontiers in Nuclear Structure, Astrophysics, and Reac-tions, Kos, Greece, 12–17 September 2005 / Ed. by S. V. Harissopulos, P. Demetriou,and R. Julin – AIP Conf. Proc. 831 (2006) 49.

[C48] M. Amoretti et al., “Progress with cold antihydrogen.” In: 13th International Workshopon Low-Energy Positron and Positronium Physics, Sao Paulo, Brazil, 27–30 July 2005/ Ed. by S. d’A. Sanchez, R. F. da Costa and M. A. P. Lima – Nucl. Instrum. Methods B247 (2006), 133.

[C47] G. Bonomi et al., “Recent results from ATHENA.” In: Second International Confer-ence on Exotic Atoms and Related Topics, Vienna, Austria, 21–25 February 2005 / Ed.by A. Hirtl et al. – Wien: Verlag der Osterreichischen Akademie der Wissenschaften(2006), p. 383.

2005

[C46] R. Funakoshi et al., “ATHENA: a high performance detector for low energy physics.”In: New Trends in High-Energy Physics, Yalta, Ukraine, 10–17 September 2005 / Ed.by P. N. Bogolyubov et al. – Kiev: Joint Institute for Nuclear Research (2005), p. 51.

[C45] A. Rotondi et al., “Results from ATHENA.” In: Eighth International Conference onLow-Energy Antiproton Physics, Bonn, Germany, 16–22 May 2005 / Ed. by D. Grzonkaet al. – AIP Conf. Proc. 796 (2005) 285.

[C44] J. Walz and A. Kellerbauer, “Cooling of antihydrogen and antiprotons to ultracold tem-peratures.” In: Eighth International Conference on Low-Energy Antiproton Physics,Bonn, Germany, 16–22 May 2005 / Ed. by D. Grzonka et al. – AIP Conf. Proc. 796(2005) 247.

[C43] K. Blaum et al., “ISOLTRAP pins down masses of exotic nuclides.” In: InternationalConference on the Interface between Nuclear Structure, Astrophysics and Reactions,University of Surrey, Guildford, UK, 5–8 January 2005 / Ed. by P. Regan and P. Steven-son – J. Phys. G 31 (2005) S1775.

[C42] C. Guenaut et al., “Mass measurements of 56–57Cr and the question of shell reincarnationat N = 32.” In: International Conference on the Interface between Nuclear Structure,

40

Astrophysics and Reactions, University of Surrey, Guildford, UK, 5–8 January 2005 /Ed. by P. Regan and P. Stevenson – J. Phys. G 31 (2005) S1765.

[C41] C. Weber et al., “Effects of the pairing energy on nuclear charge radii.” In: Fourth In-ternational Conference on Exotic Nuclei and Atomic Masses, Pine Mountain (Georgia),USA, 12–16 September 2004 / Ed. by C. J. Gross, W. Nazarewicz, and K. P. Rykaczew-ski – Eur. Phys. J. A 25 Suppl. 1 (2005) 201.

[C40] D. Rodrıguez et al., “Mass measurement on the rp-process waiting point 72Kr.” In:Fourth International Conference on Exotic Nuclei and Atomic Masses, Pine Moun-tain (Georgia), USA, 12–16 September 2004 / Ed. by C. J. Gross, W. Nazarewicz, andK. P. Rykaczewski – Eur. Phys. J. A 25 Suppl. 1 (2005) 41.

[C39] C. Guenaut et al., “Extending the mass ‘backbone’ to short-lived nuclides with ISOL-TRAP.” In: Fourth International Conference on Exotic Nuclei and Atomic Masses, PineMountain (Georgia), USA, 12–16 September 2004 / Ed. by C. J. Gross, W. Nazarewicz,and K. P. Rykaczewski – Eur. Phys. J. A 25 Suppl. 1 (2005) 35.

[C38] C. Guenaut et al., “Is N = 40‘ magic? An analysis of ISOLTRAP mass measurements.”In: Fourth International Conference on Exotic Nuclei and Atomic Masses, Pine Moun-tain (Georgia), USA, 12–16 September 2004 / Ed. by C. J. Gross, W. Nazarewicz, andK. P. Rykaczewski – Eur. Phys. J. A 25 Suppl. 1 (2005) 33.

[C37] F. Herfurth et al., “Recent high-precision mass measurements with the Penning trapspectrometer ISOLTRAP.” In: Fourth International Conference on Exotic Nuclei andAtomic Masses, Pine Mountain (Georgia), USA, 12–16 September 2004 / Ed. byC. J. Gross, W. Nazarewicz, and K. P. Rykaczewski – Eur. Phys. J. A 25 Suppl. 1 (2005)17.

[C36] M. Amoretti et al., “Cold-antimatter physics.” In: 43rd International Winter Meeting onNuclear Physics, Bormio, Italy, 13–20 March 2005 / Ed. by I. Iori and A. Bortolotti –Milan: Universita degli Studi di Milano. Ricerca Scientifica ed Educazione Permanente,Suppl. no. 124 (2005), p. 25.

[C35] C. L. Cesar et al., “Cold antihydrogen at ATHENA: Experimental observation and be-yond.” In: 19th International Conference on Atomic Physics, Rio de Janeiro, Brazil,25–30 July 2004 / Ed. by L. G. Marcassa, K. Helmerson and V. S. Bagnato – AIP Conf.Proc. 770 (2005) 33.

[C34] K. Blaum et al., “Laser ionization and Penning trap mass spectrometry – a fruitful com-bination for isomer separation and high-precision mass measurements.” In: Sixth In-ternational Workshop on Application of Lasers in Atomic Nuclei Research, Poznan,Poland, 24–27 May 2004 / Ed. by Z. Błaszczak, B. Markov and K. Marinova – Hyperf.Interact. 162 (2005) 173.

[C33] A. Kellerbauer et al., “ATHENA - First production of cold antihydrogen and beyond.”In: 3rd Meeting on CPT and Lorentz Symmetry, Bloomington (Indiana), USA, 4–7August 2004 / Ed. by V. A. Kostelecky – Singapore: World Scientific (2005), p. 38.

41

[C32] A. Variola et al., “Production of cold antihydrogen with ATHENA for fundamentalstudies.” In: Vulcano Workshop 2004: Frontier Objects in Astrophysics and ParticlePhysics, Vulcano, Italy, 24–29 May 2004 / Ed. by F. Giovannelli and G. Mannocchi –It. Phys. Soc. Conf. Proc. 90 (2005) 213).

[C31] K. Blaum et al., “ISOLTRAP mass measurements of exotic nuclides at δm/m = 10−8”In: 22nd International Nuclear Physics Conference, Goteborg, Sweden, 27 June – 2 July2004 / Ed. by B. Jonson et al. – Nucl. Phys. A 752 (2005) 317c.

[C30] G. Bonomi et al., “Antihydrogen production mechanisms in ATHENA.” In: 22nd Inter-national Nuclear Physics Conference, Goteborg, Sweden, 27 June – 2 July 2004 / Ed.by B. Jonson et al. – Nucl. Phys. A 752 (2005) 97c.

[C29] A. Kellerbauer, “Production of cold antihydrogen with ATHENA for fundamental stud-ies.” In: 39es Rencontres de Moriond, La Thuile, Italy, 21–28 March 2004 / Ed. byJ. Tran Thanh Van – Hanoi: The Gioi (2005), p. 385.

2004

[C28] A. Kellerbauer et al., “Towards high-precision mass measurements on 74Rb for a test ofthe CVC hypothesis and the unitarity of the CKM matrix.” In: 6th International Confer-ence on Radioactive Nuclear Beams, Argonne (Illinois), USA, 22–26 September 2003/ Ed. by G. Savard et al. – Nucl. Phys. A 746 (2004) 635c.

[C27] P. Delahaye, F. Ames and A. Kellerbauer, “Study of the charge exchange process atlow energy with REXTRAP.” In: 6th International Conference on Radioactive NuclearBeams, Argonne (Illinois), USA, 22–26 September 2003 / Ed. by G. Savard et al. –Nucl. Phys. A 746 (2004) 604c.

[C26] F. Herfurth et al., “Masses along the rp-process path and large scale surveys on Cu,Ni and Ga with ISOLTRAP.” In: 6th International Conference on Radioactive NuclearBeams, Argonne (Illinois), USA, 22–26 September 2003 / Ed. by G. Savard et al. –Nucl. Phys. A 746 (2004) 487c.

[C25] K. Blaum et al., “Recent results from the Penning trap mass spectrometer ISOLTRAP.”In: 6th International Conference on Radioactive Nuclear Beams, Argonne (Illinois),USA, 22–26 September 2003 / Ed. by G. Savard et al. – Nucl. Phys. A 746 (2004)305c.

[C24] N. Madsen et al., “Antihydrogen formation using cold plasmas.” In: 14th APS TopicalConference on Atomic Processes in Plasmas, Santa Fe (New Mexico), USA, 19–22April 2004 / Ed. by J. S. Cohen et al. – AIP Conf. Proc. 730 (2004) 13.

[C23] I. Johnson et al., “Detection of antihydrogen annihilations with a Si-micro-strip andpure CsI detector.” In: Eighth International Conference on Advanced Technology andParticle Physics, Como, Italy, 6–10 October 2003 / Ed. by M. Barone et al. – Singapore:World Scientific (2004), p. 473.

42

[C22] K. Blaum et al., “Study of ground- and low-lying nuclear states by combining laserionization and Penning trap mass spectrometry.” In: 32nd International Workshop onGross Properties of Nuclei and Nuclear Excitations, Hirschegg, Austria, 11–17 January2004 / Ed. by M. Buballa et al. – Darmstadt: Gesellschaft fur SchwerionenforschungmbH (2004), p. 183.

2003

[C21] A. Kellerbauer et al., “Carbon cluster ions for a study of the accuracy of ISOLTRAP.”In: 3rd Euroconference on Atomic Physics at Accelerators, Aarhus, Denmark, 8–13September 2001 / Ed. by H. Knudsen et al. – Hyperf. Interact. 146/147 (2003) 307.

[C20] K. Blaum et al., “Precision mass measurements on neutron-rich nuclei with the Penningtrap mass spectrometer ISOLTRAP.” In: 3rd International Conference on Fission andProperties of Neutron-Rich Nuclei, Sanibel Island (Florida), USA, 3–9 November 2002/ Ed. by J. H. Hamilton et al. – Singapore: World Scientific (2003), p. 655.

[C19] K. Blaum et al., “Pushing the relative mass accuracy limit of ISOLTRAP on exoticnuclei below 10 ppb.” In: 14th International Conference on Electromagnetic IsotopeSeparators and Techniques Related to their Applications, Victoria (British Columbia),Canada, 6–10 May 2002 / Ed. by J. M. ’Auria et al. – Nucl. Instrum. Methods B 204(2003) 478.

[C18] F. Herfurth et al., “Masses of nuclei close to the dripline.” In: 31st International Work-shop on Gross Properties of Nuclei and Nuclear Excitations, Hirschegg, Austria, 12–18January 2003 / Ed. by H. Feldmeier et al. – Darmstadt: Gesellschaft fur Schwerionen-forschung mbH (2003), p. 162.

[C17] F. Herfurth et al., “Mass measurements and nuclear physics – recent results from ISOL-TRAP.” In: 3rd International Conference on Trapped Charged Particles and Fundamen-tal Interactions, Wildbad Kreuth, Germany, 25–30 August 2002 / Ed. by H. Walther andD. Habs – J. Phys. B 36 (2003) 931.

[C16] K. Blaum et al., “Recent developments at ISOLTRAP: towards a relative mass accuracyof exotic nuclei below 10−8.” In: 3rd International Conference on Trapped Charged Par-ticles and Fundamental Interactions, Wildbad Kreuth, Germany, 25–30 August 2002 /Ed. by H. Walther and D. Habs – J. Phys. B 36 (2003) 921.

[C15] S. Henry et al., “Nuclear deformation and pairing energy in neutron-deficient Hg iso-topes.” In: 3rd International Conference on Exotic Nuclei and Atomic Masses, Hameen-linna, Finland, 2–7 July 2001 / Ed. by J. Aysto, P. Dendooven, and A. Jokinen –Berlin/Heidelberg: Springer (2003), p. 51.

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2002

[C14] K. Blaum et al., ”Carbon clusters for absolute mass measurements at ISOLTRAP.” In:3rd International Conference on Exotic Nuclei and Atomic Masses, Hameenlinna, Fin-land, 2–7 July 2001 / Ed. by J. Aysto et al. – Eur. Phys. J. A 15 (2002) 245.

[C13] F. Herfurth et al., “Accurate mass measurements of very short-lived nuclei nuclei: Pre-requisites for high-accuracy investigation of superallowed β-decays.” In: 3rd Interna-tional Conference on Exotic Nuclei and Atomic Masses, Hameenlinna, Finland, 2–7July 2001 / Ed. by J. Aysto et al. – Eur. Phys. J. A 15 (2002) 17.

[C12] G. Bollen et al., “New mass measurements with the ISOLTRAP spectrometer.” In: In-ternational Nuclear Physics Conference 2001, Berkeley (California), USA, 30 July – 3August 2001 / Ed. by E. Norman et al. – AIP Conf. Proc. 610 (2002) 905.

[C11] C. Scheidenberger et al., “Production and trapping of carbon clusters for absolute massmeasurements at ISOLTRAP.” In: 5th International Conference on Radioactive NuclearBeams, Divonne, France, 3–8 April 2000 / Ed. by H. L. Ravn et al. – Nucl. Phys. A 701(2002) 574c.

[C10] A. Kellerbauer et al., “A linear radiofrequency quadrupole ion trap for the cooling andbunching of radioactive ion beams.” In: 5th International Conference on RadioactiveNuclear Beams, Divonne, France, 3–8 April 2000 / Ed. by H. L. Ravn et al. – Nucl.Phys. A 701 (2002) 565c.

[C9] J. Dilling et al., “Direct mass measurements of neutron-deficient xenon isotopes withthe ISOLTRAP mass spectrometer.” In: 5th International Conference on RadioactiveNuclear Beams, Divonne, France, 3–8 April 2000 / Ed. by H. L. Ravn et al. – Nucl.Phys. A 701 (2002) 520c.

[C8] F. Herfurth et al., “Extension of Penning trap mass measurements to very short-livednuclides.” In: 5th International Conference on Radioactive Nuclear Beams, Divonne,France, 3–8 April 2000 / Ed. by H. L. Ravn et al. – Nucl. Phys. A 701 (2002) 516c.

1998–2001

[C7] A. Kellerbauer et al., “Improvement of the applicability, efficiency, and precision ofthe Penning trap mass spectrometer ISOLTRAP.” In: Atomic Physics at Accelerators,Cargese, France, 19–23 September 2000 / Ed. by D. Lunney et al. - Hyperf. Interact.132 (2001) 511.

[C6] S. Schwarz et al., “Accurate mass determination of neutron-deficient nuclides close toZ = 82 with ISOLTRAP.” In: Atomic Physics at Accelerators, Cargese, France, 19–23September 2000 / Ed. by D. Lunney et al. – Hyperf. Interact. 132 (2001) 337.

[C5] J. Dilling et al., “Mass measurements of 114-124,130Xe with the ISOLTRAP Penningtrap spectrometer.” In: Atomic Physics at Accelerators, Cargese, France, 19–23 Septem-ber 2000 / Ed. by D. Lunney et al. - Hyperf. Interact. 132 (2001) 331.

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[C4] F. Herfurth et al., “Towards shorter-lived nuclides in ISOLTRAP mass measurements.”In: Atomic Physics at Accelerators, Cargese, France, 19–23 September 2000 / Ed. byD. Lunney et al. – Hyperf. Interact. 132 (2001) 309.

[C3] G. Bollen et al., “Mass measurements on short-lived nuclides with ISOLTRAP.” In:Atomic Physics at Accelerators, Cargese, France, 19–23 September 2000 / Ed. by D.Lunney et al. – Hyperf. Interact. 132 (2001) 215.

[C2] J. Dilling et al., “Mass measurements on radioactive isotopes using the ISOLTRAPspectrometer.” In: 14th Lake Louise Winter Institute: Electroweak Physics, Lake Louise(Alberta), Canada, 14–20 February 1999 / Ed. by A. Astbury et al. – Singapore: WorldScientific (2000), p. 324.

[C1] G. Bollen et al., “A radio frequency quadrupole ion beam buncher for ISOLTRAP.” In:2nd International Conference on Exotic Nuclei and Atomic Masses, Bellaire (Michi-gan), USA, 23–27 June 1998 / Ed. by B. M. Sherrill et al. – AIP Conf. Proc. 455 (1998)965.

A.3 Popular-science articles

[P3] A. Kellerbauer, “Antimaterie – Spiegelbild oder Zerrbild. Antiwasserstoff im Labor,”Phys. Unserer Zeit 38 (2007) 168.

[P2] K. Blaum, F. Herfurth and A. Kellerbauer, “Eine Waage fur exotische Kerne,” Phys.Unserer Zeit 36 (2005) 222.

[P1] A. Kellerbauer (uncredited), “High-precision masses test the Standard Model at ISOL-TRAP,” CERN Courier 44:10 (Dec. 2004) 9.

A.4 Invited talks

[T9] 2008-09-18 “Cold antiprotons by indirect laser cooling.” 9th International Conferenceon Low-Energy Antiproton Physics, Vienna, Austria, 16–19 September 2008.

[T8] 2008-02-20 “Production of cold antihydrogen for precision studies.” 1st InternationalWorkshop on Cold Antimatter Plasmas and Application to Fundamental Physics, Oki-nawa, Japan, 20–22 February 2008.

[T7] 2007-08-02 “Antimatter gravity measurement with an antihydrogen beam.” 14th Inter-national Workshop on Low-Energy Positron and Positronium Physics, Reading, UK,1–4 August 2007.

[T6] 2007-03-20 “Antihydrogen studies with ATHENA.” DPG-Fruhjahrstagung, Dusseldorf,Germany, 19–23 March 2007.

[T5] 2004-08-04 “ATHENA – First production of cold antihydrogen and beyond.” 3rd Meet-ing on CPT and Lorentz Symmetry, Bloomington (Indiana), USA, 4–7 August 2004.

45

[T4] 2004-07-22 “Recent results from ATHENA.” Seminar uber Teilchenphysik, UniversitatBonn, Germany.

[T3] 2004-06-09 “Production and detection of cold antihydrogen with ATHENA.” Graduier-tenkolleg: Eichtheorien – Experimentelle Tests und theoretische Grundlagen, Univer-sitat Mainz, Germany.

[T2] 2004-02-25 “Recent results from ATHENA.” 39es Rencontres de Moriond: ElectroweakInteractions and Unified Theories, La Thuile, Italy, 21–28 March 2004.

[T1] 2001-04-06 “High-precision mass measurements of short-lived nuclides.” 7th EuropeanConference on Atomic and Molecular Physics, Berlin, Germany, 2–6 April 2001.

47

B Selection of most important publications

b

e positronFormationduction is

Physics Letters B 583 (2004) 59–67

www.elsevier.com/locate/physlet

Antihydrogen production temperature dependence

ATHENA Collaboration

M. Amorettia, C. Amslerb, G. Bazzanoc, G. Bonomid,∗, A. Bouchtad, P.D. Bowee,C. Canalia,f , C. Carraroa,f , C.L. Cesarg, M. Charltone, M. Doserd, A. Fontanac,h,

M.C. Fujiwarai,j , R. Funakoshij, P. Genovac,h, J.S. Hangstk, R.S. Hayanoj, I. Johnsonb,L.V. Jørgensene, A. Kellerbauerd, V. Lagomarsinoa,f , R. Landuad, E. Lodi Rizzinic,l ,

M. Macría, N. Madsenb,k, G. Manuzioa,f , M. Marchesottid, D. Mitcharde, F. Ottonec,h,H. Pruysb, C. Regenfusb, P. Riedlerd, A. Rotondic,h, G. Testeraa, A. Variolaa,

L. Venturellic,l , Y. Yamazakii, D.P. van der Werfe, N. Zurloc,l

a Istituto Nazionale di Fisica Nucleare, Sezione di Genova, 16146 Genova, Italyb Physik-Institut, University of Zurich, CH-8057 Zürich, Switzerland

c Istituto Nazionale di Fisica Nucleare, Sezione di Pavia, 27100 Pavia, Italyd EP Division, CERN, CH-1211 Geneva 23, Switzerland

e Department of Physics, University of Wales Swansea, Swansea SA2 8PP, UKf Dipartimento di Fisica, Università di Genova, 16146 Genova, Italy

g Instituto de Fisica, Universidade Federal do Rio de Janeiro, Rio de Janeiro 21945-970, Brazilh Dipartimento di Fisica Nucleare e Teorica, Università di Pavia, 27100 Pavia, Italy

i Atomic Physics Laboratory, RIKEN, Saitama 351-0198, Japanj Department of Physics, University of Tokyo, Tokyo 113-0033, Japan

k Department of Physics and Astronomy, University of Aarhus, DK-8000 Aarhus C, Denmarkl Dipartimento di Chimica e Fisica per l’Ingegneria e per i Materiali, Università di Brescia, 25123 Brescia, Italy

Received 19 November 2003; accepted 7 January 2004

Editor: W.-D. Schlatter

Abstract

Cold antihydrogen atoms were produced by mixing cold samples of antiprotons and positrons. The temperature of thplasma was increased by controlled radio-frequency (RF) heating, and the antihydrogen production was measured.is observed to decrease with increased temperature but a simple power law scaling is not observed. Significant prostill present at room temperature. 2004 Published by Elsevier B.V.

PACS: 36.10.-k; 52.70.-m

Keywords: Antihydrogen; Recombination; Nested trap; Positron plasma; Antiprotons

* Corresponding author.E-mail address: germano.bonomi@cern.ch (G. Bonomi).

0370-2693/$ – see front matter 2004 Published by Elsevier B.V.doi:10.1016/j.physletb.2004.01.009

60 ATHENA Collaboration / Physics Letters B 583 (2004) 59–67

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1. Introduction

Cold antihydrogen(H) atoms have recently beeproduced by two experiments at CERN. First ATHNA [1] and then ATRAP [2] reported the creatioof samples of cold antihydrogen by mixing antiprtons (p’s) and positrons (e+’s) at low temperature ina nested Penning trap [3]. Under these conditionstwo main processes [4] expected to be importantH formation are radiative combination and three bocombination [5–7]. The two mechanisms lead to dferent quantum state populations of the antiatoms,have different dependence on the positron plasmasity and temperature. Important insights into the fmation mechanism and state distribution can therebe obtained by studying the temperature dependeof the production of antihydrogen. A better knowledof the state distribution, and how to influence it,needed in order to prepare states that can be traand studied. For instance, precision spectroscopantihydrogen promises high precision CPT tests buing on accurate hydrogen spectroscopy [8,9]. InLetter we present the first studies of the temperadependence of antihydrogen production.

2. Antihydrogen production

2.1. Overview

The ATHENA experiment uses antiprotons delered by CERN’s Antiproton Decelerator (AD) anpositrons emitted from a22Na radioactive sourc(1.4× 109 Bq). Both thep’s and thee+’s are trappedcooled and accumulated prior to mixing in a nesPenning trap. This trap configuration allows simulneous trapping of oppositely charged particles. T3 Tesla solenoidal magnetic field which providesradial confinement also allows positrons to cool eciently (with a time constantτ � 0.5 s) to the trap temperature by the emission of synchrotron radiation [1The trap is kept at a temperature of∼ 15 K and themixing region at a pressure of less than 10−12 mbar.In a “standard mixing cycle” the central part of thnested trap is filled with about 7× 107 e+’s. Once thepositrons have self-cooled, about 104 p’s are injectedat about 30 eV and the two particle species allowto interact for about 3 minutes. At the end of the m

ing cycle the nested trap is emptied and the procrestarted.

Neutral H atoms escape the confinement regand annihilate on the trap electrodes producingaverage about five pions (charged and neutral) fthe p annihilation, and two 511 keVγ ’s from thee+annihilation (the 3γ contribution to ourH signal doesnot exceed 5% [11]). The nested trap is surroundea detector that allows reconstruction ofH annihilations[12]. Charged particles are detected by two layof double sided silicon micro-strip detectors. Treconstruction efficiency forp annihilation verticesis about 50%. Photons from positron annihilatioare detected by CsI crystals with an efficiencyabout 20% per photon. Their energy is also measuwith a resolution of 24% (FWHM). Detector readois triggered when at least three sides in the ousilicon modules are hit. Our trigger efficiency fp(H) annihilations is 85± 10% and this value habeen used to correct all the data presented here.detector intrinsic trigger dead time, in absence of rout, is about 2 µs. At the beginning of readoutdetector trigger is masked for 300 µs to avoid digcross talk. This is therefore our maximum trigger detime which is negligible given a maximum rate400 Hz. However, the complete readout of the detetakes about 10 ms and high event rates may leasaturation of the readout. This effect was monitoand corrected for. More details about the experimesetup and the data acquisition system can be foelsewhere [13].

2.2. Positron plasma temperature

Synchrotron cooling of positrons and the inteparticle Coulomb collisions are expected, in thesence of externally applied perturbations, to bringplasma into thermal equilibrium with the surroundielectrodes, which have a temperature of∼ 15 K. Inequilibrium the positron plasma rotates semi-rigidaround the magnetic field axis. Theoretical mod[10,14,15] and experimental studies [16] indicate tthe positron velocity distribution in the rotating reerence frame is Maxwellian with a thermal equilibrtion rate of a few tens of kHz [17]. The antiprotons acooled by the positrons through Coulomb collisio[18–20] in tens of ms. For heated positrons, the coing time is somewhat slower (< 1 s). At thermal equi-

ATHENA Collaboration / Physics Letters B 583 (2004) 59–67 61

ext forvals from

al and

Table 1Summary of the results of measurements with different positron plasma temperatures.T is the temperature increase. “p’s” is the total numberof antiprotons used in the mixing cycles. The “cos(θγ γ ) excess” is the opening angle excess and “peak” is the peak trigger rate (see tdetails). These quantities are available only for the high statistics samples. The integrated number of triggers for different time interthe start of mixing cycle are also reported. All the values were normalized to a standard cycle with 104 p’s. The errors inT represent themaximum systematic uncertainty. The errors in cos(θγ γ ), peak trigger rate, and number of triggers are each the combination of statisticsystematic errors

T (meV) p’s cos(θγ γ ) excess Peak (Hz) Triggers

3 s 180 s

0 (2.94 ± 0.21)×106 1.65± 0.19 454±44 441±40 2612±2403+15−3 (3.46 ± 0.25)×104 – – 395±38 2409±222

7+15−7 (4.08 ± 0.29)×104 – – 338±32 2233±206

15± 15 (1.82 ± 0.13)×106 1.08± 0.15 381±38 352±32 1981±18125± 15 (3.13 ± 0.22)×104 – – 214±22 1683±15643± 17 (1.52 ± 0.11)×106 0.65± 0.11 140±16 167±15 1388±127

121± 19 (3.22 ± 0.23)×104 – – 73±8 1003±94306± 30 (1.06 ± 0.08)×106 0.04± 0.01 22±5 33±3 827±76

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librium, due to the mass difference, the relative velity between thee+’s and thep’s is predominantly dueto the positron plasma temperature.

The positron plasma was characterized by a typlength of 32 mm, radius of 2.5 mm, particle numb7 × 107, number density 1.7× 108 cm−3 and storagetime of thousands of seconds. These quantities hbeen measured using a nondestructive plasma mdiagnostic method based on the observation offirst two axial modes of a finite temperature plas[21,22]. The reproducibility of the results, over seveweeks and under different conditions, was goMaximum variations in density of about 30% weobserved.

During mixing the positron plasma temperatucould be changed in a controlled way by RF exction of the axial dipole mode of the plasma. Heatiwas achieved by the application of a radio frequedrive to one of the electrodes with a 2 MHz span acrthe dipole mode resonance (typically around 20 MHat a sweeping frequency of 1 kHz. Excitation at tdipole mode ensures that the plasma reachesmal equilibrium rapidly [17]. A measured shift in thquadrupole frequency was used to calculate the mnitude of the temperature change with a reasonuncertainty [21,22]. The minimum measurable teperature increase was about 15 meV (� 175 K). Notethat the modes diagnostic yields only relative tempature changes and not the absolute temperature opositron plasma. The electrode temperature of 15

s

-

thus the lower limit for the unheated plasma tempature, and we adopt this as our unperturbed tempture.

Mixing of positrons and antiprotons was carriout for different positron plasma temperatures (ble 1). Four samples contained enough data to aa detailed analysis of antihydrogen production, asscribed in [1]. This set includes the so-called “comixing” where no heating was applied, as well as thsamples withT = 15± 15 meV (� 175 K), T =43± 17 meV (� 500 K) andT = 306± 30 meV(� 3500 K, “hot mixing” sample).

For the two samples in Table 1 with a temperatincrease lower than our resolution of 15 meV, a lincorrelation between the applied heating voltagethe temperature increase was assumed. A quadratihaviour, possible in this regime of low heating powwould result in very similarT ’s, the differences being well within the uncertainties associated to thetemperatures.

2.3. Antihydrogen signal

For clarification it should be stressed that in tfollowing antihydrogen production refers only to atiatoms that annihilate on the walls of the chargparticle trap within the detector volume. The dettor solid angle coverage forH emerging isotropicallyfrom the trap center and annihilating at the electrois estimated to be∼ 98% by Monte Carlo calculation

62 ATHENA Collaboration / Physics Letters B 583 (2004) 59–67

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-

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Antihydrogen formation was previously [1] demostrated by full reconstruction of the simultaneousnihilation of thep ande+. After the determination othe position of thep annihilation vertex, we search foclean evidence ofe+ annihilation 511 keV photons ithe CsI crystal data. A charged particle track interceing a crystal eliminates that crystal and its eight neest neighbors from consideration. For each of themaining crystals we require an energy deposit in511 keV window and no deposit in any of the adjacones. We select only those events which have atex and two crystals passing these criteria. The “oping angle”(θγ γ ) is the angle, as seen from the annilation vertex, between these two crystals. An ideaHevent will have an opening angle of 180◦, correspond-ing to cos(θγ γ ) = −1. H annihilations may also produce events with cosθγ γ > −1, since the 511 keVγ ’sfrom the positron annihilation may be undetected areplaced by low energyγ ’s. These backgroundγ ’s aregenerated in electromagnetic showers created byenergyγ ’s coming from neutral pion decay. Such paof photons have no angular correlation with thetiproton vertex. This is confirmed by the opening agle distribution of a Monte Carlo simulation of pureHannihilations (Fig. 1(a)).

The opening angle distributions for four diffeent temperatures are shown in Fig. 1(b)–(e). All dtributions except that for hot mixing show an ecess of events at cos(θγ γ ) = −1. The “opening an-gle excess”, defined as the number of events wcos(θγ γ ) � −0.95 exceeding the central plateau (sTable 1), is shown as a function of the temperatin Fig. 3(a). This number is proportional to the tonumber ofH atoms produced during a standard ccle.

In order to further studyH formation at variouspositron temperatures we analyze our measuremin a variety of ways that may be used as proxiesthe direct detection of the antihydrogen annihilatevent. We have shown in a previous publication [1that in cold mixing the antihydrogen annihilatioaccount for a significant fraction (∼ 65%) of thetrigger rate. Fig. 2 shows the trigger rates infirst 3 s of mixing for the four samples with higstatistics. In Table 1 the number of triggers in the tiwindows 0–3 s and 0–180 s, where 0 is the starmixing and 180 s is the maximum mixing interval areported. These values are corrected for the trig

Fig. 1. Distribution of cos(θγ γ ) for different positron plasmatemperatures. (a) Monte Carlo simulation of a pureH sample,(b)–(e) measured distributions for positron plasma temperatwith high statistics. The distributions were normalized to a standmixing cycle with 104 p’s.

efficiency. The total number of triggers during mixinas a function of the positron plasma temperaturshown, for all the samples, in Fig. 3(b). The hmixing data were interpreted as the backgroundto p-only annihilations and were subtracted from tother samples. The temperature dependence otrigger data is very similar to that of the opening anexcess. This suggests that the integrated numbetriggers, after hot mixing background subtraction

ATHENA Collaboration / Physics Letters B 583 (2004) 59–67 63

e complete

Fig. 2. Trigger rates in the first 3 seconds for 4 different positron plasma temperatures corresponding to high statistics samples. Thsamples have been scaled to a single standard mixing cycle with 104 p’s.

inin

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a good proxy for antihydrogen formation not onlycold mixing, as previously shown in [11], but alsothe heated samples described here.

We have also looked at the “peak trigger radefined as the maximum value of the detector trigrate after the start of mixing, excluding the fir20 ms when somep’s can be lost immediately upothe injection into the nested trap. Note that for tsamples where antihydrogen production (Fig. 2)present a dramatic increase in the rate of annihilatis observed when antiprotons are injected intopositron plasma. A more detailed discussion ofantihydrogen formation time dependence is beythe scope of this Letter, but we note that the deca

the trigger signal in time is not due only to depletiof the antiproton sample due toH production. Spatiadecoupling of the two particle clouds also plays a roThe peak trigger rate as a function of the plastemperature is shown in Fig. 3(c) and the valucorrected for the trigger efficiency, are reportedTable 1. We have previously shown [11] that integraover the first second of mixing, more than 85%the triggers are due toH production. We expect thipercentage to be even higher for the peak trigrate. If we use the hot mixing as a background (Table 1) we can estimate this fraction to be arou95%, corresponding to an absolute instantaneouHrate of 432± 44 Hz.

64 ATHENA Collaboration / Physics Letters B 583 (2004) 59–67

Theyngle excessnot

Fig. 3. Temperature dependence ofH production using different variables. All the quantities are normalized to the cold mixing sample.are displayed as a function of the absolute positron plasma temperature assuming a cold mixing temperature of 15 K. (a) Opening afor the high statistics samples, (b) number of triggers for all the samples (thehot mixing sample has been used as background, thus it isshown), (c) peak trigger rate for the high statistics samples.

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3. Discussion

As indicated earlier, two processes have trationally been expected to be relevant for formatof H during mixing of p’s ande+’s. In the radiativeprocess, a photon carries away the excess momtum and energy, and the formed atoms are stronbound with typical principal quantum numbersn < 10(Eb > 136 meV). In zero magnetic field the rate fthis process is expected to scale approximatelyT −0.63 [7]. In the three-body process, an additionpositron carries away excess momentum and eneFormation by this mechanism leads initially to weakbound states withEb ∼ kBT (1.3 meV at 15 K),

-

that are easily ionized by collisions in the positrplasma. Some of these atoms will collisionally dexcite and become more tightly bound. The expectemperature dependence in an infinite positron plais T −9/2 for formation of states that are resilient to rionization [23]. The threshold, also called the “bottneck”, below which atoms will survive collisional ionization isEth

b ∼ 4kBT (5.2 meV at 15 K) [23].We must first note that the three curves in Fig

contain slightly different information. The openinangle excess is a definitive measurement of the tintegrated antihydrogen production for the 180mixing cycle. The same is true of the total numbof triggers after background subtraction. Both

ATHENA Collaboration / Physics Letters B 583 (2004) 59–67 65

uchs,

s ofrateiontheest

(c)-ev

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these integrated plots are sensitive to effects sas spatial decoupling of the two particle cloudand in that sense cannot be used as indicationinstantaneous combination rate. The peak triggeris thus a “cleaner” measurement of the combinatrate, reflecting the conditions of best overlap attime when we believe that the antiprotons are closto thermal equilibrium with the positrons.

We thus examine the peak trigger rates in Fig. 3for compatibility with the predictions for the two production mechanisms. Several general features areident. First, the antihydrogen production is observto decrease with increased positron plasma tempture, as expected. (This effect was used in previwork to suppress the antihydrogen formation [1].) Iinteresting to note that antihydrogen is clearly presfor room temperature positrons. The second mainture is that the formation does not scale as a sple power law with the positron temperature. Theis a clear turnover of the rate at low temperatuFurthermore, all attempts to fit the data with comnations of power laws, e.g., representing a mixtof two- and three-body processes, are unsuccesThe presence of the latter is expected to be mostnounced at temperatures below∼ 10 meV (� 100 K)[24]; the lower temperature data are however chaterized by a leveling-off, rather than an increase. Tnaive scaling for the three-body reaction,T −9/2, isclearly inconsistent with our data. It should be nothat collisional relaxation and finite transit time of tantiprotons through the positron plasma can leada different temperature scaling for the three-bodyaction [7,25,26].

We have also considered whether the radiareaction is the dominant process. The agreementhis model is reasonable, at least as far as the scawith temperature is concerned. Even though a simpower law is not able to fully reproduce the behavioof our data a best-fit power law to the peak triggrate curve (Fig. 3(c)) yields a dependence ofT −0.7±0.2

(compared toT −0.63 in [7]). We next consider a simplestimate of the absolute magnitude for the radiaprocess. Using the radiative combination cross secσrad given in [5,27], summed over all the Rydbestates able to survive the field ionization and assuma Maxwellian distribution for the positron plasmthe radiative combination rateRrad can be expresseas [24]

-

.

Rrad= Npne+[

m

2πkBT

]3/2

(1)×∫

vσrad(v)e−mv2/2kBT d3v,

where m is the reduced mass,v is the modulus ofthe relative velocity betweenp’s ande+’s, Np the to-tal number ofp, ne+ the positron plasma density and3v = 4πv2 dv in the case of pure isotropy. Followinour simple assumptions, the peak trigger rate shobe comparable toRrad. Given a temperature of 15 Kand assuming complete overlap between the twoticle clouds, we calculated an antihydrogen prodtion rate due to radiative combination in the ATHENconditions of about 40 Hz for 10 000p’s and 1.7 ×108 cm−3 positron plasma density. If we compare thvalue with our measured value of 432± 44 Hz weclearly see that the experimental result is one orof magnitude higher. In other words the absolute msured production rate is not obviously compatible wa simple radiative calculation. Note that any posseffects of the magnetic field are not taken into accoin the simple calculation above.

The dynamics of the antihydrogen formation atransport to the walls is intricate. In addition to tprocesses mentioned above, radiative and three-combination into well-defined quantum states,particles in a strong magnetic field may also foweakly bound, “guiding center” atoms [23]. Anweakly-bound antihydrogen atoms formed mayionized by collisions in the plasma or by the electfields of the trap or the positron plasma itself. Tatoms formed in an excited state will tend to dectowards the ground state and become stabilized agionization. The detectable antihydrogen flux is thdetermined by the competition of the formation/decchain with the ionization processes.

For all of our detection schemes, the antihydgen atoms must drift to the wall and annihilate theThe antiatoms must pass the combined fieldsthe positron plasma and the nested trap withouting ionized. Roughly speaking, loosely bound atowill be ionized by electric fields greater thanF =(Eb/0.38 meV)2 [28], whereEb is their binding en-ergy in meV andF is expressed in V cm−1. Thepeak electric field may be calculated from the positplasma measurements and the known electrode couration, and lies between 40 and 60 V cm−1 depending

66 ATHENA Collaboration / Physics Letters B 583 (2004) 59–67

tus

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thefirstuc-een

fiten-dlowwionm-on,ug-om-icerv-ess-er

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on the drift direction of the antiatom. In our apparathe escaping atoms must thus haveEb > 2.4 meV tobe able to reach the wall.

The turnover in the production rate at low tempeture is not yet understood. There is a minimum velity scale associated with the positron plasma rotatbut this velocity is radius-dependent and even the mimum (about 104 m s−1) is too small to explain the position of the observed turnover. This turnover mayassociated with the complex equilibrium between fmation and ionization processes, although experimtal uncertainty in the measured temperature chamay also be important.

4. Conclusions

Summarizing, the temperature dependence ofantihydrogen production has been studied for thetime. A clear decrease of the antihydrogen prodtion with the positron plasma temperature has bseen, but a simple power law scaling does notthe data. The naive three-body temperature depdence(T −9/2) is not consistent with our data anthe expected predominance of this mechanism be∼ 100 K is not supported by the leveling-off at lotemperatures. The fall-off in antihydrogen productis slow enough that it is still measurable at room teperature in the ATHENA apparatus. This observaticoupled with the behavior at high temperature, sgests that the radiative mechanism cannot be cpletely excluded in ATHENA, leading to antiatomstates that are more tightly bound than those obsable using field ionization techniques. Neverthelthe radiativeH production rate prediction is not obviously compatible with our measurement, the formbeing an order of magnitude lower.

Theoretical guidance is necessary for further prress in understanding the complex interplay of pduction and ionization processes in ATHENA. Teffect of the magnetic field, the polarization of tpositron plasma by the injected antiprotons, androle of guiding center atoms need to be considein detail in order to fill in the picture. Simulation othe dynamics of antiproton slowing and combinatprocesses is certainly needed for the conditions ofexperiment. Simulations are in progress that sugthat the finite transit time of the antiprotons throu

the positron plasma plays an important role for thbody processes [26]. The experimental challengesemerge from our study include precise determinaof the positron temperature and density, determinaof the spatial overlap of the positron and antiproclouds, and analysis of the detailed time-dependdynamics of the positron–antiproton interaction. Tcurrent inability to diagnose tightly bound statesalso a barrier to understanding, highlighting the deability of studying laser interactions with antiatomsthe earliest possible time.

The unique positron plasma diagnostics and ctrol developed for ATHENA have made measuremeof antihydrogen production as a function of positrplasma temperature possible. The detection menism employed in ATHENA also offers a first look inthe dynamical time development of the combinatprocess. The promise of understanding and, perhmore importantly, controlling this complex procewith a view towards trapping of neutral antihydrogis now within experimental reach.

Acknowledgements

This work was supported by the following agecies: Istituto Nazionale di Fisica Nucleare (ItalyConselho Nacional de Pesquisa e Desenvolvime(CNPq), Fundacao de Amparo a Pesquisa do Esdo Rio de Janeiro (FAPERJ) e Fundacao CCMN/UF(Brazil), Grant-in-Aid for Creative Basic Researof Monbukagakusho (Japan), the Swiss National Sence Foundation, the Danish Natural Science ReseCouncil, the UK Engineering and Physical ScienResearch Council.

References

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b

alt types ofproduction.K, where

Physics Letters B 590 (2004) 133–142

www.elsevier.com/locate/physlet

Dynamics of antiproton cooling in a positron plasma duringantihydrogen formation

ATHENA Collaboration

M. Amorettia, C. Amslerb, G. Bonomic, A. Bouchtac, P.D. Bowed, C. Carraroa,e,C.L. Cesarf, M. Charltond, M. Doserc, V. Filippini g,h, A. Fontanag,h, M.C. Fujiwarai,

R. Funakoshij, P. Genovag,h, J.S. Hangstk, R.S. Hayanoj, L.V. Jørgensend,A. Kellerbauerc, V. Lagomarsinoa,e, R. Landuac, D. Lindelofb, E. Lodi Rizzinil,

M. Macría, N. Madsenk, G. Manuzioa,e, P. Montagnag,h, H. Pruysb, C. Regenfusb,A. Rotondig,h, G. Testeraa, A. Variolaa,∗, L. Venturellil , D.P. van der Werfd,

Y. Yamazakii

a Istituto Nazionale di Fisica Nucleare, Sezione di Genova, 16146 Genova, Italyb Physik-Institut, University of Zurich, 8057 Zürich, Switzerlandc Department of Physics, CERN, 1211 Geneva 23, Switzerland

d Department of Physics, University of Wales Swansea, Swansea SA2 8PP, UKe Dipartimento di Fisica, Università di Genova, 16146 Genova, Italy

f Instituto de Fisica, Universidade Federal do Rio de Janeiro, Rio de Janeiro 21945-970, Brazilg Istituto Nazionale di Fisica Nucleare, Sezione di Pavia, 27100 Pavia, Italy

h Dipartimento di Fisica Nucleare e Teorica, Università di Pavia, 27100 Pavia, Italyi Atomic Physics Laboratory, RIKEN, Saitama 351-0198, Japan

j Department of Physics, University of Tokyo, Tokyo 113-0033, Japank Department of Physics and Astronomy, University of Aarhus, 8000 Aarhus C, Denmark

l Dipartimento di Chimica e Fisica per l’Ingegneria e per i Materiali, Università di Brescia, 25123 Brescia, Italy

Received 27 February 2004; accepted 23 March 2004

Available online 6 May 2004

Editor: W.-D. Schlatter

Abstract

We demonstrate cooling of 104 antiprotons in a dense, cold plasma of∼108 positrons, confined in a nested cylindricPenning trap at about 15 K. The time evolution of the cooling process has been studied in detail, and several distincbehavior identified. We propose explanations for these observations and discuss the consequences for antihydrogenWe contrast these results with observations of interactions between antiprotons and “hot” positrons at about 3000antihydrogen production is strongly suppressed. 2004 Elsevier B.V. All rights reserved.

PACS: 52.40.Mj; 36.10.-k; 52.20.Hv; 52.27.Jt

0370-2693/$ – see front matter 2004 Elsevier B.V. All rights reserved.doi:10.1016/j.physletb.2004.03.073

134 ATHENA Collaboration / Physics Letters B 590 (2004) 133–142

Keywords: Antihydrogen; Cooling; Nested trap; Positron plasma; Antiprotons

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1. Introduction

In 2002 ATHENA Collaboration announced thfirst production and detection of antihydrogen atoat cryogenic temperature[1]. Another experiment subsequently reported observing antihydrogen[2]. Theseresults open the door to fundamental investigationthe properties of neutral, antiatomic matter. Specscopic comparisons of hydrogen and antihydrogenprovide sensitive tests of CPT symmetry, and the fiinvestigation of the behavior of antimatter in a gratational field can be contemplated.

In ATHENA antihydrogen is produced by mixingcloud of antiprotons with a positron plasma in an eltromagnetic trap. The expected reaction mechanismfavor low relative velocities, the rates for the radtive and three-body processes varying asT −0.63 andT −4.5, respectively[3]. Since at thermal equilibriumthe velocity scales as the square root of the masgood approximation is to considerT as the positronplasma temperature. To obtain low relative antiprotonand positron velocities, we exploit the low mass oflatter. In a high magnetic field, positrons rapidly loenergy by synchrotron radiation and come into therequilibrium with the surroundings. The cooling timconstant in the 3 T field in ATHENA is about 0.5the ambient temperature is about 15 K. Antiprotocan then be sympathetically cooled by the positronthe two clouds of particles are permitted to interact

Here we demonstrate cooling of “slow” (∼30 eV)antiprotons by a dense, spheroidal cloud of positroThe cooling is monitored for various interaction timby destructive measurements of the energy distribuof the remaining antiprotons. The result is a complrecord of the cooling process that provides a mcomprehensive description than has hitherto beeavailable[2,4,5]. Furthermore, we are able to correlathe evolution of the cooling process with that of ttrigger rate of our unique antihydrogen annihilatidetector [6]. This establishes, for the first time,link between antiproton cooling dynamics in a nes

* Corresponding author.E-mail address: alessandro.variola@cern.ch (A. Variola).

potential configuration and the production of coantihydrogen.

It is also important to note that, although tantiproton numbers are similar, the ratio of positroto antiprotons is about 104 in the current experimencompared to about 60 in the earlier work[4]. Thus,forces due to the space charge of the positron cloare important to the dynamics of the cooling, athe time scales involved are very different from thoobserved previously[2,4].

2. Antihydrogen production

The ATHENA antihydrogen apparatus[7] consistsof four parts: a positron accumulator, an antiprocatching trap, a mixing trap and an antihydrogdetector. In the positron accumulator[9] about 1.5 ×108 positrons are accumulated in cycles of roug5 minutes. They are then transferred to the mixtrap with an efficiency of about 50%; here thcool by synchrotron radiation in the 3 T field. Thresult is a high density (1–2× 108 cm−3) spheroidalpositron plasma with a length of about 30 mm andiameter that can vary from∼4–8 mm. The averagpositron plasma characteristics measured duringcooling measurements using a plasma mode anatechnique[10,11] were: radius,r ∼ 2.8 mm, density,n ∼ 1.1× 108 cm−3 and aspect ratioα ∼ 5.5.

The catching trap is a Penning–Malmberg trapwhich antiprotons, supplied by the CERN antiprotdecelerator (AD)[12], are trapped and then cooledCoulomb collisions in an electron cloud. Antiprotonstogether with the electrons, are subsequently traferred to the adjacent mixing region, and the electronremoved by applying fast, pulsed electric fields. Aresult about 104 antiprotons are available for mixinwith the positrons[1].

2.1. The nested trap, mixing antiprotons withpositrons

The technique used to mix the antiproton apositron clouds is based on the so-called nested

ATHENA Collaboration / Physics Letters B 590 (2004) 133–142 135

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Fig. 1. (a) Potential energy diagrams for antiprotons on the axof the nested trap are illustrated both with (solid line) and with(dashed line) positrons. The energy regions I to III described intext are indicated. (b) Potential energy diagrams at different rad

tential configuration[13], which permits simultaneous axial confinement of oppositely charged partic(Fig. 1(a)). In the ATHENA nested trap, cold positronare confined in the region that constitutes the ctral well. Note that the positron space charge effectively flattens the on-axis potential in the mixing rgion [14]. The space charge potential has been calated using the positron plasma parameters giventhe mode analysis measurements. For the purposdiscussion we will take this flattened level to be tzero of antiproton energy. Antiprotons with negatenergies are axially separated from the positron cland cannot recombine. It is important to stress tthe zero energy level is dependent on the appliedspace charge potentials and varies across the radithe trap. This radial dependence has been calculand is illustrated inFig. 1(b)where the nested potential configurations for different radii are shown. In thfollowing we consider mainly the longitudinal motioreferring to the on-axis antiprotons; the effects of th

f

f

radial distribution and off-axis potential variations wbe pointed out when they play a role in the analysis

To initiate antihydrogen production, a bunchantiprotons is injected into the mixing trap at∼30 eV(arrow in Fig. 1(a)). When the positron plasmain thermal equilibrium with the environment we cathis procedure “cold mixing”. In ATHENA it is alsopossible to control the positron plasma temperaduring the mixing by exciting its axial dipole modresonance (at around 20 MHz)[11]. A radio-frequencydrive with a 2 MHz span across the dipole modea sweeping frequency of∼1 kHz was applied. Theresulting shift in the quadrupole frequency providethe magnitude of the plasma temperature chaWhen antiprotons are injected into a positron plasheated to∼3000 K, the cycle is termed as “homixing”.

3. Antiproton cooling measurement technique

After injection the antiprotons traverse the copositron cloud and lose energy through Coulocollisions. To measure the energy spectrum ofantiprotons the confining potential is reduced in stand the annihilation of the released antiprotonsrecorded at each step.Fig. 2 shows the sequenceemployed; the delay between the different potenconfigurations is∼100 µs and the duration of evestep is∼50 µs. The energy resolution is determinby the step size of the confining potential and isthe order of a few eV, depending on the detaipotential configuration of each step. The chargpions produced by antiproton annihilation are counby means of a scintillator system read by phomultipliers. The read out system has a dual puresolution of∼50 ns. The signals are then recordwith a multi-scaler module which links the delaythe dump with the antiproton energy in the nested tr

The antiproton dump takes place in two diffeent stages, namely a left well dump (LWD, sFig. 2(a)) and a subsequent right well dump (RWseeFig. 2(b)). In the LWD, all antiprotons with positive energies as well as those in the left well with neative energies are released sequentially. In the RWonly those antiprotons in the right well with negatienergies are released. The positrons are also releduring the RWD. The above-mentioned procedure

136 ATHENA Collaboration / Physics Letters B 590 (2004) 133–142

thethe

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naly

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Fig. 2. Schematic of the different on-axis potentials making uptwo ramps used for the dump. The antiprotons dumped duringfirst ramp are indicated in grey, the ones dumped during the seone are represented in white. For clarity, only every other step oramp is shown.

lows a single snapshot of the antiproton energy sptrum to be obtained. To derive the time evolutionthe antiproton energy distribution during the cooliprocess we performed series of measurements wthe particles were dumped in a controlled mannevarious pre-determined times after injection. Durithese measurements the reproducibility of the positronplasma characteristics was assured by the mode asis diagnostics.

4. Results

Fig. 3shows the results of measurements in whthe antiproton energy was measured as a functiothe interaction time during cold mixing. By integratinthe appropriate equation of motion we have takenaccount the correction to the antiproton energyto the time-varying potentials during the ramp. Th

-

Fig. 3. Antiproton energy spectra for different interaction times. Theinteraction time is shown on the left, the maximum peak height ineach distribution is indicated on the right. The vertical thick greylines divide the three energy regions. The measurements shown hereare cross-normalized using the measured AD beam intensity[8].

ATHENA Collaboration / Physics Letters B 590 (2004) 133–142 137

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effect is often referred to as “adiabatic cooling” ahere leads to a correction of no more than 10%.

As a control, a measurement was performed wout positrons in the central well (labelled as “noe+”in Fig. 3); the antiprotons were dumped after∼180 s,which is the standard antiproton–positron mixing timduring antihydrogen production runs. Note that allthe antiprotons are released during the LWD, theymain at the injection energy and the RWD is empty:cooling is observed. This confirms that our procedfor removal of the cooling electrons, outlined abois effective. We observe that antiproton cooling to thebottom of the lateral wells only occurs in the presenof electrons, and should not be mistaken for positcooling.

The remaining spectra inFig. 3 show the energydistributions for different interaction times. Thobelow the curve representing the nested well apotential show the results of the LWD; those abovthe RWD.

In general, a redistribution of antiprotons frothe injection energy to lower energies is a cleindication that cooling takes place. Qualitatively, tdata separate into three distinct energy ranges: I,injection and cooling region at about 15–40 eV, II,intermediate region between 0 and∼15 eV, and III,the negative energy region of the two lateral wells. Tborder between region I and II is chosen in a way tradial effects due to off-axis potential variations cbe taken into account; under experimental conditionthis assures that all the antiprotons that are in therequilibrium with the positron plasma but not on ttrap axis are included in region II (seeFig. 1(b)).

In our simplified picture the dynamics can thbe discussed in terms of the redistribution of pacles between these regions. To do this quantitativwe determine the fraction of antiprotons remainingeach energy region as a function of interaction tifor the “cold” and the “hot” mixing cycles (Fig. 4(a)and (c)respectively: note the logarithmic time scalWe stress that this is only a cooling process diagntic. Since the normalization is done with respect tototal number of remaining antiprotons all the informtion on the antiprotons not present in the dump, dto losses or antihydrogen production, are lost in tanalysis. The correlation between the different coing phases and antihydrogen production is establisby examining the background-corrected trigger r

Fig. 4. (a) Fraction of remaining antiprotons in each energy raas a function of the interaction time for cold mixing. (b) Detectrigger rate for a standard cold mixing cycle (background correctedas a function of time. The inset shows an expansion of time betw0 and 0.2 seconds illustrating the onset of antihydrogen producat ∼20 ms. (c) Same analysis as in (a) for a∼3000 K positronplasma. The lines are to guide the eye. The vertical dottedindicate the three time intervals discussed in the text.

of the annihilation detector against interaction tim(Fig. 4(b)). Our analysis has shown the trigger ratebe a good proxy for antihydrogen production and ssequent annihilation[15]. Furthermore, it was showthat on average around 65% of the cold mixing cytrigger rate is due to antihydrogen formation withpeak of the production in the first second where, itrigger rate signal greater than 300 Hz,∼85% is iden-tified as antihydrogen. We estimate that about 15%

138 ATHENA Collaboration / Physics Letters B 590 (2004) 133–142

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the injected antiprotons are converted into antihydgen atoms that can escape the potentials and betected by the detector[15]. The background is consttuted by antiprotons annihilating on residual gas mocules, with an average trigger rate of a few Hz.

Both sets of data indicate three distinct time scaof evolution. In the first stage, fort � 20 ms,Fig. 4(a)shows that about 40% of the injected antiprotonsrapidly cooled to region II with an initial cooling ratof about 2.5 keV s−1. The inset ofFig. 4(b)illustratesthat there is a much reduced antihydrogen producduring this fast cooling phase. For intermediate tim(20 ms� t � 1 s), the evolution is characterized ba loss of population in region II and a growth in tnumber of antiprotons in the lateral wells (region IIin which the antiprotons no longer have spatial ovlap with the positrons. The transition zone betweregions II and III is the energy range in which tantiprotons are near to thermal equilibrium with tpositrons and therefore have a high probability ofcombination (seeSection 4.2). The inset inFig. 4(b)shows the onset and sharp rise in antihydrogenduction between 20 and 30 ms. Finally, fort � 1 s,we note a slow feeding of antiprotons from regiointo the other energy regions, resulting in all antiptons ending up in regions II or III by aboutt = 50 s.As Fig. 3indicates, this time range is characterizedenergy loss and spreading of the remaining “hot”jected antiprotons. The time constant is very long copared to those of the previous stages. In this time raFig. 4(b)shows a decrease of the trigger rate.

We can gain some general insights from the abobservations for each stage, as follows.

4.1. Phase 1—fast cooling

The fast cooling time constant (t ∼ 10 ms) foraround 40% of the antiprotons is consistent with∼4 ms timescale that is expected for∼40 eV antipro-tons to thermalize[16,17], when taking into accounthe time spent outside the positron plasma.1 The cool-ing time is strongly dependent on the antiproton retive velocity [16,17] which explains its reduction be

1 Following their dynamics during the fast cooling by meansa numerical code, we found that the antiprotons spend∼1/3 of thetotal time inside the positron plasma.

-tween 10 and 20 ms (seeFigs. 3, 4). Once thermaequilibrium is approached the antiprotons are ablediffuse inside the positron cloud. Consequently,time spent in the plasma increases, enhancing thetihydrogen formation probability. Indeed, it is at theend of the fast cooling period that the observed ahydrogen production starts to rise rapidly and peafter some tens of ms (Fig. 4(b)). The most likely ex-planation for the fact that only∼40% of the antipro-tons participate in this initial cooling is the incompleradial overlap between the positron plasma and thetiproton cloud.

Note that in the ATHENA experimental conditionin the fast cooling process, the deposition of thetire kinetic energy of the injected antiprotons into tpositron cloud would only raise the positron tempature by about 25 K without affecting their dynamics. This was confirmed by monitoring the plasma wthe modes analysis technique[11]. In the intermediatetime range, we expect that the energy deposited inpositron plasma is removed by synchrotron radiatwithin ∼0.5 s.

4.2. Phase 2—thermal equilibrium

In Fig. 3 we observe that between 20 and 30 mthe distribution of cooled antiprotons shifts to lowenergies very close to zero and even begins to croson-axis potential characteristic of thermal equilibriubetween the positrons and antiprotons. As staearlier, this is the time at which we observe a vrapid increase in antihydrogen production (Fig. 4(b)).Fig. 4 shows that there is a corresponding decreasthe region II population in favor of region III wherthe two antiparticles are axially separated. Whthe cross-over from region II to region III depenon the exact position of this border in the left-wdump, with its inherent calibration uncertainty (∼2 Vdetermined by the dump step size), it is clear afrom the right-well dump that at around this timsome antiprotons attain negative energies and areseparated from the positrons. We suggest two poscontributing factors for this:

(1) stochastic feeding of antiprotons into the latewells due to collisions in the lateral wells thtransfer energy from the longitudinal to the radmotion;

ATHENA Collaboration / Physics Letters B 590 (2004) 133–142 139

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(2) production of axially moving weakly bound Rydberg antihydrogenatoms[2], which can be ionizedat the longitudinal extremes of the nested pottial, trapping the antiproton in the lateral wells.

If we roughly estimate the ATHENA experimental conditions for the antiprotons, i.e., densityn ∼104 cm−3, average speed∼ of a few 103 ms−1 (tak-ing into account the dynamics in the lateral wells),maximum antiproton–antiproton collision rate nvb2

(where b is the classical distance of minimum aproach) is of the order of a few Hz. This cannot explthe rapid rise of the lateral well population in the fi500 ms. Thus, one possibility is that the lateral wantiprotons arise mainly due to ionized weakly bouRydberg antihydrogen atoms. Moreover, the obsetion that these antiprotons end up with energies inarrow band just below zero, thereby coinciding wthe maximum electric fieldsfor stripping the weaklybound antihydrogen atoms, would seem to corrorate the importance of this mechanism for producaxially separated antiprotons.

That some axial separation takes place has bconfirmed by a dedicated re-injection experimentThe length of the lateral wells was adiabaticacompressed (by varying the applied potentials) athey were filled. This led to an adiabatic heating[18]of a fraction of the separated antiprotons resultingtheir re-injection into the positron plasma where thcan recombine.

The result is shown inFig. 5, where the triggerpeak corresponding to the formation of antihydrogon re-injection is evident. Detailed analysis usingATHENA vertex detector confirms the productionantihydrogen upon re-injection.

4.3. Phase 3—slow cooling

For t � 1 s, it is evident that there is cooling othe antiprotons that stillpopulate region I (radiallyseparated) with a very long time constant. This scooling phase could be due to essentially two caus

(1) The first is cooling in the tails of the radial ditribution of the positron plasma, where the rais much lower than in the plasma center. Accoing to cold fluid theory[19], the radial tails havean extent equal to the Debye length which,

Fig. 5. Trigger rate during re-injection after 40 s. The correspondinpeak is mainly due to antihydrogen production. In the inset,on-axis potentials applied to re-inject the antiprotons into thepositron plasma, are displayed (dashed lines).

the ATHENA positron plasma density and temperature conditions, is a few tenths of microThis cannot explain the large effect evidentthe experimental data. However, it is possible tcold fluid theory might not be strictly valid fothe ATHENA case of a two component plasmIf we consider centrifugal separation[20] of thepositrons and antiprotons, the ATHENA paramters correspond to the partial separation regiThis would significantly alter the tails of thpositron distribution. It should be noted thougthat centrifugal separation usually only deals wsame sign charged plasmas. Understanding odetailed dynamics of centrifugal separationoppositely charged plasmas in a nested trap pably await additional theoretical work. The effeneeded to explain the slow cooling observedour measurements does not need to be very laA density tail in the distribution of 10−3 to 10−4

over a length scale of the order of the plasmadius outside the positron plasma would be sucient.

(2) Supposing that the antiprotons radius is consein the nested trap, another source of the scooling could be a slow radial expansionthe positron plasma that gradually envelopsinitially radially separated antiprotons. This radtransport has been investigated in ATHENA.our normal experimental conditions (i.e., thopertaining to the data shown inFigs. 3 and 4),

140 ATHENA Collaboration / Physics Letters B 590 (2004) 133–142

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monitoring the positron plasma radius with tmode analysis technique[11], we observe anexpansion of roughly 0.1 mm in the first 10 s aof ∼0.25 mm in the full cycle of 180 s. It shoulbe noted that this expansion does not significaaffect the space charge potential of the positplasma.

Two other experimental observations indicate tthe slow cooling takes place on the initial radiaseparated antiprotons:

(a) Strong evidence is given by measurementsformed when the positron plasma shape wastered by applying a rotating wall electric field[21]and the antiprotons were dumped 10 ms afterjection. The rotating wall was used both in epansion and compression mode. The resultsshown inFig. 6. The peak in region II representhe antiprotons that radially overlap the positrcloud (i.e., are cooled) while region I represethe radially separated antiprotons. The peakregion II is enhanced when the positron plasis expanded while it almost disappears whenplasma is radially compressed. Furthermore, thare more than twice as many antiprotons ingion I after compression than after expansion. Tredistribution between these two regions reflectthe degree of radial overlap between the antipton cloud and the positron plasma.

(b) In Fig. 3, for long interaction times, a seconpeak is formed in region II. The energy separatbetween the zero energy level and the peak is∼5–6 eV. This is compatible (within the experimenaccuracy of∼2 V) with the 4 V that separatethe potential on axis with the one at a radius∼3 mm (seeFig. 1(b)).

Fig. 4(a)shows that the percentage of region I atiprotons decreases slowly to zero, mostly in favorthe region II, providing a slow source of new antiprtons for antihydrogen production. Looking at the dtector trigger rate, fort > 1 s, we observe antihydrogen production decaying with a time constant of ab50 s indicating a possible slow feeding of antiprototo the positron plasma. It is also important to note tin Fig. 3, the position of the region III peak right wepopulation remains stable during the whole proce

Fig. 6. Antiproton dump results for three different positron plascharacteristics: expanded(α ∼ 7), not compressed(α ∼ 20), com-pressed(α ∼ 80). The differences in the peak in region II are edent. In the first case 40% of the population is in region I and 60%region II. A substantial difference is noticed when the rotating wawas not applied: 71% of the antiprotons are in region I and only 2in region II. This behavior is enhanced by compressing the plas83% of the antiprotons are in region I and 17% in region II.

This supports the contention that other mechanismcooling (e.g., due to electrons) are absent duringmixing procedure.

4.4. Heated positron plasma

We have compared the above results to thosetained by repeating the experiment with a heated (T ∼3000 K) positron plasma (“hot mixing”).Fig. 4(c)il-lustrates the results of this measurement. The incooling is about a factor of 100 slower, the regioantiprotons declining to∼60% of the initial value inabout∼1 s. This observation is also in good agreem

ATHENA Collaboration / Physics Letters B 590 (2004) 133–142 141

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with theory[16] where the estimated cooling time∼0.4 s. There is no subsequent loss of region IItiprotons, suggesting that the positron plasma heaeffectively inhibits the recombination process. Indeewe observe that antihydrogen production is stronsuppressed under these conditions[3]. After 50 s about20% of the hot antiprotons have still not cooled.

5. Summary and discussion

In summary, we have studied positron cooliof antiprotons in a previously unexplored regimepositron number and density. Although many obsertions still have to be better understood, some genfeatures of the cooling process have been identifietheir link with antihydrogen production assessed aexplanations for the antiproton behavior suggesFor mixing with cold positrons, we observe rapid coing (t ∼ 10 ms) to energies corresponding to thmal equilibrium of the two populations. After this wnotice a rapid onset of antihydrogen production wrates exceeding 300 Hz during the first second. Olonger timescale (t > 1 s) a slower cooling processobserved, consistent with the decay of antihydroproduction characterized by a 50 s time constant.

The following conclusions can be drawn from theobservations:

• Antihydrogen production starts after the antipton population has been cooled close to therequilibrium.

• Initially only the antiprotons that radially overlawith the positron cloud are cooled and quickrecombine.

• After about 500 ms a small fraction of the atiprotons start to axially separate. These then ctribute to the lateral wells population. Re-injectioand additional recombination of antiprotons cbe obtained by squeezing the length of the laterawells (adiabatic heating).

• Those antiprotons which are initially radialseparated from the positrons cool slowly possidue to tails in the positron distribution or thslow radial expansion of the positron plasma. Tprovides a new source of antiprotons suitableantihydrogen formation.

• When the positron plasma is heated to∼3000 Kthe initial cooling is about a factor of 100 sloweand no antihydrogen production is observed.

Thus, the analysis provides a consistent picturecharged particle dynamics and production of antidrogen, including the effect of heating the positroFurther understanding of the positron–antiprotonteraction may be obtainable by numerical simution of the interaction dynamics, but crucial informtion about the antiproton radial density distributioncurrently lacking. A complete understanding of tprocesses involved would be valuable in optimizthe antihydrogen production rate and the antihydgen energy distribution. In this goal a next step mbe the study of antihydrogen production as a functof the energy of injection of the antiprotons. Alsointerest for future experiments is the dependencthe cooling dynamics on the antiproton–positron raIt is therefore important to consider the energeticspositron cooling of a much larger number of antiptons, in order to optimize their reaction rate.

Acknowledgements

This work was supported by the INFN (ItalyCNPq (Brazil), MEXT (Japan), RIKEN (Japan), SN(Switzerland), SNF (Denmark) and the EPSRC (UK

References

[1] M. Amoretti, et al., Nature (London) 419 (2002) 456.[2] G. Gabrielse, et al., Phys. Rev. Lett. 89 (2002) 213401.[3] M. Amoretti, et al., Phys. Lett. B 583 (2004) 59.[4] G. Gabrielse, et al., Phys. Lett. B 507 (2001) 1.[5] H. Higaki, et al., Phys. Rev. E 65 (2002) 046410.[6] C. Regenfus, Nucl. Instrum. Methods A 501 (2003) 65.[7] M. Amoretti, et al., Nucl. Instrum. Methods A 518 (2004) 67[8] M.C. Fujiwara, M. Marchesotti, Nucl. Instrum. Methods A 48

(2002) 162.[9] L.V. Jørgensen, et al., in: F. Anderegg, L. Schweikhard, C

Driscoll (Eds.), Nonneutral Plasma Physics IV, AIP CoProc. 606 (2002) 35.

[10] M. Amoretti, et al., Phys. Rev. Lett. 91 (2003) 055001.[11] M. Amoretti, et al., Phys. Plasmas 10 (2003) 3056.[12] S. Maury, Hyperfine Interact. 109 (1997) 43.[13] G. Gabrielse, et al., Phys. Lett. A 129 (1988) 38.[14] J.J. Bollinger, D.J. Wineland,D.H.E. Dubin, Phys. Plasmas

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[15] M. Amoretti, et al., Phys. Lett. B 578 (2004) 23.[16] L. Spitzer, Physics of Fully Ionised Gases, Interscience, N

York, 1962.[17] Y. Chang, C.A. Ordonez, Phys. Rev. E 62 (2000) 6.[18] B.R. Beck, Ph.D. Thesis, University of California, San Dieg

CA, 1990.

[19] L. Turner, Phys. Fluids 30 (1987) 3196.[20] T. O’Neil, Phys. Fluids 24 (1981) 1447.[21] X.-P. Huang, et al., Phys. Rev. Lett. 78 (1997) 875.

PRL 94, 033403 (2005) P H Y S I C A L R E V I E W L E T T E R S week ending28 JANUARY 2005

Spatial Distribution of Cold Antihydrogen Formation

N. Madsen,1 M. Amoretti,2 C. Amsler,3 G. Bonomi,4 P. D. Bowe,5 C. Carraro,2 C. L. Cesar,6 M. Charlton,5 M. Doser,4

A. Fontana,7,8 M. C. Fujiwara,9,10 R. Funakoshi,9 P. Genova,7,8 J. S. Hangst,1 R. S. Hayano,9 L. V. Jørgensen,5

A. Kellerbauer,4 V. Lagomarsino,2,11 R. Landua,4 E. Lodi-Rizzini,7,12 M. Macri,2 D. Mitchard,5 P. Montagna,7,8 H. Pruys,3

C. Regenfus,3 A. Rotondi,7,8 G. Testera,2 A. Variola,2 L. Venturelli,12 D. P. van der Werf,5 Y. Yamazaki,10 and N. Zurlo12

(ATHENA Collaboration)

1Department of Physics and Astronomy, University of Aarhus, DK-8000 Aarhus C, Denmark2Istituto Nazionale di Fisica Nucleare, Sezione di Genova, I-16146 Genova, Italy

3Physik-Institut, Zurich University, CH-8057 Zurich, Switzerland4PH Department, CERN, Geneva, Switzerland

5Department of Physics, University of Wales Swansea, Swansea SA2 8PP, United Kingdom6Instituto de Fisica, Universidade Federal do Rio de Janeiro, Rio de Janeiro 21945-970, Brazil

7Istituto Nazionale di Fisica Nucleare Sezione di Pavia, I-27100 Pavia, Italy8Dipartimento di Fisica Nucleare e Teorica, Universita di Pavia, I-27100 Pavia, Italy

9Department of Physics, University of Tokyo, Tokyo 113-0033, Japan10Atomic Physics Laboratory, RIKEN, Saitama 351-0198, Japan

11Dipartimento di Fisica di Genova, I-16146 Genova, Italy12Dipartimento di Chimica e Fisica per l’Ingegneria e per i Materiali, I-25123 Brescia, Italy

(Received 5 October 2004; published 27 January 2005)

0031-9007=

Antihydrogen is formed when antiprotons are mixed with cold positrons in a nested Penning trap. Wepresent experimental evidence, obtained using our antihydrogen annihilation detector, that the spatialdistribution of the emerging antihydrogen atoms is independent of the positron temperature and axiallyenhanced. This indicates that antihydrogen is formed before the antiprotons are in thermal equilibriumwith the positron plasma. This result has important implications for the trapping and spectroscopy ofantihydrogen.

DOI: 10.1103/PhysRevLett.94.033403 PACS numbers: 36.10.–k, 34.80.Lx, 52.20.Hv

Cold antihydrogen ( �H) formation was reported by theATHENA Collaboration [1] at the CERN Antiproton Dece-lerator [2] in September 2002. Similar results were re-ported shortly thereafter by the ATRAP Collaboration[3]. Both experiments form the �H atoms by mixing samplesof antiprotons ( �p) with positrons (e�) in a nested Penningtrap.

The spatial distribution of the emerging �H atoms cangive crucial insights into the nature and dynamics of theformation process, and by inference the distribution ofstates formed. More knowledge of the latter, and how toinfluence it, is needed in order to prepare states that can betrapped and studied. For instance, precision spectroscopyof �H building on accurate hydrogen spectroscopy [4,5]promises high precision CPT tests. In this Letter wepresent evidence, using the directly measured spatial dis-tribution, that �H is formed before the �p attain thermalequilibrium with the e�.

The ATHENA mixing trap, comprising a series ofhollow cylinders, has the axial (z) potential configurationof a nested Penning trap, which permits two plasmas ofopposite charge to come into contact [6]. A 3 T axialmagnetic field ensures transverse confinement of the par-ticles. The mixing trap is kept at �15 K. A detector for �pand e� annihilations surrounds the trap in barrel geometry.

05=94(3)=033403(4)$23.00 03340

Details of the experimental apparatus can be found inRef. [7].

Antihydrogen production is carried out by first loadingthe mixing trap with �7� 107 e�, which cool to thecryogenic temperature by the emission of synchrotronradiation, and then by injecting about 104 �p that interactthrough the Coulomb interaction with the e� plasma.When �p are mixed with cryogenic e� we refer to theprocedure as ‘‘cold’’ mixing. Alternatively, the e� plasmamay be heated by radio frequency excitation [8]. Mixingwith a plasma where the temperature (Te�) has been in-creased by 3500 K we term ‘‘hot’’ mixing.

We let the �p interact with the e� for about 180 s beforeejecting both species and restarting the cycle. A �p mayundergo one of several fates. Apart from forming �H, a �pmay annihilate on residual gas, drift to and annihilate onthe cylindrical walls, or survive until the final dump of allspecies. Neutral �H atoms drift away from the formationregion until they annihilate on the electrodes of the mixingtrap. The �H detector can observe charged particle tracks,and from these we can reconstruct the vertices of �p anni-hilations. The detector also observes the 511 keV photonsfrom the e� annihilation [1,9].

In earlier work we relied on the simultaneous annihila-tion of both �p and a e� in order to detect �H production [1].

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Detection of e� annihilations is inefficient and limits �Hdetection efficiency to less than 0.25%, whereas �p annihi-lations have about 25% chance of being detected andreconstructed. Using only �p vertices may thus significantlyenhance our detection efficiency. Recently we showed thatthe bulk of the �p annihilation events we observe duringcold mixing of �p and e� stem from �H annihilations [10].This was demonstrated by comparing the results from coldmixing with those from hot mixing, where �H production issuppressed [1]. The difference in the number of �p annihi-lations between cold and hot mixing was shown to be dueentirely to �H production.

Using the detector we can extract the spatial distributionof the observed �H annihilations. Earlier we showed that the�H distribution projected into a plane perpendicular to thetrap axis (z) is rotationally symmetric [1]. No time depen-dent change of the �H distribution during individual mixingcycles has been observed. The time resolution of changesin the �H spatial distribution is limited by statistics to�1 s.Figure 1(a) shows the z distribution of �p annihilationvertices from 305 full cold mixing cycles. The distribution

Axial Position (z) [cm]

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FIG. 1 (color online). Axial (z) vertex distributions for (a) allvertices during cold mixing (1:75� 105 vertices). (b) Axialvertex distributions for �p annihilating in a nested trap withoute� (5717 vertices). (c) Shaded area: Cold mixing with hotmixing subtracted and using a spatial cut of x > 0 and y > 0(see text) (4:9� 104 vertices). Full circles: �p annihilations withtwo back-to-back 511 keV photons during cold mixing (488events, scaled to the area under the shaded curve). Solid line:Detector response function from Monte Carlo simulations.

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has two distinct features. The first is a broad, smooth,peaked distribution. The second consists of the two smallerpeaks on either side of the distribution. We have deter-mined that the latter peaks are due to �p-only annihilationsbecause they disappear when selecting events with twoback-to-back 511 keV photons and are also present in thehot mixing distribution where �H production is negligible.

For comparison we also recorded the distribution ofannihilations when the �p were injected into a nested trapwithout e�, so that there was no �H production. Figure 1(b)shows the z distribution of annihilations from 24 mixingcycles under these circumstances. We observe the smallpeaks seen on the side of the cold mixing distribution andno broad central feature.

The �p-only annihilations in the two peaks are alsolocalized in the transverse plane. This phenomenon, whichmakes it possible to spatially separate �H annihilations from�p-only annihilations, is discussed in detail in Ref. [11]. Inthe region x > 0 and y > 0, where x and y are the horizon-tal and vertical directions, respectively, we observe no�p-only annihilations in the measurements presented here.To increase the signal to background ratio on �H data weremove �p-only annihilations by selecting only verticesfrom this region. The resulting z distribution with hotmixing subtracted is shown in Fig. 1(c). The hot mixingwas normalized to the same beam intensity as the cold. Forcomparison we also show the z distribution of �p annihila-tions that were accompanied by simultaneous back-to-back511 keV gammas from e� annihilation using the sameselection criteria as in Ref. [1]. The good agreement be-tween these two distributions means that we can use thefull cold mixing distribution with the xy cut applied and thehot mixing subtracted (the shaded distribution in Fig. 1(c)]as the distribution of �H annihilations. The detector re-sponse function, shown in Fig. 1(c), is the efficiency ofthe detector for �p annihilation events on the trap wall(electrodes). The response function was calculated byMonte Carlo by evenly distributing �p annihilations onthe trap walls and simulating the detector response [7].

Using the same method as above we have also extractedthe axial distributions for �H produced with heated samplesof e�. Figure 2 shows the axial distribution for �H annihi-lations on the walls for cold mixing [from Fig. 1(c)] and formeasurements with the e� plasma heated by 175 and500 K. There is no change in the distribution as a functionof e� temperature, although the total number of eventsvaries strongly [12]. Also shown in Fig. 2 is a simplecalculation of the z distribution resulting from isotropicemission of �H from the ellipsoidal positron plasma.

The e� plasma is typically 2.5 mm in radius (re�), is32 mm in length (le�), and has a density of ne� � 1:7�108 cm�3 [8]. The thermal velocities of 15 K e� and �p areve�

th � 1:5� 104 m s�1 and v �pth � 350 m s�1, respectively.

The space charge of the e� plasma generates a radial Efield and causes the equilibrium state of the cold plasma to

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PRL 94, 033403 (2005) P H Y S I C A L R E V I E W L E T T E R S week ending28 JANUARY 2005

be one of laminar rotational flow. With our typical plasmaparameters, the frequency of rotation is �80 kHz, corre-sponding to a surface velocity of 1:3� 103 m s�1.Temperatures are thus given in this rotating frame. A �pin the trap exhibits cyclotron rotation around the magneticfield lines with a frequency of 46 MHz. A radial electricfield causes a guiding-center E� B drift motion in theazimuthal direction, independent of charge and mass.However, the difference in mass between �p and e� causesa difference in centrifugal potential such that the �p tends toseparate outwards. For our densities and temperatures thiseffect is small and slow (separation time �1000 s [13,14])compared to the �H production rate. We thus consider theantiproton radial distribution to be static during antihydro-gen production. The �p move axially in and out of the e�

plasma as time passes. The axial oscillation frequency atinjection is �100 kHz, small compared to the cyclotronfrequency which sets the time scale for the onset of theE�B drift motion. We thus simplify the analysis byassuming that �p inside the e� plasma, where �H may beformed, rotate with the positrons. In the following, thermalequilibrium refers to a state where T �p � Te� in this rotat-ing frame.

The �pwere precooled by being embedded in an electron(e�) plasma of similar dimensions as the e� plasma. Thee� are ejected before the �p are mixed with the e�. Detailedstudies of the cooling of the �p by the e� in our apparatussuggest that the �p cloud is radially larger than the e�

plasma [15]. As the rotation velocity in the e� plasma issmall compared to ve

�

th and ve�

th � v �pth, it has negligible

influence on the �H formation rate. We therefore assumethat �H is formed homogeneously throughout the rotatingellipsoidal e� plasma. Another scenario would be forma-tion on the surface of the e� plasma only, something onecould imagine if the centrifugal separation was fast. Thisonly strengthens the arguments to follow. With these re-flections in mind we henceforth assume homogeneousformation throughout the e� plasma.

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We can model the axial distribution by randomly dis-tributing �H in a selected formation volume and assigning toeach �H a velocity from a three-dimensional Gaussianvelocity distribution characterized by transverse (T?�p ) and

axial (Tjj�p) temperatures and an azimuthal velocity given bythe radial position of the �H. We use two different tempera-tures to describe nonequilibrium conditions. The intersec-tion of the �H undisturbed path with the cylindricalelectrodes is then calculated. Then the vertex reconstruc-tion resolution of the detector (� � 4 mm) and the re-sponse function are folded onto the result. The �p, due totheir mass, dominate the momentum of the �H, and wetherefore neglect Te� in this model.

Figure 3 shows a number of calculated distributionsusing the model described above. Also shown is the mea-sured cold mixing distribution. The model does not repro-duce the observations with Tjj�p � T?�p . A longer e� plasmagives a wider distribution, but the necessary length(�60 mm) to match the observed distribution is muchlarger than that measured. If we assume T?�p � 15 K, themodel matches the observed cold mixing distribution withTjj�p � 10 2� � T?�p (solid curve in Fig. 3). This gives a

lower limit of Tjj�p � 150 K. The �p that form �H are thereforenot in thermal equilibrium with the e�. We cannot deter-mine T �p of the �p that form �H from these measurements.However, as we increase T?�p the necessary difference

between the Tjj�p and T?�p to model the observations de-creases asymptotically to a factor 2:3 0:6 (shown inFig. 3). This is because the influence of E� B rotationon the distribution decreases with increasing temperature.Thus even with no influence from E� B rotation wecannot find consistency with thermal equilibrium; i.e.,our conclusion is independent of the absolute e� tempera-ture. Comparing the model distributions we find that for

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T �p * 103 K the influence of the E� B rotation is negli-gible. If Te� < 103 K, and the �p are in thermal equilibriumwith the e�, the �H distribution should thus change when thee� are heated. We observe no change (Fig. 2) also indicat-ing that the �p forming �H are not in thermal equilibriumwith the e�.

That the �H is formed before thermal equilibrium be-tween �p and e� is achieved indicates that the formationrate of �H is high compared to the �p cooling rate. Theformation rate is expected to scale inversely with somepower of the relative velocity [12]. In the literature this rateis often given as a function of the temperature, as thermalequilibrium between the particle species is assumed.Because of the much larger mass of the �p, the relativevelocity is dominated by the e� velocity as long as T �p &

2000� Te� . For Te� � 15 K this is equivalent to T �p �

30 000 K or a �p kinetic energy of 2.6 eV. The �p injectionenergy is�15 eV. Our earlier studies of the dynamics of �pcooling during �H formation were not precise enough toresolve whether �H formation sets in at a relative energy ofless than 2.6 eV, as they resolved only the energy spread ofthe �p to the �2 eV level. [15]. In those experiments thecooling time was measured to be 10–20 ms, in goodagreement with recent theoretical estimates [16]. For com-parison, an estimate of the 3-body formation rate usingRef. [17], using 104 �p and our e� plasma parameters givesa rate of �8 kHz at a temperature of 30 K, roughlyequivalent to the relative velocities of 30 000 K �p interact-ing with 15 K e�. This rate is very high compared to thecooling rate and allows many �p to form �H at high tem-perature. Recent simulations by Robicheaux indicate that�H is formed with high axial momentum (i.e., high Tjj�p) [18].

The high production temperature found could explainthe high �H velocities measured by the ATRAPCollaboration [19]. They measured velocities equal to an�H temperature of �2� 103 K. Their method, however,measures only weakly bound �H atoms that can be fieldionized by a static electric field (�75 V cm�1).Furthermore, the �p were actively driven through a e�

plasma with many fewer e� and much lower density thanin this experiment. In the experiments presented here al-most all �H that may survive the combined electric fields ofthe trap and the e� plasma are observed [12].

If, indeed, the �H are formed before equilibrium as ourresults indicate, it could be an obstacle to the trapping of �H,and thus precision �H spectroscopy. Typical neutral trapshave depths about 1 K. If �H atoms are formed at some102 K, very few will be trapped. Lowering Te� may nothelp as formation is fast compared to the cooling. Toproduce cold �H, it is thus necessary to have cold �p beforemixing with e�. A possible solution could be to invert thecurrent mechanism for formation. That is, trap the �p in thecenter of the nested trap, possibly with some electrons to

03340

keep them cold, and then pass e� through them, reinjectingthem regularly as has already been done with �p [20].Positronium formation or axial separation of �p and e�

are both potential obstacles in this scheme. An alternativescheme that should also produce �H at or close to ambienttemperature would be to form �H by �p positronium colli-sions [21,22].

To summarize, we have studied the spatial distributionof the �H annihilations during mixing of �p and e�. We findthat the distribution of �H emerging from the formationregion is independent of the e� temperature and enhancedin the axial direction. The latter assumes homogeneousformation throughout the e� plasma, and rotation of the�p with the e�. We argue that this indicates that �H is notformed under conditions of thermal equilibrium betweenthe e� and the �p. The lower limit of the formation tem-perature is Tjj�p � 150 K and T?�p � 15 K. This result indi-cates that the nested trap scheme as currently deployed isinadequate for producing �H that may be magneticallytrapped and used for precision spectroscopy. More studiesare needed to determine to what extent this problem maybe circumvented.

This work was supported by CNPq, FAPERJ, CCMN/UFRJ (Brazil), INFN (Italy), MEXT (Japan), SNF(Switzerland), SNF (Denmark), and EPSRC (U.K.).

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[1] M. Amoretti et al., Nature (London) 419, 456 (2002).[2] S. Maury, Hyperfine Interact. 109, 43 (1997).[3] G. Gabrielse et al., Phys. Rev. Lett. 89, 213401 (2002).[4] M. Niering et al., Phys. Rev. Lett. 84, 5496 (2000).[5] C. L. Cesar et al., Phys. Rev. Lett. 77, 255 (1996).[6] G. Gabrielse et al., Phys. Lett. A 129, 38 (1988).[7] M. Amoretti et al., Nucl. Instrum. Methods Phys. Res.,

Sect. A 518, 679 (2004).[8] M. Amoretti et al., Phys. Rev. Lett. 91, 055001 (2003).[9] C. Regenfus, Nucl. Instrum. Methods Phys. Res., Sect. A

501, 65 (2003).[10] M. Amoretti et al., Phys. Lett. B 578, 23 (2004).[11] M. C. Fujiwara et al., Phys. Rev. Lett. 92, 065005

(2004).[12] M. Amoretti et al., Phys. Lett. B 583, 59 (2004).[13] T. M. O’Neil, Phys. Fluids 24, 1447 (1981).[14] T. M. O’Neil (private communication).[15] M. Amoretti et al., Phys. Lett. B 590, 133 (2004).[16] Y. Chang and C. A. Ordonez, Phys. Rev. E 69, 037401

(2004).[17] M. E. Glinsky and T. M. O’Neil, Phys. Fluids B 3, 1279

(1991).[18] F. Robicheaux, Phys. Rev. A 70, 022510 (2004).[19] G. Gabrielse et al., Phys. Rev. Lett. 93, 073401 (2004).[20] G. Gabrielse et al., Phys. Rev. Lett. 89, 233401 (2002).[21] J. W. Humberston et al., J. Phys. B 20, L25 (1987).[22] M. Charlton, Phys. Lett. A 143, 143 (1990).

T h e o p e n – a c c e s s j o u r n a l f o r p h y s i c s

New Journal of Physics

A novel cooling scheme for antiprotons

Alban Kellerbauer1,3 and Jochen Walz2

1 Physics Department, CERN, 1211 Geneve 23, Switzerland2 Institut für Physik, Johannes-Gutenberg-Universität Mainz,55099 Mainz, GermanyE-mail: a.kellerbauer@cern.ch and jwalz@uni-mainz.de

New Journal of Physics 8 (2006) 45Received 11 August 2005Published 29 March 2006Online at http://www.njp.org/doi:10.1088/1367-2630/8/3/045

Abstract. We propose a novel technique which uses laser-cooled negativeosmium ions for sympathetic cooling of antiprotons. Temperatures down to thesub-millikelvin range might be achievable. These antiprotons could be used toform antihydrogen at ultra-cold temperatures, thus allowing efficient magnetictrapping of antihydrogen for high-resolution laser spectroscopy. Antihydrogenat sub-millikelvin temperatures might also enable first direct measurements ofthe gravitational acceleration of antimatter. Currently, no other technique existswhich allows the cooling of large numbers of antiprotons to temperatures belowthat of the surrounding trap.

Contents

1. Introduction 22. Indirect laser cooling 33. Negative osmium ions 44. Discussion 5

4.1. Production of an Os− plasma . . . . . . . . . . . . . . . . . . . . . . . . . . . 54.2. Injection of p into the Os− plasma . . . . . . . . . . . . . . . . . . . . . . . . 64.3. Laser cooling and repumping . . . . . . . . . . . . . . . . . . . . . . . . . . . 74.4. Removal of Os− ions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

5. Conclusion 8Acknowledgment 9References 93 Author to whom any correspondence should be addressed.

New Journal of Physics 8 (2006) 45 PII: S1367-2630(06)05727-21367-2630/06/010045+9$30.00 © IOP Publishing Ltd and Deutsche Physikalische Gesellschaft

2 Institute of Physics �DEUTSCHE PHYSIKALISCHE GESELLSCHAFT

1. Introduction

The antihydrogen (H) atom offers unique opportunities for high-precision tests of CPT symmetry,the invariance of physical laws under the simultaneous inversion of charge, parity and time.CPT violation could manifest itself by the non-identity of any of the fundamental propertiesof a particle–antiparticle pair. Several such comparisons have already been carried out to highprecision on pairs of subatomic particles [1]–[3]. It must be pointed out, however, that CPTviolations, according to different theoretical models, would not necessarily be visible in all ofa particle’s properties. Thus, the existing tests do not preclude deviations in other properties.Current efforts towards the production of cold antihydrogen were spawned by the immenseprogress, over the past decades, in precision Doppler-free two-photon laser spectroscopy onthe hydrogen atom. Currently, the transition frequency between the 1s ground state and the 2smetastable excited state of hydrogen can be measured to about 2 parts in 1014 [4]. The sametechnique, or a variation thereof, could eventually allow a comparison of the hydrogen andantihydrogen atomic spectra to a similar or even higher relative precision.

In addition to these tests of the CPT symmetry, antimatter atoms can also be used to testgeneral relativity. Quantum field theories of the gravitational force allow for the existence ofscalar and vector gravitons, which would lead to a deviation from the inverse-square law ofthe gravitational force for antimatter, and thus a violation of the weak equivalence principle(WEP). While the universality of free fall is extremely well tested for ordinary matter [5], nocorresponding measurements have ever been performed on the gravitational acceleration ofantimatter. For the simpler quantum gravity models, however, a violation of the WEP can beconstrained to the 10−6 level from existing high-precision experiments with ordinary matter[6]. Gross violations can be excluded on the grounds of energy conservation and other basicconsiderations [7]. Antimatter gravity studies have been hampered by the fact that only chargedparticles of antimatter were available, and that for those the electromagnetic forces—even fromstray fields—by far outweighed the gravitational force. Neutral antihydrogen holds the promiseof allowing the first-ever WEP test with anti-atoms. Such experiments could be carried out ina manner analogous to ordinary-matter atomic fountains [8] or using interferometric methods[9]. In order to achieve relative precisions at the 10−6 level, either method would require largenumbers of cold H at temperatures well below 4 K and even below the Doppler cooling limit ofTD = 2.4 mK using the Lyman-α transition in antihydrogen.

The production of cold antihydrogen was first accomplished by two experiments installedat the CERN antiproton decelerator (AD) [10]. In 2002, both ATHENA [11] and ATRAP[12] observed large amounts of H produced from cold positrons and antiprotons (p) confinedsimultaneously in Penning traps. Subsequent measurements by ATRAP of the H’s velocitydistribution [13] and by ATHENA of the spatial distribution of antihydrogen emission [14] bothsuggest that the temperature of the produced antihydrogen is several times larger than that ofthe positron plasma, which is in thermal equilibrium with the surrounding trap at liquid-heliumtemperature or slightly above. This probably means that the recombination rate is much higherthan the antiproton cooling rate. While the anti-atoms produced by ATHENA and ATRAP arecertainly ‘cold’ compared to those previously created in-beam [15, 16], they are most probablyfar from the temperatures required for precision tests. One of the most promising routes towardssuch ultra-cold antihydrogen is the cooling of the antiprotons prior to recombination.

ATHENA has attempted to achieve this by extending the sideband cooling technique [17]to non-neutral buffer gases [18], thus making it applicable to antiprotons, which would rapidly

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3 Institute of Physics �DEUTSCHE PHYSIKALISCHE GESELLSCHAFT

annihilate with a neutral buffer gas. While the first results are encouraging, this technique allowsat best the cooling of antiprotons to the temperature of the electron plasma and thus of thesurrounding trap. The technique laid out in the present paper overcomes that limitation.

2. Indirect laser cooling

The simplest form of laser cooling is based on the directional absorption of a photon by excitationof an atomic or ionic system, followed by the spontaneous emission of a photon when the systemde-excites at some later time. For this ‘Doppler cooling’[19], the frequency of the light is detunedslightly to the red, or low-frequency side, of the transition frequency f0 by �f . Due to theDoppler effect, a photon can therefore only be absorbed by particles moving towards the lightsource with velocity v = c(�f/f0), thereby reducing their momentum. The mean momentumtransferred in the subsequent isotropic emission is zero; as a result of many absorptions andemissions the particle is cooled. The cooling action is countered by a smaller heating effect dueto the spontaneously emitted photons. It limits the temperature that can be achieved with thistechnique to the Doppler temperature TD, which is proportional to the natural linewidth of thetransition.

Elementary particles cannot be directly laser-cooled. They can, however, transfer theirkinetic and thermal energy to other charged particles which are in turn cooled—‘sympatheticcooling’. This technique has been instrumental in antihydrogen production, where antiprotons arecooled sympathetically with positrons which have thermalized by emitting synchrotron radiation[20]. In conjunction with laser cooling, it was first used to cool 198Hg+ ions by the lighter laser-cooled 9Be+ ions [21]. Recently, the sympathetic cooling of a species much lighter than theactively cooled ions has been demonstrated [22]. About 1000 positrons were cooled in a denseplasma of 9Be+ ions confined in a room-temperature Penning trap. Due to a lack of reliabletechniques for the measurement of the positron temperature, only an upper limit of the achievedtemperature, 5 K, could be given.

If the two species contained in a two-component plasma have different mass, theycentrifugally separate into shells [23]. At first sight, this can be viewed as detrimental to thesympathetic-cooling process. However, such a radial separation does not preclude further coolingof one population by the other, so long as the gap between the two species remains smallwith respect to the damping interaction, which is of course always the case with the Coulombinteraction. Furthermore, the centring of the lighter species is highly desirable, as it leads to areduction of its rotational velocity. Without this effect, the velocity of particles near the edge ofthe plasma can be many orders of magnitude larger than the thermal velocity in the co-rotatingframe.

The present proposal is based on a combination of the two techniques described above:a large collection of atomic ions is laser-cooled to temperatures near the Doppler limit. Theyin turn sympathetically cool a smaller number of antiprotons to the same temperature. Usingthis technique, a collection of antiprotons (or, for that matter, any other charged particles) can inprinciple be cooled to the Doppler temperature of the laser-cooled species. If antihydrogen is thenproduced from these cold antiprotons by use of a technique that avoids reheating, antihydrogenwill be formed at essentially the p’s temperature due to the large mass ratio of the constituentsantiproton and positron. Such a scheme for H production, based on multiple resonant charge-exchange processes [24], has recently been demonstrated by ATRAP [25].

New Journal of Physics 8 (2006) 45 (http://www.njp.org/)

4 Institute of Physics �DEUTSCHE PHYSIKALISCHE GESELLSCHAFT

Figure 1. Energy level diagram for Os−. The arrow indicates the transitionapplicable for laser cooling. Modified from figure 1 of [26] with permission© 2000 by the American Physical Society.

In order to minimize annihilation with the baryons contained in atomic ions, antiprotonscan of course only be cooled by negative ions. Due to a lack of excited bound states in negativeatomic ions with opposite parity compared to the ground state, no laser cooling of negative ionshas ever been attempted or achieved.As we will discuss below, a system with such a configurationof states has recently been identified.

3. Negative osmium ions

In negative ions, the nuclear attraction is strongly suppressed. Most elements nevertheless formstable negative ions due to the correlation energy, the energy gained when all Z + 1 electronsadjust their motions such as to minimize the overlap of their wavefunctions in accordancewith the Pauli exclusion principle (exchange correlation) and electrostatic repulsion (Coulombcorrelation). When one of the electrons is excited, it essentially moves around a neutral atomiccore. Negative ions therefore have no Rydberg series, but only a few, if any, bound excited states.Until very recently the only bound excited states of negative ions that had been identified hadthe same parity as the ground state. That means that electric-dipole transitions between them areforbidden and that their absorption cross-sections are correspondingly small.

Only a few years ago, the first bound state of a negative ion with opposite parity compared tothe ground state was identified in the transition metal osmium [26]. The atomic level diagram ofsingly negative and of neutral osmium, with the tentative term assignments for the negative ion,is shown in figure 1, with the excited bound state identified as 5d6 6s2 6p 6Doja. The excitationenergy of the state was found to be 1.066 eV, which corresponds to a wavelength of 1163 nm, inthe near infrared (IR) region. The absorption cross-section for this state is σa ≈ 6 × 10−16 cm2

and its Einstein A coefficient Aa ≈ 104 s−1. It was deduced that the bound–bound transitionis an electric-dipole transition, since all known magnetic-dipole transitions have Einstein A

coefficients which are many orders of magnitude smaller. This electric-dipole transition should

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5 Institute of Physics �DEUTSCHE PHYSIKALISCHE GESELLSCHAFT

be well-suited for the laser cooling of a collection of Os− ions. With a natural linewidth of� = Aa/(2π) ≈ 10 kHz, the Doppler cooling limit of the negative osmium ions, and thus inprinciple also of the sympathetically cooled antiprotons, is TD ≈ 0.24 µK.

4. Discussion

The proposed scheme, which we have outlined in the preceding sections, thus consists of thefollowing discrete steps:

1. Produce antiprotons, load them into a trap, and pre-cool them sympathetically with electrons.

2. Produce negative osmium ions, load them into a (different) trap, and pre-cool themsympathetically with electrons.

3. Inject the antiprotons into the negative-ion plasma.

4. Laser-cool the negative ions and wait until the antiprotons are sympathetically cooled bythe negative ions.

5. Remove the negative ions from the trap without reheating the antiprotons.

Of these, only the first has so far been experimentally demonstrated. In the following, weshall consider the practical implications of the remaining steps in detail and in particular discussmechanisms which can lead to the premature loss of negative ions or antiprotons. In performingquantitative estimates, we shall assume that 106 negative osmium ions are used to cool about 104

antiprotons.

4.1. Production of an Os− plasma

Current designs of high-intensity negative-ion sources are based upon the sputtering of atomsof a desired element from a surface by means of positive ions [27]. Commercially availablenegative-ion sources of the Middleton type use caesium as the sputtering ion. Measurementswith a standard cathode loaded with osmium powder have shown that osmium readily formsa negative ion [28]. A current of 10 µA of 192Os− (41% abundance) was easily produced andsustained for many hours. It should therefore be straightforward to load about 106 Os− ions into ahigh-field (3–6 T) Penning trap. These will form a spheroid plasma that performs a rigid rotationabout the magnetic-field axis. With a characteristic trap dimension d = 14 mm, a magnetic-fieldmagnitude |B| = 6 T, a confining electric potential of U0 = 10 V, and an azimuthal plasma area ofπr2

0 = 10 mm2, the resulting half-length is z0 = 3.2 mm, the plasma density n = 2.4 × 107 cm−3

and the rotational frequency νrot = 5.8 kHz.Ions in a plasma can experience very strong electric fields as they interact in Coulomb

collisions. While the Os− ion is in its highest bound state, there is a risk of the excess electronbeing detached in these strong fields. The probability per unit time W for the breakup of atomsin static electric fields can be estimated according to the expression [29]

W = B2(2L + 1)

2γML

ML!(L + ML)

(L − ML)!

(2γ2

F

) 2Zγ

−ML−1

e− 2γ3

3F , (1)

New Journal of Physics 8 (2006) 45 (http://www.njp.org/)

6 Institute of Physics �DEUTSCHE PHYSIKALISCHE GESELLSCHAFT

where B is a constant that describes the behaviour of the electron inside the atom, γ is related tothe binding energy ε via γ = (−2ε)1/2, L is the orbital angular momentum, ML is its projection,Z is the nuclear charge, and F is the electric-field magnitude. All quantities in equation (1) are inatomic units. For the negative osmium ion in the 6Do

a state (Z = 0, L = 2 and ε = 11.5 meV) andusing B = 0.1 and ML = 2, the calculated breakup lifetime 1/W is practically infinite for fieldsup to 2 kV cm−1, is of the order of 1 s for 3 kV cm−1, then falls off to ms for F = 4 kV cm−1.

The ions’ approach is closest in the case of a head-on collision, i.e., for an impact parameterb = 0, and that case can thus be used to obtain a lower bound on the separation. In such acollision, the distance of closest approach rmin is reached when the initial kinetic energy inthe centre-of-mass frame is fully converted to potential (Coulomb) energy. The electric fieldF = e/(4πε0r

2min) experienced by the collision partners in Os−–Os− collisions reaches several

10 kV cm−1 at a temperature of 300 K, then falls off to about 6 kV cm−1 at 170 K and drops toabout 2 kV cm−1 at 100 K. Since only a fraction of all ions is found in the excited state, thebreakup rates are decreased by the same factor. These calculations show that pre-cooling of theOs− ions to liquid-nitrogen temperature or slightly above is necessary in order to avoid breakupat the onset of laser cooling. This can be achieved by sympathetic cooling with an electronplasma preloaded into a cryogenic trap which has cooled to the trap temperature by emission ofsynchrotron radiation.

4.2. Injection of p into the Os− plasma

Once the Os− ions have been pre-cooled to a temperature below which auto-neutralization canno longer occur, the smaller collection of p can be injected into the plasma. During the injectionprocess, the antiprotons will initially carry some kinetic energy. Due to the smaller number andmass of the antiprotons, heating of the osmium ions during this phase can be neglected. Untilthe antiprotons are fully thermalized, as well as during the subsequent indirect laser coolingphase, they have ample opportunity to be captured into negative osmium ions, and thus be lostirrecoverably. Such loss can occur either by collisional neutralization followed by capture intothe neutral osmium atom:

p + Os −→ Os+p + e−, (2)

or by direct capture according to the reaction

p + Os− −→ Os+p + 2e−. (3)

Since neutralized Os atoms rapidly leave the trap (see section 4.4 below), subsequentantiproton capture is highly unlikely. Depending on the initial antiproton energy, direct capturemay, however, be a source for p loss.

Calculations of the cross-section for direct capture according to equation (3) unfortunatelyonly exist for the analogous formation of protonium in p–H− collisions [30, 31]. The latter ofthese were performed using the classical-trajectory Monte Carlo method with full four-bodydynamics. Since classically the H− ion is unstable, quantum-mechanical information was addedby using an effective three-body potential to bind the second electron. The calculations yielda rather flat capture cross-section for centre-of-mass energies between 5 and 20 eV, with sharpcut-offs both to the low-energy and the high-energy sides [31].

While the capture cross-section for the negative osmium ion is certainly higher than thatof the negative hydrogen ion for energies above threshold, the behaviour at low energy isdominated by the Coulomb repulsion. The threshold value itself should therefore only depend

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7 Institute of Physics �DEUTSCHE PHYSIKALISCHE GESELLSCHAFT

on the ionic radius, which is almost the same for hydrogen and osmium (Os− is actually smallerthan H−). The rate for the direct capture process is thus essentially zero for centre-of-massenergies below 2.5 eV. If some care is taken to transfer the p without reheating them (i.e., byballistic transfer), it should be possible to keep their temperature well below the threshold valueof several 104 K.

4.3. Laser cooling and repumping

Cooling of Os− ions from 80 K (≈84 m s−1) to 1 mK (≈0.30 m s−1) requires the absorption ofabout 3 × 105 photons, which at a transition rate per atom of (dNa/dt)abs = 1000 s−1 takes about5 min. The wavelength for excitation from the ground to the excited bound state (1163 nm)is convenient for laser instrumentation, as tunable continuous-wave (cw) lasers based onhigh-power laser diodes and optical parametric oscillators (OPOs) are available. Using thecross-section σa ≈ 6 × 10−16 cm2 given above for the absorption into the excited bound stateof Os− and assuming a laser focal area of 10 mm2 and full overlap of the laser beam with theconfinement region, a desired transition rate per atom of (dNa/dt)abs = 1000 s−1 will require alaser power of about 30 mW.

The bound 6Doa state in Os− can not only decay to the 4Fe

9/2 ground state but also to some ofthe intermediate states of even parity. Due to the selection rules of the electric-dipole transition(�J = 0, ±1), only the 4Fe

5/2 and the 4Fe7/2 states can be populated. The branching ratios into these

states and their lifetimes have not been measured. The lifetimes have, however, been calculatedusing the Dirac–Fock and relativistic configuration interaction methods [32] and found to beτ5/2 = 5.8 s and τ7/2 = 0.46 s. These long lifetimes (with respect to the transition rate for lasercooling) mean that the states will probably have to be optically repumped to the ja state. The laserwavelengths required for the repumping of the lower-lying bound states of negative osmium areλ5/2 = 3.81 µm and λ7/2 = 2.29 µm. Assuming resonant cross-sections similar to that from theground state and assuming furthermore that none of the states is populated with a rate of morethan 1/10 the laser cooling rate, the required power for the repumping lasers is P5/2 ≈ 0.9 mWand P7/2 ≈ 1.5 mW.

The absorption of a second photon by the ion in the 6Doa state leads to a detachment of the

excess electron and neutralization. This process has a cross-section about a factor 10 lower thanthe resonant excitation to the bound state, but at a laser power of 30 mW nevertheless takes placeat a rate of about 90 s−1. It therefore constitutes a competing ‘decay’ branch for the 6Do

a state,with a branching ratio of about 8%. In the course of the laser cooling, several 104 osmium ionscan be lost in this way, but the recoil imparted on the neutralized Os atoms is small compared tothe rotational velocity in the plasma. Therefore, again, the atoms will quickly leave the plasmaradially and collisions with antiprotons or negative ions are unlikely. As the detachment ratescales linearly with the laser power, whereas the decay rate from the 6Do

a state to the ground stateis independent from it, the laser power can be somewhat reduced if re-heating by the ejectedosmium atoms turns out to be a problem.

4.4. Removal of Os− ions

After a sufficient waiting time to allow for the indirect laser cooling of the antiprotons, theosmium ions will have to be removed in order to obtain only a collection of ultra-cold p. Thiscan be achieved very conveniently by resonant photo-neutralization of the negative ions. For this

New Journal of Physics 8 (2006) 45 (http://www.njp.org/)

8 Institute of Physics �DEUTSCHE PHYSIKALISCHE GESELLSCHAFT

purpose, the ions are resonantly excited to the unbound 6Dob state with laser light at 1.081 eV

(wavelength 1147 nm). Assuming that the laser employed for the laser cooling can be tunedto this slightly lower wavelength, it can be used for the neutralization despite the fact that theabsorption cross-section into the jb state is about an order of magnitude lower than that into thebound ja state. At a transition rate of roughly 100 s−1, all Os− ions will be neutralized after a fewtens of ms.

The neutralization process may, however, lead to antiproton loss via capture of p intoneutral osmium atoms. This capture reaction is, for instance, employed in the formation ofantiprotonic helium atoms by ASACUSA [33]. The capture cross-section diverges as the centre-of-mass energy tends to zero. However, due to the rigid rotation of the plasma, the neutralizedosmium ions are ejected radially outward at the velocity they had just prior to neutralization. Thecentrifugal velocity exceeds the thermal velocity and the recoil due to emission of the electronin the photo-neutralization (which are of the same order) for all radii greater than about r0/500.If centrifugal separation is complete before the neutralization of the negative ions is carried out,the elongated p cloud at the centre of the plasma is unperturbed by the removal of the Os−.In order to consider the possibility of incomplete radial separation, we shall consider a uniformp density throughout the Os− plasma and an osmium ion which is neutralized close to the axis.

At the very low centre-of-mass energies discussed here, lower yet than those at whichthe adiabatic-ionization model applies [34], antiproton capture proceeds via Langevin orbiting(p wave) processes due to an induced dipole polarization, and the Langevin cross-section[35, 36] is

σorb = π

√2α

Ecm, (4)

where α is the polarizability of the atom and Ecm is the centre-of-mass energy of the collision(all in atomic units). As this model requires that many angular-momentum partial waves occur,equation (4) is valid only as long as the centre-of-mass energy fulfils the relation [34]

Ecm � 1

αµ, (5)

where µ is the reduced mass. The cold collisions incurred at even lower energies, at radii belowr ≈ r0/10, are dominated by s waves. Their cross-sections have no relationship to the Langevincross-section, but they have the same energy dependence. Since we expect the p wave to havea sin2 distribution and the s wave to have an isotropic one, we may use twice the Langevincross-section as an upper bound for the capture cross-section as Ecm tends to zero.

If we consider an ion neutralized at radius r = r0/100 under the plasma conditions describedabove, and using α(Os) = 8.5 Å, the capture cross-section is at most σcapt = 2 × 10−10 cm2 andthe probability of a capture (per Os atom) is only P = npσcaptr0 ≈ 10−5. Thus, under the worstpossible assumptions, only 10 out of the original 104 antiprotons are lost at this stage.

5. Conclusion

Precision experiments to test antimatter gravity will most likely require anti-atoms colder thanthey can be produced with existing techniques, including laser cooling using Lyman-α radiation.We have presented a scheme based on indirect laser cooling of elementary particles whichshould allow the production of H at temperatures well below 1 mK. Quantitative estimates of

New Journal of Physics 8 (2006) 45 (http://www.njp.org/)

9 Institute of Physics �DEUTSCHE PHYSIKALISCHE GESELLSCHAFT

the negative-ion and antiproton losses incurred at the different steps of the scheme as well ascalculations of the required laser power suggest that this novel method is feasible with currentlyexisting technology. While not strictly required for spectroscopic tests of CPT symmetry usingantihydrogen, the application of this technique should greatly increase the fraction of producedantihydrogen which can be trapped in a magnetic trap.

Acknowledgment

The authors thank R C Bilodeau (WMU and LBNL), J S Cohen (LANL), R Landua (CERN)and G Testera (INFN Genoa) for fruitful discussions.

References

[1] Van Dyck R S Jr, Schwinberg P B and Dehmelt H G 1987 Phys. Rev. Lett. 59 26[2] Gabrielse G et al 1999 Phys. Rev. Lett. 82 3198[3] Hsiung Y B 2000 Nucl. Phys. B (PS) 86 312[4] Niering M et al 2000 Phys. Rev. Lett. 84 5496[5] Adelberger E G, Heckel B R and Nelson A E 2003 Ann. Rev. Nucl. Part. Sci. 53 77[6] Adelberger E G et al 1991 Phys. Rev. Lett. 66 850[7] Nieto M M and Goldman T 1991 Phys. Rep. 205 221[8] Peters A, Chung K Y and Chu S 1999 Nature 400 849[9] Phillips T J 1997 Hyperfine Interact. 109 357

[10] Hemery J Y and Maury S 1999 Nucl. Phys. A 655 345c[11] Amoretti M et al 2002 Nature 419 456[12] Gabrielse G et al 2002 Phys. Rev. Lett. 89 213401[13] Gabrielse G et al 2004 Phys. Rev. Lett. 93 073401[14] Madsen N et al 2005 Phys. Rev. Lett. 94 033403[15] Baur G et al 1996 Phys. Lett. B 368 251[16] Blanford G et al 1998 Phys. Rev. Lett. 80 3037[17] Savard G et al 1991 Phys. Lett. A 158 247[18] Kellerbauer A et al 2006 Phys. Rev. A in press[19] Hänsch T W and Schawlow A L 1975 Opt. Commun. 13 68[20] Gabrielse G et al 2001 Phys. Lett. B 507 1[21] Larson D J et al 1986 Phys. Rev. Lett. 57 70[22] Jelenkovic B M et al 2003 Phys. Rev. A 67 063406[23] O’Neil T M 1981 Phys. Fluids 24 1447[24] Hessels E A, Homan D M and Cavagnero M J 1998 Phys. Rev. A 57 1668[25] Storry C H et al 2004 Phys. Rev. Lett. 93 263401[26] Bilodeau R C and Haugen H K 2000 Phys. Rev. Lett. 85 534[27] Middleton R 1983 Nucl. Instrum. Methods 214 139[28] Middleton R 1989 http://tvdg10.phy.bnl.gov/cookbook (unpublished)[29] Smirnov B M and Chibisov M I 1966 Sov. Phys.—JETP 22 585[30] Bracci L, Fiorentini G and Pitzurra O 1979 Phys. Lett. B 85 280[31] Cohen J S 1987 Phys. Rev. A 36 2024[32] Norquist P L and Beck D R 2000 Phys. Rev. A 61 014501[33] Yamazaki T et al 2002 Phys. Rep. 366 183[34] Cohen J S 2004 Phys. Rev. A 69 022501[35] Langevin P 1905 Ann. Chim. Phys. 5 245[36] Gioumousis G and Stevenson D P 1958 J. Chem. Phys. 29 294

New Journal of Physics 8 (2006) 45 (http://www.njp.org/)

Sideband cooling of ions in a non-neutral buffer gas

A. Kellerbauer,1,* M. Amoretti,2,3 G. Bonomi,1 P. D. Bowe,4 C. Canali,2,3 C. Carraro,2,3 C. L. Cesar,5 M. Charlton,4

M. Doser,1 A. Fontana,6,7 M. C. Fujiwara,8 R. Funakoshi,9 P. Genova,6,7 R. S. Hayano,9 I. Johnson,10 L. V. Jørgensen,4

V. Lagomarsino,2,3 R. Landua,1 E. Lodi Rizzini,11,7 M. Macrí,2,3 N. Madsen,12 D. Mitchard,4 P. Montagna,6,7

L. G. C. Posada,9 A. Rotondi,6,7 G. Testera,2,3 A. Variola,4 L. Venturelli,11,7 D. P. van der Werf,4 Y. Yamazaki,8 andN. Zurlo11,7

�ATHENA Collaboration�1Department of Physics, CERN, 1211 Genève 23, Switzerland

2Dipartimento di Fisica, University of Genoa, 16146 Genova, Italy3INFN Sezione di Genova, 16146 Genova, Italy

4Department of Physics, University of Wales Swansea, Swansea SA2 8PP, United Kingdom5Instituto di Fisica, Federal University of Rio de Janeiro, Rio de Janeiro 21945-970, Brazil

6Dipartimento di Fisica Nucleare e Teorica, University of Pavia, 27100 Pavia, Italy7INFN Sezione di Pavia, 27100 Pavia, Italy

8Atomic Physics Laboratory, RIKEN, Saitama 351-0198, Japan9Department of Physics, University of Tokyo, Tokyo 113-0033, Japan

10Physik-Institut, University of Zürich, 8057 Zürich, Switzerland11Dipartimento di Chimica e Fisica per l’Ingegneria e per i Materiali, University of Brescia, 25123 Brescia, Italy

12Department of Physics and Astronomy, University of Aarhus, 8000 Aarhus C, Denmark�Received 11 November 2005; published 19 June 2006�

We have investigated an extension of the buffer gas cooling technique to a non-neutral buffer gas. Theproposed scheme will allow efficient mass-selective centering of ions confined in a Penning trap in situationswhere the use of a neutral damping agent is not possible. The present paper reviews the principle of thetechnique and reports on evidence for sideband cooling of antiprotons in an electron gas, obtained with theATHENA apparatus at CERN’s Antiproton Decelerator facility.

DOI: 10.1103/PhysRevA.73.062508 PACS number�s�: 36.10.�k, 52.20.Hv, 52.27.Jt

I. INTRODUCTION

The studies of ground-state properties of elementary par-ticles, of exotic atoms, and of antimatter bound states all relyon long observation times, which can be achieved by con-finement in a trap. The prominent tool for the confinement ofcharged particles over macroscopic times is the Penning trap,which combines radial confinement by a strong axial sole-noidal magnetic field with a three-dimensional quadrupolarelectric field for axial confinement. The motion of single ions�22� in a Penning trap has been fully described both classi-cally and quantum mechanically �1�.

ATHENA is an experiment installed at the CERN Anti-proton Decelerator �AD� �2� whose goal is the productionand detection of copious amounts of cold antihydrogen �H�atoms. The centerpiece of the ATHENA apparatus is a longcylindrical electromagnetic trap whose electrostatic poten-tials can be freely set to form one or several Penning trapsfor particle capture, cooling, and manipulation. Ultimately,the produced cold anti-atoms are intended to be used for atest of CPT/Lorentz symmetry by comparing their atomicspectrum with that of their ordinary-matter counterparts aswell as for a first-ever test of gravitational attraction on an-timatter. All of these proposed high-precision experimentsmay require antihydrogen atoms trapped in magnetic-

multipole traps and laser-cooled to temperatures in the mKrange. Appreciable fractions of antihydrogen can be confinedin such traps only if they are produced at temperatures com-parable to the trap depth, i.e., roughly 0.5 K.

Using confined antiproton �p� and positron �e+� plasmas,ATHENA achieved the first production of cold antihydrogenin 2002 �3�, a result that was subsequently confirmed by theATRAP experiment using a different detection technique �4�.Observations by ATRAP on the H velocity distribution �5�and by ATHENA on the spatial distribution of antihydrogenemission �6� both suggest that using the nested-well tech-nique �7�, in which hot antiprotons are launched into a pos-itron plasma at liquid-helium temperature or slightly above,the temperature of the produced antihydrogen is severaltimes larger than that of the positrons. This means that therecombination rate is probably much higher than the antipro-ton cooling rate. Even if that were not the case, the cooled pwould still be subject to the rigid rotation of the positronplasma, i.e., the antiproton temperature is defined in thecorotating frame of the positron plasma. Depending on theplasma parameters, this may add a significant azimuthalcomponent to the kinetic energy of the produced antihydro-gen, which scales with the square of the p’s radial amplitude.

Furthermore, with a view to maximizing the lifetime of ane+ plasma in a magnetic-multipole trap, such as those re-quired for the capture of neutral H, a plasma with a rathersmaller radius than those currently used may be necessary. Inorder to still guarantee a good radial overlap of the antipro-tons with the plasma, and to ensure the stability of the anti-

*Author to whom all correspondence should be addressed. Elec-tronic address: a.kellerbauer@cern.ch

PHYSICAL REVIEW A 73, 062508 �2006�

1050-2947/2006/73�6�/062508�9� ©2006 The American Physical Society062508-1

proton cloud itself, it may be necessary to center the p beforecombining them with the positrons.

Recently, an alternative scheme for H production has beendemonstrated �8�. It uses multiple resonant charge exchangeprocesses to create antihydrogen in a well-defined quantumstate �9�. Since the antiprotons are not moved to a differenttrap region after cooling, the H are produced essentially atthe temperature of the p prior to recombination. In this way,assuming sufficient care was taken not to reheat the antipro-tons while ejecting the electrons that were used to cool them,antihydrogen can be produced at the temperature of the sur-rounding trap �though this has not yet been experimentallyverified�. Unfortunately, this method only allows the produc-tion of very few atoms of antihydrogen, compared withmany millions created to date using the nested-well tech-nique.

Ions in a Penning trap can be cooled by introducing adissipative mechanism that removes energy from the motion�10�. The first realization of this technique made use of atuned circuit to damp the signal induced in the trap elec-trodes by an electron’s axial motion �11�. This scheme wasnot applicable to heavy ions, however, due to the muchweaker signal induced by their slower motions, a limitationthat was overcome with the introduction of a neutral buffergas as the cooling medium �12�. This so-called sidebandcooling technique is widely used today for the cooling andmass separation of collections of heavy ions in dilute neutralbuffer gases.

For the cooling of hadronic antiparticles, no neutral gasesare available that would not rapidly lead to the annihilationof the stored ions. We have therefore undertaken a studywhose aim it was to extend this established cooling tech-nique to non-neutral buffer gases. In this paper, we report onmeasurements performed with the ATHENA experiment atCERN, with a view to using this technique for the coolingand centering of antiprotons prior to recombination. Antihy-drogen formed from such precentered antiprotons will beproduced at or near the temperature of the surrounding trap.

II. PRINCIPLE

A. Motion of ions in an ideal Penning trap

An ideal Penning trap is achieved by superimposing ahomogeneous magnetic field of magnitude B, oriented alongthe z axis,

B = Bz �1�

and a three-dimensional electrostatic quadrupolar potential,

� = U02z2 − r2

2z02 + r0

2 , �2�

where z0 and r0 are the characteristic dimensions of the trapand U0 is the applied potential difference. The motion of anion with mass m in this combined potential is described by aset of differential equations �1� which have the solutions

z = Azcos��zt − �z� and �3a�

r = R−� cos��−t − �−�− sin��−t − �−� � + R+� cos��+t − �+�

− sin��+t − �+� � , �3b�

with

�± =1

2��c ± ��c

2 − 2�z2� , �4�

where �z=�4qU0 / �m�2z02+r0

2�� is the axial frequency, �c

=qB /m is the cyclotron frequency of an ion in a purely mag-netic field, and R±, �±, and �± are the amplitudes, frequen-cies, and phases of the so-called modified cyclotron motionand the magnetron motion, respectively.

A charged particle confined in a Penning trap thus per-forms the superposition of three simple harmonic motions,an axial mode and two radial modes. In most Penning trapsdevised for precision experiments, the magnetic field is ofthe order of several tesla while the electrostatic potentialsrarely exceed a few volts. Under these circumstances, thefollowing hierarchy in the frequencies is observed:

�+ � �z � �− �5�

and the frequency of the modified cyclotron motion can thusbe several orders of magnitude larger than that of the mag-netron motion. In an axially harmonic potential, an importantrelationship between the ion motions is that the sum of thefrequencies of the radial modes is exactly the true cyclotronfrequency,

�+ + �− = �c. �6�

For a further treatment of the azimuthal ion motion, theradial equation of motion is most conveniently expressed in acoordinate system spanned by two canonical vectors V±,given by

V± = r − ��r � z �7�

with the inverse transformation

r = −1

�+ − �−�V+ − V−� � z . �8�

This leads to the coupled equations of motion

V± = �±V± � z �9�

with the solutions

V± = A±� cos��±t − �±�− sin��±t − �±� � , �10�

where the A± are amplitudes that depend on the initial con-ditions and which are related to the radial amplitudes by

R± =A±

�+ − �−. �11�

B. Quadrupolar excitation of the azimuthal ion motion

The radial motions of confined ions can be excited withexternal oscillating electric fields. The type of excitation that

KELLERBAUER et al. PHYSICAL REVIEW A 73, 062508 �2006�

062508-2

is of significance for cooling techniques is that performedwith an azimuthal quadrupolar field. Figure 1 shows how aring electrode is split in order to conveniently create the po-tentials that lead to such oscillating fields. The quadrupolarpotential is of the form

�q = aUq

r02 cos��qt − �q��x2 − y2� , �12�

where Uq is the amplitude of the applied potential and a is ageometrical factor that takes into account the shape of thering electrode in the azimuthal plane. In the following, onlythe resonant case with �q=�c will be considered.

The additional force on the confined particles due to thisquadrupolar potential leads to the following modified equa-tions of motion:

V± = �±� Vy±

− Vx±� + k0 cos��qt − �q��Vy

+ − Vy−

Vx+ − Vx

−� , �13�

where

k0 = 2aqUq

mr02

1

�+ − �−. �14�

These can be solved with an ansatz analogous to Eq. �10�,but where the amplitudes A±�t� are now allowed to vary withtime �13�.

Neglecting high-frequency modulations of A±�t� and fur-thermore assuming that the amplitudes only change slowlyand the radial motions thus remain circular, one obtains adifferential equation for the canonical amplitudes,

A± = �1

2k0A�e±i�� �15�

with ��=�q−�+−�−, which can be solved to yield the ra-dial amplitudes,

R±�t� = �R±�0�cos k0

4t � R��0�e±i��sin k0

4t� . �16�

The quadrupolar excitation thus leads to a coupling of themagnetron and modified-cyclotron motions. In a way similarto a system of coupled pendula, the motions are continuallyconverted into each other with a conversion frequency �B=k0 /2. This process is shown in Fig. 2 for ��=0 andR+�0�=0. The degree of conversion is proportional to theamplitude Uq of the applied field and the duration Tq of theexcitation. Their product is called the coupling strength ofthe quadrupolar excitation. In analogy with Rabi oscillationsbetween the states of a two-level atomic system, the excita-tion that leads to a full conversion from one motion to an-other is called a pulse.

C. Damping and cooling

1. Frictional damping

Ions lose kinetic energy in collisions with neutral atomsthat have either been deliberately introduced into the trap orthat remain as residual gas even under ultrahigh-vacuumconditions. The average force exerted on the particle can beapproximated by a viscous-damping force,

Fv = − r , �17�

where is a constant damping coefficient �14� which de-pends on the ion species and the buffer gas used �15,16�.

The modified equation of motion under the influence ofthis friction force becomes

V± = �±�− Vy±

Vx± � −

m

1

�+ − �−��+Vx

+ − �−Vx−

�+Vy+ − �−Vy

−� . �18�

Using the ansatz and approximation already discussed above,one obtains the canonical amplitudes

A± = �±A± �19�

with

FIG. 1. Electrode geometry for the application of a quadrupolarradiofrequency potential. The figure shows an azimuthal cutthrough the ring electrode of a Penning trap, which is fourfoldsegmented to allow a quadrupolar excitation. When the potential isapplied between the two pairs of opposing segments, the resultingpotential has approximately a quadrupolar shape.

FIG. 2. Evolution of the radial amplitudes R± for ��=0 andR+�0�=0, as a function of the duration of the quadrupolar excitationTq.

SIDEBAND COOLING OF IONS IN A NON-NEUTRAL... PHYSICAL REVIEW A 73, 062508 �2006�

062508-3

�± = �

m

�±

�+ − �−. �20�

and the radial amplitudes

R±�t� = R±�0�e�±t. �21�

While the modified cyclotron motion diminishes, the am-plitude of the magnetron motion slowly increases until theions eventually hit the trap electrodes and are lost. The effectof frictional damping on the radial motions is illustrated inFig. 3�a�. In typical trap configurations in which Eq. �5�holds, the time constants of the change in amplitudes are�+=1/�+�m / and �−=1/�−��m /���+ /�−�. The cyclo-tron centering is thus a much faster process than the magne-tron expansion. According to Eq. �21�, the modified cyclo-tron amplitude is reduced to zero after a sufficiently longcooling time. In a real system, however, in which the cooling

is provided by a buffer gas with a finite temperature of itsown, the final cyclotron radius will be R+,th�vth /�+, wherevth is the thermal velocity of the ion at the temperature of thebuffer gas.

2. Sideband cooling

The sideband cooling technique �12� is based on the real-ization that the two effects expressed in Eqs. �16� and �21�can be combined. The coupling of the two radial motions bya quadrupolar excitation at the true cyclotron frequency �ccircumvents the problem of an increased magnetron radius inthe presence of damping. As shown in Fig. 3�b�, this tech-nique allows the cooling of both radial motions. It is rou-tinely used in beam preparation traps of experiments inwhich clean samples of radioactive ions are required forhigh-precision measurements, such as ISOLTRAP �17� atCERN/ISOLDE, which pioneered the technique. The buffergases of choice are mainly hydrogen, helium, and nitrogen atpressures from 10−2 to 10−4 Pa.

D. Non-neutral buffer gas

In principle, the damping of an ion’s radial motions canbe achieved with charged particles instead of neutral buffergas atoms. While the presence of a non-neutral plasma in thetrap strongly modifies the confining electrostatic potential asseen by the ions, it is important to note that in the case of auniform-density buffer gas plasma, the radial electric fieldinside the plasma is proportional to the radius and thus thequadrupolar shape of the overall potential is retained. Themotion of the ions in the combined potential is thus formallyidentical to that in the unperturbed Penning trap. While theoscillation frequencies of the ions are modified, the impor-tant relation of Eq. �6� continues to hold.

The fact that the buffer gas particles are charged leads tothe following important differences and their respective im-plications.

�i� The excitation of the motion of the ions by an externaloscillating field is hampered by the space charge of thecharged buffer gas. In order for the exciting field to penetratethe buffer gas plasma, its plasma frequency �p must besmaller than the excitation frequency �exc. This places a se-vere restriction on the buffer gas density, which in the case ofour setup corresponds to an upper limit of about 2.6�107 cm−3.

�ii� The collisions between the ions and the buffer gas arenot hard-ball collisions, as approximated in the case of aneutral collision partner, but Coulomb interactions with infi-nite range. The damping coefficient of the dissipative forceacting upon the ions is no longer constant but now dependson the ions’ velocity �18�,

nn = −m��v �

v , �22�

where v is the instantaneous velocity of the ion and ��v � isthe coefficient of dynamical friction, itself a complicatedfunction of v . If v is much larger than the root-mean-squarevelocity of the buffer gas particles, the coefficient behaves as

FIG. 3. Azimuthal projection of the trajectory of an ion in abuffer-gas-filled Penning trap. The hard-ball collisions between ionsand buffer gas atoms are approximated by a viscous-drag force. �a�Without excitation, the cyclotron radius decreases, whereas themagnetron radius increases with a longer time constant. �b� Reso-nant quadrupolar excitation at the true cyclotron frequency leads toa continuous conversion of magnetron motion into cyclotron mo-tion. The radii of both modes are decreased and the ion is centered.

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nn v −3. The equation that describes the radial amplitudes

�Eq. �21�� can be adapted to the new situation by allowingfor a varying cooling rate �±�t� and time “constant” �±�t�.The evolution of the particle trajectories under the influenceof a friction force with a variable damping coefficient asgiven by Eq. �22� cannot be solved analytically. Neverthe-less, aside from an increase in damping at reduced ion ve-locities, it is obvious that the overall qualitative behaviorshown in Fig. 3�b� is retained.

�iii� The overall time required for the centering of a col-lection of ions is limited by the larger of the two time con-stants for conversion and cooling. When using a neutralbuffer gas, one can easily adjust its pressure in order toachieve sufficiently fast cooling. In the case of a chargedbuffer gas, the density of the charged buffer gas is limited bythe plasma frequency condition given above, and the coolingtime constant will be correspondingly long. Therefore, theexcitation amplitude must either be kept small or the excita-tion must be stopped after one full pulse. In the latter case,since the cooling transfers part of the radial energy back tomagnetron motion, the excitation must probably be appliedrepeatedly, leaving ample time for cooling between succes-sive excitations.

These considerations show that buffer gas cooling with anon-neutral buffer gas should be possible, but that unlike inthe neutral case the plasma density and excitation amplitudeare strongly correlated and cannot be chosen independently.

III. SETUP

The ATHENA apparatus �19� consists of three main com-ponents, shown in Fig. 4: The antiproton �p� capture trap, themixing trap, and the positron �e+� source and accumulator.The former two are located in the 3-T field of a supercon-ducting magnet whose bore is kept at liquid-nitrogen tem-perature. A liquid-helium cryostat, whose cold nose pro-trudes into the magnet bore and encloses the trap, reduces thetemperature of the trap region further to about 15 K.

The bunch of about �2–3��107 antiprotons that is ex-tracted from the Antiproton Decelerator �AD� every80–100 s undergoes a final deceleration step in a thin��50 �m� aluminum degrader foil, and about 104 p aretrapped by high-voltage electrodes in the capture trap, a cy-lindrical Penning trap whose electrodes have an inner diam-eter of 25 mm. After the independent p stacking and e+ ac-

cumulation phases, the positron plasma and the antiprotonbunch are transferred to the mixing trap, where they arebrought into overlap and antihydrogen production takesplace.

The measurements reported here were performed in thecapture trap, whose geometry is shown in Fig. 5�a�. Variabledc potentials can be applied to the electrode segments,thereby allowing the creation of axial potential wells for theconfinement of charged particles.

In preparation for antiproton capture, electrons are pre-loaded into the capture trap from an electron source mountedon a support about 2 m downstream into a very broad poten-tial well with a small local maximum at the ring electrode.The BaO disk cathode of the electron gun produces a steadycurrent of electrons of up to 10 �A. Typically during theoperation of the electron gun, the electrodes CMP3LA orCMP3LB �see the electrode labels in Fig. 5� are kept at anegative voltage in order to reflect the beam back toward thesource. Over a loading time of several seconds, a small por-tion of the produced electrons is trapped in a narrow well inthe center of the capture trap. By choosing different trappingelectrodes and potential shapes, electron clouds with differ-ent characteristics can be loaded.

Plasmas containing about 3�108 electrons at a density ofabout 108 cm−3 are thus prepared in a harmonic well cen-tered at the ring electrode �Fig. 5�b��. The plasma parameterslength l, density n, and aspect ratio �, as well as the changein its temperature �T, can be determined usingATHENA’s plasma diagnostics system �20� by measuring thefrequencies of the first two axial plasma modes. After thecapture and cooling of the antiprotons, some or all of theelectrons can be ejected from the potential well by applyingshort electric pulses �about 100 ns duration� to electrodeCMP3LA. The antiprotons with their 2000 times higher massare practically unaffected by the electron ejection pulses. Af-ter these manipulations, the only p left in the capture trap arethose which initially had radial overlap with the electronplasma.

Since electrode CMP1L was the only fourfold split elec-trode in the capture trap, the antiprotons �along with the re-maining electrons, in the case of cooling measurements� hadto be moved to the location of that electrode. For this pur-pose, the trap potentials for trapping as shown in Fig. 5�b�were adiabatically changed to the values displayed in Fig.5�c�, with a small square 25-V well at CMP1L. That configu-ration was maintained also during the excitation of the radial

FIG. 4. Overview of the ATH-ENA apparatus. Shown on the leftis the superconducting 3-T sole-noid magnet which houses thecapture trap, the mixing trap, andthe antihydrogen annihilation de-tector. On the right, the radioac-tive sodium source for the posi-tron production and the 0.14-Tpositron accumulation Penningtrap.

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motions. Away from the trap axis, this applied square poten-tial leads to an anharmonic potential and thus to a modifiedmagnetron frequency and a deviation from the equality ex-pressed in Eq. �6�. This means that a signal at the cyclotronfrequency cannot excite all particles confined in the squarewell, but only those for which the relation �exc=�−�+�+holds within the bandwidth defined by the excitation dura-tion.

In order to carefully control the duration Tq, the amplitudeUq, and the frequency �exc of the quadrupolar excitation, adigital signal processor �DSP� was used for the signal gen-eration. The DSP �Analog Devices ADSP-2191� interfaceswith a numerically controlled oscillator, which is program-mable with a serial word of 32 bits, thereby allowing a fre-quency resolution of 1 Hz. The DSP output is then fed intoan active power splitter that delivers two pairs of symmetricsignals with equal amplitude and opposite phase, as requiredfor quadrupolar excitation. The maximal duration of the pro-grammed waveform depends on the firmware code, but wasTq,max=2.55 ms for most of the measurements reported here.With the amplifier setup as described above, the maximalDSP output amplitude of 200 mV corresponded to anamplifier/splitter output of up to 2.6 V �both into a 50-�load�. While it was not possible to measure directly the ac-tual signal applied to the electrodes, we estimate that theattenuation due to the 2-m-long coaxial cable �Lakeshore,type SS� with stainless-steel conductor and braided stainless-

steel shield is about a factor of 2. In the following, the mea-sured amplitudes as applied to the electrical vacuumfeedthrough are given.

IV. MEASUREMENTS AND RESULTS

For the measurements described in this section, antipro-tons were captured and cooled in the capture trap filled withabout �2–3��108 electrons. After a cooling phase of severalseconds, all or most of the electrons were removed from thetrap, thus retaining the cooled antiprotons with a very smallcyclotron amplitude of a few �m but finite magnetron radii.

A. Signal for the conversion of radial motions

As discussed earlier, a quadrupolar excitation at the cy-clotron frequency can convert the magnetron motion of all orsome of the antiprotons to cyclotron motion. Note that eventhough the cyclotron frequency, and thus the kinetic energyof that motion, are much larger than in the case of the mag-netron motion, the final cyclotron radius is at most as large asthe initial magnetron radius. Quadrupolar excitation at thecyclotron frequency can therefore not lead to a radial loss ofparticles that have been successfully captured and sympa-thetically cooled.

Contrary to this expectation, a “loss,” i.e., a shortfall ofantiprotons counted in the trap dumps �toward the HVL elec-

FIG. 5. �a� Geometry of theantiproton capture trap, as it wasin operation in 2003. The CMP1Lelectrode is split fourfold to allowazimuthal quadrupolar excitation.�b� Axial electric dc trap potentialfor antiproton capture. �c� Axialelectric dc trap potential duringsideband excitation. The dottedand solid lines show the potentialsat the electrodes and on the trapaxis, respectively. �d� Magnetic-field magnitude on the trap axis,measured with a Hall probe. �Notethe scale—the relative differencebetween the local minimum andmaximum of the magnetic-fieldmagnitude in this trap region isonly about 5�10−4.�

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trode� after the end of the excitation cycle was observed. Noantiproton annihilations were recorded during or after side-band excitation. This observation can be explained with theconcurrence of two effects. First, the excited antiprotonshave a large orbital magnetic moment associated with thecyclotron motion,

� =1

2e�+R+

2 . �23�

Second, measurements with a Hall probe have shown thatATHENA’s superconducting magnet exhibits small local in-homogeneities of the magnetic field which can reach relativemagnitudes of about 5�10−4 over the extent of the capturetrap. The magnetic-field magnitude in the trap region isshown in Fig. 5�d�. The magnetic-field gradient exerts aforce on the magnetic moments of the ions and pulls themtoward the positive z direction �toward the HVR electrode�.

According to Eq. �23�, the magnitude of the force scaleswith the square of the cyclotron amplitude at the time of thedump, which in turn is equal to the initial magnetron ampli-tude. It can reach about 25 eV m−1 near the trap center forions with R+�3 mm, high enough to prevent ejection ofsuch antiprotons from the trap. We will present experimentalevidence for this hypothesis below. In the following, a short-fall of antiprotons in the final dump is interpreted as an ex-citation at the true cyclotron frequency and conversion ofmagnetron motion to cyclotron motion.

B. Sideband excitation of antiprotons in vacuum

The absolute magnitude of the magnetic field in the cap-ture and mixing trap region is known from the Hall probemeasurements mentioned above to better than 10−3. For ex-citation durations of several ms, however, the frequencybandwidth is less than 500 Hz, leading to a resolving powerof roughly 105 for the cyclotron frequency of antiprotons�about 45 MHz�. It was therefore necessary to initially deter-mine the exact cyclotron frequency. For this purpose, weconducted sweeps of quadrupolar excitation pulses aroundthe expected cyclotron frequency. As the conversion signalwas observed, the sweep range was successively reduced un-til the frequency was found to be about 45.511 MHz. Figure6 shows a scan, in discrete steps, of the excitation frequency.A clear disappearance signal is observed at �exc=�c.

It is immediately obvious from Fig. 6, as well as from theother measurements described below, that only a fraction of20–40 % of antiprotons appear to be affected by the excita-tion. This is due to the fact that ions with smaller initialmagnetron radii are not strongly confined by the magnetictrapping effect and are therefore dumped despite successfulconversion of the radial motions. The observed fraction ofaffected antiprotons, therefore, only constitutes a lowerbound, and it is conceivable that the motions of most ions arein fact converted. Nevertheless, since the coupling frequencyvaries slightly with the radial position of the antiprotons, it isalso possible that the excitation signal is not in resonancewith all of the ions.

The coupling strength UqTq required for two full conver-sions �2�, according to Eqs. �14� and �16�, should be about

3.3 mV s, using a geometrical factor a=0.90 as calculatednumerically for our trap geometry. In order to determine itsactual value and to demonstrate the conversion back fromcyclotron to magnetron motion, we recorded the p disappear-ance as a function of the excitation amplitude for a fixedexcitation duration at the cyclotron frequency. The result,shown in Fig. 7�a�, is a confirmation of the resonant excita-tion and loss mechanism. The coupling strength required fortwo full conversions �second maximum of the graph in Fig.7�a�� was found to be UqTq=2.1 mV s. The figure also shows

FIG. 6. Number of antiprotons observed in the dump after qua-drupolar excitation. A fit to the data points �solid line� allows adetermination of the cyclotron frequency. See the text for an expla-nation of the loss mechanism.

FIG. 7. Number of antiprotons observed in the dump as a func-tion of the coupling strength UqTq of the quadrupolar excitation. �a�Without buffer gas. �b� With electron buffer gas, number of elec-trons Ne− =3�106.

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that about 15% of the excited ions are not recovered. Thiseffect sets in within the first two conversions and thereforeappears to shift the first minimum of the graph toward highercoupling strengths.

C. Sideband excitation of antiprotons in an electron buffer gas

As the next logical step toward sideband cooling, the qua-drupolar excitation was applied in the presence of electronsas a buffer medium. To this end, fewer electron kickoutpulses at lower voltages were applied to electrode CMP3LA,such that between 1 and 3�106 electrons remained in theharmonic potential along with the antiprotons. While thedensity and spatial extent of the remaining electron plasmaare important parameters for this technique, they could notbe measured directly with the plasma mode diagnostics sys-tem due to the small number of electrons. A measurement ofthese quantities just before the kickout and transfer to elec-trode CMP1L should, however, yield an indication on thedensity and a lower �upper� limit of the plasma radius�length� after these manipulations. One can thus infer that theelectron buffer gas plasmas used in the following had a den-sity n= �1–2.5��107 cm−3, a radius r�3 mm, and a lengthl�2.5 mm.

Given these plasma properties, the sideband excitationfrequency is higher than any of the main axial collectivemodes of the electron plasma �20�. Furthermore, excitationwith a quadrupolar oscillating potential whose axis of sym-metry coincides with the trap axis should drive neither axialnor azimuthal plasma modes �a small mechanical misalign-ment and a dipolar field component can of course not beruled out�. Therefore, it is expected that the excitation has noinfluence on the temperature of the electrons, even though asmall heating effect cannot be excluded. Moreover, no lossof electrons was observed. While the full mode diagnosticssystem was not available, in some cases the dipole plasmamode was detectable. Tests without antiprotons confirmedthat neither the amplitude nor the width of the dipole reso-nance changed measurably after applying the quadrupolarexcitation at 45 MHz and thus confirmed that the number ofelectrons was unchanged. Any heating of the electron plasmathat does not lead to particle loss would be compensated bycooling due to synchrotron radiation and would merely delaythe sympathetic cooling by the synchrotron cooling time,which is roughly 0.4 s.

The coupling strength measurement as described in theprevious section was then repeated in the presence of theelectron buffer gas at the same excitation frequency. As canbe seen from the resulting graph, shown in Fig. 7�b�, themaximum available coupling strength was not sufficient toachieve two full pulses, i.e., conversion back to magnetronmotion. The required coupling strength can, however, be es-timated to be at least three times higher than in vacuum.

The effect of the cooling and subsequent reappearance ofantiprotons that have been temporarily trapped in a magneticbottle was demonstrated by a measurement of the number ofantiprotons observed in the final dump as a function of thewaiting time after having applied a full pulse. Figure 8shows that the p which are absent from the dump if it takes

place immediately after the excitation reappear after a suffi-cient waiting time. The figure confirms that the particleswere not actually lost, but still present within the trap,thereby supporting our hypothesis for the disappearancemechanism. The nonlinear shape of the cooling curve on alogarithmic scale shows the variability of the cooling time“constant” due to a charged buffer gas. From the first fewdata points of the graph, a cooling time constant of the modi-fied cyclotron motion of about 5 s can be inferred. Further-more, the figure shows that in the absence of the electronbuffer gas, the antiprotons whose motions have been con-verted are not recovered, even after very long waiting times.

This means that after at most 15 s, the cyclotron ampli-tudes of those antiprotons that have been resonantly excitedin the presence of the electron buffer gas have returned totheir initial values before the excitation, i.e., a few �m. Atthe same time, barring the existence of an anomalous out-ward radial transport during the cooling of the cyclotron mo-tion, also the magnetron amplitudes have been considerablyreduced. Assuming a complete conversion of the radialmodes, the final magnetron radius should be of the sameorder as the cyclotron radius. An anomalous radial transportseems improbable because no antiproton loss is observed formany tens of minutes during storage with electrons. As iscommon in this kind of electromagnetic trap, the storagetime is limited by asymmetries in the confining fields, but thetime scale of transport due to asymmetries is typically muchlonger than the cooling time of the cyclotron motion.

At identical amplitudes, the rotational kinetic energy ofions that perform cyclotron motion is many orders of mag-nitude higher than that of ions that perform magnetron mo-tion, as follows from Eq. �5�. Assuming a process exists thatcouples the two motions in the absence of external excita-tion, it is therefore conceivable that a substantial amount ofkinetic energy is transferred back to the magnetron modewhile the cyclotron motion is being cooled. The hard-ballcollisions encountered in interactions with a neutral buffergas can constitute such a process, but the infinite-range Cou-

FIG. 8. Cooling of the modified cyclotron motion. Antiprotonsmissing from a dump immediately after the quadrupolar excitationwith a pulse are recovered after a sufficiently long waiting timeafter the excitation. The data points taken in the absence of elec-trons show that the excited antiprotons are not cooled and thereforenot recovered in the dump even after waiting times of many tens ofseconds.

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lomb interaction between the confined ions and a non-neutralbuffer gas approximates the viscous force of Eq. �17� welland a coupling of the radial motions should be negligible. Ifsuch a reheating of the magnetron motion turns out to besubstantial, the cyclotron cooling rate must be increased suchthat conversion and cooling take place simultaneously. Thiscan be achieved by maximizing the buffer gas density withinthe constraints discussed in II D.

On very long time scales, centrifugal separation of theconfined species can set in due to their different mass �21�.This effect will eventually push the antiprotons outside of theboundary of the electron cloud. After a sideband excitationand sufficient waiting time to allow for the cooling of thecyclotron motion, the buffer gas will therefore have to beremoved from the trap. It remains to be checked whether theejection of the electrons will disturb and reheat the cooledand centered antiprotons. This should not be the case if thekickout pulse for this operation is applied in a completelyaxially symmetric manner and if furthermore there is no cou-pling between radial and axial motions due to a deviation ofthe trap axis from the magnetic-field orientation.

V. CONCLUSIONS AND OUTLOOK

We have proposed a scheme for the centering of antipro-tons prior to mixing with positrons for recombination. Ourinitial experimental investigations using the ATHENA appa-ratus indicate that the fourfold segmented ring electrode of acylindrical Penning trap can be used to convert the radialmotions of antiproton clouds containing several thousandparticles.

By use of a unique diagnostics scheme based on the pres-ence of magnetic-field inhomogeneities in the trap region,conversion between the radial modes has been demonstratedin vacuum. The complete mapping out of the conversionover more than one pulse in the presence of several 106

electrons, however, was hampered by a lack of available cou-pling strength.

Lastly, the cooling of the modified cyclotron motion fol-lowing a full conversion has been shown and a cooling timeconstant of roughly 5 s was inferred. The reappearance ofpreviously “lost” ions supports our hypothesis for the lossmechanism and diagnostics method.

The work presented here was subject to the limitation thatantiprotons supplied by the AD are scarce and have to beshared among several experiments. Nevertheless, the first re-sults are encouraging and consistent with antiproton center-ing. Further studies are required in order to unambiguouslydemonstrate and quantify the reduction of the magnetron am-plitude. If the scheme can be successfully incorporated intothe antihydrogen production cycle, it will not only allow theproduction of H as cold as the surrounding trap, but alsoincrease the production rate due to better overlap between pand e+, as well as improve the overlap with laser beams forstimulated recombination or laser cooling.

ACKNOWLEDGMENTS

We thank CERN, its AB Department, and the AD team forthe excellent antiproton beam. This work was supported bythe funding agencies CNPq �Brazil�, INFN �Italy�, MEXT�Japan�, SNF �Switzerland�, SNF �Denmark�, and EPSRC�UK�.

�1� L. S. Brown and G. Gabrielse, Rev. Mod. Phys. 58, 233�1986�.

�2� J. Y. Hémery and S. Maury, Nucl. Phys. A 655, 345c �1999�.�3� M. Amoretti et al., Nature �London� 419, 456 �2002�.�4� G. Gabrielse et al., Phys. Rev. Lett. 89, 213401 �2002�.�5� G. Gabrielse et al., Phys. Rev. Lett. 93, 073401 �2004�.�6� N. Madsen et al., Phys. Rev. Lett. 94, 033403 �2005�.�7� G. Gabrielse et al., Phys. Lett. A 129, 38 �1988�.�8� C. H. Storry et al., Phys. Rev. Lett. 93, 263401 �2004�.�9� E. A. Hessels, D. M. Homan, and M. J. Cavagnero, Phys. Rev.

A 57, 1668 �1998�.�10� D. Wineland and H. Dehmelt, Int. J. Mass Spectrom. Ion Phys.

16, 338 �1975�; 19, 251 �1976�.�11� R. S. Van Dyck, Jr., P. B. Schwinberg, and H. G. Dehmelt, in

New Frontiers in High Energy Physics, edited by B. Kursuno-glu, A. Perlmutter, and L. F. Scott �Plenum, New York, 1978�,p. 159.

�12� G. Savard et al., Phys. Lett. A 158, 247 �1991�.�13� G. Bollen et al., J. Appl. Phys. 68, 4355 �1990�.�14� E. W. McDaniel and E. A. Mason, The Mobility and Diffusion

of Ions in Gases �Wiley, New York, 1973�.�15� H. W. Ellis et al., At. Data Nucl. Data Tables 17, 177 �1976�.�16� H. W. Ellis et al., At. Data Nucl. Data Tables 22, 179 �1978�.�17� G. Bollen et al., Nucl. Instrum. Methods Phys. Res. A 368,

675 �1996�.�18� L. Spitzer, Physics of Fully Ionized Gases, 2nd ed. �Wiley,

New York, 1962�, Chap. 5.�19� M. Amoretti et al., Nucl. Instrum. Methods Phys. Res. A 518,

679 �2004�.�20� M. Amoretti et al., Phys. Rev. Lett. 91, 055001 �2003�.�21� T. M. O’Neil, Phys. Fluids 24, 1447 �1981�.�22� In the following, an ion is understood to mean any charged

particle, elementary or composite.

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Search for Laser-Induced Formation of Antihydrogen Atoms

M. Amoretti,1 C. Amsler,2 G. Bonomi,3,4 P. D. Bowe,5 C. Canali,1,6 C. Carraro,1,6 C. L. Cesar,7 M. Charlton,8

A. M. Ejsing,5 A. Fontana,4,9 M. C. Fujiwara,10 R. Funakoshi,10 P. Genova,4,9 J. S. Hangst,5 R. S. Hayano,10

L. V. Jørgensen,8 A. Kellerbauer,11,* V. Lagomarsino,1,6 E. Lodi Rizzini,12,13 M. Macrı,1 N. Madsen,5 G. Manuzio,1,6

D. Mitchard,8 P. Montagna,4,9 L. G. C. Posada,10 H. Pruys,2 C. Regenfus,2 A. Rotondi,4,9 H. H. Telle,8 G. Testera,1

D. P. Van der Werf,8 A. Variola,1 L. Venturelli,12,13 Y. Yamazaki,14 and N. Zurlo12,13

(ATHENA Collaboration)

1Istituto Nazionale di Fisica Nucleare, Sezione di Genova, 16146 Genova, Italy2Physik-Institut, Zurich University, 8057 Zurich, Switzerland

3Dipartimento di Ingegneria Meccanica, Universita di Brescia, 25123 Brescia, Italy4Istituto Nazionale di Fisica Nucleare, Universita di Pavia, 27100 Pavia, Italy

5Department of Physics and Astronomy, University of Aarhus, 8000 Aarhus C, Denmark6Dipartimento di Fisica, Universita di Genova, 16146 Genova, Italy

7Instituto de Fisica, Univesidade Federal do Rio de Janeiro, Rio de Janeiro 21945-970, Brazil8Department of Physics, University of Wales Swansea, Swansea SA2 8PP, United Kingdom

9Dipartimento di Fisica Nucleare e Teorica, Universita di Pavia, 27100, Pavia, Italy10Department of Physics, University of Tokyo, Tokyo 113-0033, Japan

11Physics Department, CERN, 1211 Geneva 23, Switzerland12Dipartimento di Chimica e Fisica per l’Ingegneria e per i Materiali, Universita di Brescia, 25123 Brescia, Italy

13Istituto Nazionale di Fisica Nucleare, Gruppo Collegato di Brescia, 25123 Brescia, Italy14Atomic Physics Laboratory, RIKEN, Saitama 351-0198, Japan

(Received 14 July 2006; published 22 November 2006)

Antihydrogen can be synthesized by mixing antiprotons and positrons in a Penning trap environment.Here an experiment to stimulate the formation of antihydrogen in the n � 11 quantum state by theintroduction of light from a CO2 continuous wave laser is described. An overall upper limit of 0.8% with90% C.L. on the laser-induced enhancement of the recombination has been found. This result stronglysuggests that radiative recombination contributes negligibly to the antihydrogen formed in the experi-mental conditions used by the ATHENA Collaboration.

DOI: 10.1103/PhysRevLett.97.213401 PACS numbers: 36.10.�k, 25.43.+t

In 2002, two experiments at CERN, first ATHENA [1]and then ATRAP [2], reported the production of coldantihydrogen ( �H) by mixing antiprotons and positrons atlow temperature in a nested Penning trap [3]. The ultimategoal of these experiments is to test matter-antimatter(CPT) symmetry by means of precision two-photon spec-troscopy of the �H 1S-2S transition, and, hence, the devel-opment of methods to enhance the production of cold,ground-state �H atoms is of great importance.

In this Letter, we report the result of the first suchattempt, i.e., to stimulate the formation of �H in the n �11 quantum state (which would radiatively deexcite to theground state) by introducing � � 11 �m laser light from aCO2 laser into the ATHENA apparatus [4]. In Ref. [1], weused antiprotons delivered by CERN’s AntiprotonDecelerator and a low energy positron beam derivedfrom a 22Na radioactive source (1:4� 109 Bq). Both the�p and the e� were trapped, cooled, and accumulated inseparate traps prior to moving, and subsequently mixing,them in a common trap (called the mixing trap). Thepositron accumulation trap was located inside a room

temperature vacuum chamber in a 0.14 T magnetic field.The antiproton capture trap and the mixing trap werelocated in the 3 T field of a superconducting magnet, wherethe temperature was maintained at about 15 K, in ultrahighvacuum conditions.

The detector surrounding the mixing trap allows thedifferent events which occur after mixing to be fully iden-tified through the decay products of the annihilations(charged mesons from �p, � from e�), making possiblethe vertex reconstruction of antiproton and positron anni-hilations [5,6].

In the ‘‘standard mixing cycle,’’ the mixing trap, con-figured as a nested Penning trap [3], allows the simulta-neous trapping of oppositely charged particles. The centralpart of the trap is filled with 3–7� 107e�. Once these haveself-cooled by emission of synchrotron radiation, about104 �p are injected and the two particle species interact foraround 1 min. At the start of each mixing cycle, theantiprotons are cooled by their passage through the posi-tron plasma, and after a few tens of milliseconds �H for-mation begins [7,8]. At the end of the mixing cycle, the

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0031-9007=06=97(21)=213401(4) 213401-1 © 2006 The American Physical Society

nested trap is emptied and the number of both positronsand antiprotons are counted before the process is restarted.

In so-called cold mixing, when the positron temperatureis that of the trap at 15 K, most of the annihilations comefrom �H atoms that escape and annihilate on the trap walls;the background is due to a small fraction of antiprotonsannihilating near the trap center on residual gas atoms orions.

In the hot mixing cycle, when the positron plasma isheated by exciting its axial dipole resonance (around20 MHz [9]), �H production is observed to decrease withtemperature [8]; when the positron plasma is heated up to8000 K, only background events are observed [1,8].

These mixing experiments may be analyzed with theknowledge that the two main processes expected to resultin �H formation are the two-body radiative capture (e� ��p! �H� �) and three-body combination (e� � e� ��p! �H� e�) [10].

Given a temperature of 15 K, and assuming completeoverlap between the two particle clouds (formed by 104 �pand a positron plasma of density 1:7� 108 cm�3), theexpected two-body radiative �H production rate at the be-ginning of the mixing is about 40 s�1, an order of magni-tude lower than our measured value of 432� 44 s�1 [8].Thus, the measured production rate is not obviously com-patible with a simple radiative calculation assuming ther-mal equilibrium.

On the other hand, the naive scaling for the three-bodyreaction, T�9=2 [10,11], is clearly inconsistent with ourdata [8]. However, simulations of three-body capture in anested trap have shown that this reaction is a multistepprocess that strongly depends on the plasma conditions andon the trap dynamics, so that collisional relaxation and thefinite transit time of the antiprotons through the positronplasma give a shallower temperature scaling [12,13].

In an effort to clarify the situation, we have investigatedthe radiative �H formation mechanism by attempting tostimulate capture using laser light. Laser-stimulatedelectron-proton recombination for the conditions encoun-tered in ion storage rings was first examined in Ref. [14],and the first observations of laser-induced recombinationobtained with merged beams of protons and electrons werereported in Refs. [15,16]. In a steady state situation, thelaser-mediated electron-proton recombination rate is givenby [17]

R�E�n;l � NpN�E�wnlrabsn;l �E��n;l

rabsn;l �E� � �n;l

; (1)

where E is electron energy, N�E� is the level populationfunction of a continuum Coulomb state according to thepositron density and the Maxwell-Boltzmann distribution,wnl is the statistical weight of the lower level �n; l�, Np isthe number of protons, rabs

n;l is the induced radiation absorp-tion rate, and �n;l is the spontaneous radiative decay rate ofthe level �n; l�. The absorption rate rabs

n;l is inversely pro-portional to the energy difference between the continuum

and level �n; l� and, thus, inversely proportional to thestimulating photon energy. Thus, Eq. (1) suggests thathigh power densities and small laser photon energiesshould promote high enhancement factors. In effect,electron-proton-stimulated recombination with a laser on/off ratio ’ 4 has been observed in a single-pass mergedbeam experiment with a 15 W continuously operating CO2

laser beam (� � 10:5 �m) crossing the interaction region[16].

This type of technique has been implemented byATHENA, using a CO2 laser to stimulate the radiativeformation of �H in the quantum state with n � 11. Thetransition originates in the continuum, and therefore therecombination rate is affected neither by the (finite)Doppler profile width prevalent at T � 15 K nor by thelaser bandwidth (��L ’ 100 MHz); this is because thelevel population and oscillator strength are nearly constantwithin these widths.

The laser-stimulated positron-antiproton recombinationprocess can be described by an equation analogous toEq. (1), but now using the number of antiprotons andpositrons. Therefore, summing over all the accessible finalstates in Eq. (1), considering the Doppler width, the laserbandwidth, the effect of the 3 T magnetic field (for theZeeman splitting of the energy levels in the Paschen-Back regime), and a laser power of 100 W cm�2 (� �10:96 �m), and assuming a complete overlap between104 antiprotons and a positron plasma of 108e� cm�3,we can calculate the expected stimulated formation ratefor our laser runs. We obtain a rate of about 60 �H atoms s�1

under equilibrium conditions at 15 K. The saturation powerdensity is of the order of 1000 W cm�2. Since at thispositron plasma density the expected spontaneous radiativetransition rate is ’ 24 s�1, the predicted enhancementbetween laser on and laser off is about �60� 24�=24 �3:5. The antiproton motion in the axial direction in and outof the e� cloud has not been taken into account. However,at the energies (relative to the e�) at which �H is formed [7],the time spent in the lateral wells of the nested trap isnegligible, since the �p have an additional kinetic energy ofup to ’ 15 eV there.

The previous estimate does not consider nonradiativecollisional recombination processes, which in our caseseem to be dominant (at least 90% at the beginning ofthe mixing cycle [8]). We note also that collisional for-mation favors high-n states which can be ionized by thelaser. This effect is proportional to the flight time of theformed �H in the laser light and on relaxation properties ofthe final state, i.e., by the spontaneous radiative decay tolower levels not influenced by the laser. If we consider thespontaneous radiative decay of states and assume that the�H atoms are formed in equilibrium with the 15 K positronplasma (flight time of about 1 �s in the laser light), we cancalculate the behavior of the ionization rate as a function ofthe principal quantum number. We find, for the 11D state, aradiative rate of 1:37 �s�1 and an ionization rate of0:86 �s�1. For 11< n< 60, the ionization rate is always

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lower than the radiative one. For example, for a �H atom inthe 20P and 20D states, we find ionization probabilities of35% and 22%, respectively. Since in our case the tempera-ture of the formed �H atoms is higher than the temperatureof the positron plasma [18], we estimate an interaction timeof 100 ns, resulting in ionization probabilities 10 timeslower. Nevertheless, there is a finite probability for thelaser to ionize some Rydberg states; however, a quantita-tive estimation cannot be made without detailed knowledgeof the �H velocity and quantum state distributions, which iscurrently not available.

The ATHENA experimental apparatus has been modi-fied to allow the insertion of laser light into the mixing trap.A CO2 continuous wave laser was used with a tunablewavelength of 9:5< �< 11:2 �m; most of the data(345 runs) were collected with � � 10:96 �m. The e�

plasma was typically 1 mm in radius, and the laser beamwaist in the mixing region was about 2 mm with a typicalpeak intensity of 160 W cm�2 at 10 W power.

The path of the laser beam through the interaction regionwas well constrained mechanically. Parallel displacementsof the laser beam (� 1:5 mm each side of the nominalcentral position) caused partial occlusion, and stability wasassured by optimizing and continuously monitoring thelaser power transmitted through the apparatus. In order toexclude suboptimal overlap, the �H production rate wasmeasured with the laser displaced 1 mm in each of thefour directions, and no significant difference was observed.To ensure the same mixing environment, the laser beamwas chopped at a frequency of 25 Hz, recording the state ofthe laser (on or off) simultaneously with the annihilationevents. In this way, 156 160 annihilation events were col-lected in 345 cold mix runs, each with a duration of 50 s.

The time distribution of the �p annihilation vertices onthe trap wall for all of these runs is presented in Fig. 1. Thisdistribution is due mainly to �H annihilating on the trap wallwith a background due to �p annihilating on the residual gasatoms in the trap center [19]. The curve can be fitted withtwo exponentials (not shown in the figure), having timeconstants of �11:2� 1:4� and �76:8� 8:3� s, respectively.This time behavior is characteristic for our �H formation

procedure, where different cooling regimes have beenobserved [7].

The radial vertex density, shown in Fig. 2, represents the�p annihilation vertex position as reconstructed by the hitsof the charged mesons in the two silicon strip layers of thedetector. The antiatoms annihilating on the trap wall at aradius of 1.25 cm give rise to a peak in the distribution,smeared by the resolution of the vertex algorithm (1.8 mmalong the trap axis and 3.5 mm in the transverse direction)[4]. By fitting this distribution with the sum of the mea-sured background from the hot mix runs (see Fig. 2) andthe vertex density for pure �H annihilation from ourMonte Carlo simulation [19], we obtain the fraction of �Hevents of �67� 4�%. Taking into account the efficienciesas in Ref. [19], in total we produced about 7� 105 �H,corresponding to an observed mean rate of 40 s�1, andan overall yield of �20� 4�%.

The cosine of the opening angle distribution, shown inFig. 3, represents the angle ��� between the two 511 keV �rays recorded in time coincidence with the charged-particlehits, as seen from the charged-particle vertex. The clearexcess at cos����� � �1 (corresponding to back-to-backemission of the two � from the e� � e� annihilation) is

FIG. 1 (color online). Vertex time distribution (log scale) forlaser off (line) and laser on (crosses). Inset: The same for the first12 s in decimal scale.

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proof of the presence of antihydrogen [1,19]. These dis-tributions show no evidence for laser-stimulated �H forma-tion. This conclusion does not depend upon variations inthe temporal or spatial cuts applied to the vertex and angledistributions.

To be more quantitative, we consider the number ofvertices over the entire 50 s mixing period and in thesubintervals 1< t � 10 s and 10< t < 50 s, a demarca-tion prompted by the two time components present in ourdata (the results are insensitive to small variations of thewidths of these intervals). In this analysis, we also use asubsample of particularly well reconstructed vertices, us-ing the quality index from the vertex algorithm; since thisindex is calculated on the basis of statistical estimatorsonly, the vertex quality selection has no physical bias [4].

The number of vertices recorded in different time win-dows is listed in Table I. A radial cut from 0:7< r <2:5 cm (see Fig. 2) was applied to these data. Althoughthis cut tends to suppress the background which is mainlyin the trap center, similar results are obtained withoutradial cuts. The small effect that we observe from Table Iis a 2:2� deficit of laser on events in the interval 10< t <50 s (vertex quality applied).

Since in the region 0:7< r< 2:5 the signal and back-ground percentages are �87� 4�% and �13� 4�%, respec-tively, from Table I we find 90% C.L. upper limits of 3.8%for the enhancement in the 1; 10 s time interval (corre-sponding to 1:5 �H s�1 from our observed mean �H rate of40 s�1) and of �3:6% for the deficit in the 10; 50 sinterval (corresponding to 1.4 ionized �H s�1). In the wholetime interval 1< t < 50 s and without vertex quality, weobtain a 90% C.L. upper limit for laser enhancement of0.8%, corresponding to 0:3 �H s�1. The conclusion is notchanged when the opening angle distributions are analyzedwithin the same time intervals, though the statistical sig-nificance is lower.

Investigations were also performed with different lasertunings in the range � � 10:16 �m to � � 11:03 �m, inorder to investigate whether a dependence on detuningcould be observed. No statistically significant variationsbetween laser on and off were found.

Considering the predicted enhancement factor of 3.5 dueto the laser radiation with respect to the spontaneousradiative formation, and that 67% of the data are due to�H annihilations, it follows from Table I that, to observe a5� difference between laser on and off annihilations, aradiative component>1:5% of the total recombination rateis required [8]. In spite of this, we observe a null lasereffect on �H production. Barring the unlikely possibility of asuboptimal overlap between the antiprotons and the laserbeam, this result suggests that spontaneous two-body ra-diative formation in conditions of thermal equilibriumgives a negligible contribution to the �H formation in theATHENA nested trap. Other results also indicate that �Hformation does not occur under conditions of thermalequilibrium between the �p and the e� [8,18,20], and it is

likely that three-body capture and collisional processes arethe dominant mechanisms. Moreover, the laser ionizationof the high-n Rydberg states formed in this way couldmask a small contribution from laser-induced radiativerecombination.

In this scenario, to date most �H which has been detectedhas been produced in weakly bound Rydberg states. Theseresults will provide a major impetus for the search for new,efficient methodologies for the production of cold ground-state antihydrogen.

*Present address: Max Planck Institute for Nuclear Physics,Postfach 103980, 69029 Heidelberg, Germany.

[1] M. Amoretti et al. (ATHENA Collaboration), Nature(London) 419, 456 (2002).

[2] G. Gabrielse et al., Phys. Rev. Lett. 89, 213401 (2002).[3] G. Gabrielse et al., Phys. Lett. A 129, 38 (1988).[4] M. Amoretti et al. (ATHENA Collaboration), Nucl.

Instrum. Methods Phys. Res., Sect. A 518, 679 (2004).[5] C. Regenfus, Nucl. Instrum. Methods Phys. Res., Sect. A

501, 65 (2003).[6] M. C. Fujiwara et al. (ATHENA Collaboration), Phys.

Rev. Lett. 92, 065005 (2004).[7] M. Amoretti et al. (ATHENA Collaboration), Phys. Lett. B

590, 133 (2004).[8] M. Amoretti et al. (ATHENA Collaboration), Phys. Lett. B

583, 59 (2004).[9] M. Amoretti et al. (ATHENA Collaboration), Phys. Rev.

Lett. 91, 055001 (2003); Phys. Plasmas 10, 3056 (2003).[10] A. Muller and A. Wolf, Hyperfine Interact. 109, 233

(1997).[11] M. Holzscheiter, M. Charlton, and M. M. Nieto, Phys.

Rep. 402, 1 (2004).[12] F. Robicheaux, Phys. Rev. A 70, 022510 (2004).[13] P. O. Fedichev, Phys. Lett. A 226, 289 (1997).[14] R. Neumann et al., Z. Phys. A 313, 253 (1983).[15] U. Schramm et al., Phys. Rev. Lett. 67, 22 (1991).[16] F. B. Yousif et al., Phys. Rev. Lett., 67, 26 (1991).[17] A. Wolf, Hyperfine Interact. 76, 189 (1993).[18] N. Madsen et al. (ATHENA Collaboration), Phys. Rev.

Lett. 94, 033403 (2005).[19] M. Amoretti et al. (ATHENA Collaboration), Phys. Lett. B

578, 23 (2004).[20] G. Gabrielse et al., Phys. Rev. Lett. 93, 073401 (2004).

TABLE I. Integrated number of vertices in the arrowed regionshown in Fig. 2 for different time windows t1; t2 in seconds.

Vertex Time window (s)Run quality 1; 50 1; 10 10; 50

Laser on No 59 496 18 457 41 039Laser off No 59 611 18 353 41 258On-off �115� 345 104� 192 �219� 287Laser on Yes 34 731 10 938 23 793Laser off Yes 35 039 10 760 24 279On-off �308� 434 178� 241 �486� 219

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Temporally Controlled Modulation of Antihydrogen Production and the Temperature Scalingof Antiproton-Positron Recombination

M. C. Fujiwara,1,2,* M. Amoretti,3 C. Amsler,4 G. Bonomi,5,6 A. Bouchta,7 P. D. Bowe,8 C. Canali,3,9 C. Carraro,3,9

C. L. Cesar,10 M. Charlton,11 M. Doser,7 A. Fontana,6,12 R. Funakoshi,13 P. Genova,6,12 J. S. Hangst,8 R. S. Hayano,13

L. V. Jørgensen,11 A. Kellerbauer,7 V. Lagomarsino,3,9 R. Landua,7 E. Lodi-Rizzini,14,15 M. Macri,3 N. Madsen,8,11

G. Manuzio,3,9 D. Mitchard,11 P. Montagna,6,12 H. Pruys,4 C. Regenfus,4 A. Rotondi,6,12 G. Testera,3 A. Variola,3

L. Venturelli,14,15 D. P. van der Werf,11 Y. Yamazaki,2 and N. Zurlo14,15

(ATHENA Collaboration)

1TRIUMF, 4004 Wesbrook Mall, Vancouver, British Columbia, V6T 2A3, Canada2Atomic Physics Laboratory, RIKEN, Saitama 351-0198, Japan

3Istituto Nazionale di Fisica Nucleare, Sezione di Genova, I-16146 Genova, Italy4Physics Institute, Zurich University, CH-8057 Zurich, Switzerland

5Department of Mechanical and Industrial Engineering, University of Brescia, I-25123 Brescia, Italy6Istituto Nazionale di Fisica Nucleare, Sezione di Pavia, I-27100 Pavia, Italy

7Physics Department, CERN, 1121 Geneva 23, Switzerland8Department of Physics and Astronomy, University of Aarhus, DK-8000 Aarhus C, Denmark

9Dipartimento di Fisica di Genova, I-16146 Genova, Italy10Instituto de Fisica, Universidade Federal do Rio de Janeiro, Rio de Janeiro 21945-970, Brazil

11Department of Physics, Swansea University, Swansea SA2 8PP, United Kingdom12Dipartimento di Fisica Nucleare e Teorica, Universita di Pavia, I-27100 Pavia, Italy

13Department of Physics, University of Tokyo, Tokyo 113-0033, Japan14Istituto Nazionale di Fisica Nucleare, Gruppo Collegato di Brescia, I-25123 Brescia, Italy

15Dipartimento di Chimica e Fisica per l’Ingegneria e per i Materiali, I-25123 Brescia, Italy(Received 2 October 2007; published 30 July 2008)

We demonstrate temporally controlled modulation of cold antihydrogen production by periodic RFheating of a positron plasma during antiproton-positron mixing in a Penning trap. Our observations haveestablished a pulsed source of atomic antimatter, with a rise time of about 1 s, and a pulse length rangingfrom 3 to 100 s. Time-sensitive antihydrogen detection and positron plasma diagnostics, both capabilitiesof the ATHENA apparatus, allowed detailed studies of the pulsing behavior, which in turn gaveinformation on the dependence of the antihydrogen production process on the positron temperature T.Our data are consistent with power law scaling T�1:1�0:5 for the production rate in the high temperatureregime from �100 meV up to 1.5 eV. This is not in accord with the behavior accepted for conventionalthree-body recombination.

DOI: 10.1103/PhysRevLett.101.053401 PACS numbers: 36.10.�k, 34.80.Lx, 52.27.Jt

Antihydrogen ( �H), a bound state of an antiproton ( �p) anda positron (e�), is the simplest form of atomic antimatter,and as such is an excellent system for probing the funda-mental symmetries between matter and antimatter.Following the production of slow antihydrogen by theATHENA [1] and ATRAP [2] experiments, a new field ofcold antiatom studies is emerging.

We have shown previously [1,3] that �H can be producedcontinuously for up to 180 s by mixing cold plasmas of �pand e�. In this letter, we demonstrate temporally con-trolled production of �H by applying a modulated RF fieldto heat the e� plasma. Our observations establish a pulsedsource of cold �H atoms, with a rise time of about 1 s andpulse lengths ranging from 3 s to 100 s. We note thattemporal control of recombination via modulation of col-lision energies has previously been used to elucidate as-pects of recombination physics [4].

We also report detailed studies of the temperature de-pendence of �H formation, utilizing the pulsed �H signal.Optimizing �p-e� recombination is important for realiza-tion of the ambitious goal of �H trapping [5], but a thoroughquantitative understanding of the process has yet toemerge, despite on-going theoretical efforts: see, e.g.,[6–12]. We have developed a novel method of monitoring�H production during the synchrotron cooling of the e�

plasma. Our data probe the previously unexplored plasmatemperature range up to 1.5 eV, and suggest power lawscaling of antihydrogen formation that deviates substan-tially from that assumed for conventional three-bodyrecombination.

The ATHENA antihydrogen apparatus [13], located atthe Antiproton Decelerator (AD) facility at CERN, con-sisted of several modular components, including �p andmixing traps (both held at 15 K in a 3 T solenoid field),

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the e� accumulator [14], a Si vertex detector [15,16],external detectors [17] and the associated control systems.

A few times 107 �p, obtained at 5.3 MeV from the AD,are slowed by degrader foils to <5 keV, and about 104 arecaptured in the �p trap. After being sympathetically cooledwith preloaded cold electrons [18], the �p are moved to themixing trap. Positrons are accumulated in a Surko-typenitrogen buffer gas trap [19] and transferred using a pulsedelectric field into the mixing region [14]. Typically 104 �pand around 5� 107 e� are mixed by injecting the formerinto the e� plasma in a nested potential well configuration[20]. Our e� plasma had a typical density of a few�108 cm�3, and a length of 3 cm. When an �H atom isformed, it may escape the electromagnetic confinement ofthe Penning trap and annihilate on collision with the trapwall. Such events are detected by a position sensitiveimaging detector [15]; the positions of �p annihilations(vertices) are determined by tracking the trajectories ofthe charged products (mostly pions) using the Si vertexdetector [16], while 511 keV � rays from e� annihilationsare detected by segmented CsI crystals. The detectionsystem allows time-dependent determination of �H produc-tion [3]. It is this ability, coupled with the real-time plasmatemperature control and diagnosis techniques developed in[21], that enabled the detailed studies reported here. Notethat we detect here only �H atoms that survive ionizationfrom the ambient electric fields to reach the trap walls.

In our previous studies [1,3,22], �H formation could besuppressed by continuously heating the e� plasma with RFtuned to the dipole plasma modes [21]. The e� temperature

could also be modulated by applying periodic RF, with theplasma temperature returning rapidly (after �1 s) to thebase temperature when the heating was turned off [21]. InFig. 1, we demonstrate that �H formation can be modulatedby applying such periodic heating to the e� plasma.

Figure 1(a) displays the time and axial position distri-butions of �p annihilation vertices in which the RF wasapplied with a square wave modulation with a 15 s off–15 son cycle. In Fig. 1(b) the RF modulation is applied with theopposite phase. In both cases, the annihilation events aredramatically suppressed, within a time &100 ms after theRF was turned on. The annihilations recovered within afew seconds once the RF was turned off, as the e� tem-perature return to base (see below). The RF-off vertexposition distributions (see Fig. 1, lower panel) are consis-tent with �H production [3,23], while those for RF-onsuggest annihilations dominantly on residual gas, or pos-sibly trapped ions [24]. The accompanying angular distri-bution of 511 keV � rays gave a well-established signaturefor simultaneous annihilations of �p and e� [1,3]. We havealso demonstrated �H production with modulation periodsranging from 3 to 100 s.

In order to understand the temporal behavior of the �Hmodulation, we consider a simple model as follows: turn-ing on the RF heats the e� plasma by �T, immediatelysuppressing �H production. When the RF is turned off, thee� plasma self-cools via emission of synchrotron radiationwith a time constant �e � 0:5 s to the equilibrium tem-perature T0, with �H formation recovering with a similartime constant. If the temperature evolution of the e�

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plasma, illustrating modulated �H produc-tion. (a) Heat on-off, and (b) off-oncycles. In the upper panels the heat offperiod is shaded.

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plasma is known, the temperature dependence of �H for-mation can be deduced, which in turn provides informationon �H formation dynamics in a nested trap.

We quantitatively test this model, focusing on the on-set of antihydrogen production upon turning the heatingoff. The e� cooling time �e at B � 3 T can be calculatedfrom [25]: �e � 0:43 s. Experimental measurements,however, are reported to give higher values than this esti-mate [25,26]. Given the importance of this parameter inour later fits, we determine this cooling rate via analysisof the quadrupole plasma modes frequency f in offline(e�-only) measurements, based on the method reported in[21]. The e� are heated by applying modulated RF with a5 s on—5 s off cycle. According to the cold fluid model[27,28], �T is proportional to f2 � f2

0 where f0 is theequilibrium value. The evolution of the modes frequencyafter RF removal, f�t�, can be fitted to: f�t�2 ���T exp��t=�e� � f2

0, to extract �e and f0. The constant� is uncalibrated for these measurements, but is not usedfor the determination of �e (� will be calibrated for the �Tmeasurements below). Figure 2 illustrates the exponentialnature of the plasma temperature evolution, where f2�t� �f2

0 is plotted for 3 different initial heating amplitudes. Fromthe data, we obtain �e of 0.42 s (for an RF amplitude of5 mV), 0.50 s (13 mV), and 0.52 s (25 mV), giving anaverage of �e � 0:48� 0:05 s. A possible systematic shiftof �e with the heating amplitude is included in ouruncertainty.

We now present a series of �H modulation data, with anRF modulation cycle of 5 s off–3 s on. Seven periods of theon-to-off transition occurring during the 70 s mixing timewere summed over typically 10 mixing cycles for eachinitial temperature, such that about 70 transitions per dataset were used for the analysis. We consider here the anni-

hilation rate from the detector trigger signal, rather than thereconstructed vertex rate. The former has negligible deadtime compared to the latter (at the cost of having noposition information), and hence can provide more accu-rate time information. In Fig. 3 annihilation time distribu-tions are shown for (a) �T � 870 meV (error bars), and(b) 270, 400, 870, 1150, and 1470 meV (histograms). �T isobtained from the modes measurements [21], with � nowcalibrated using the resonance line shape to give the abso-lute temperature increase.

In order to fit these data, a temperature power scaling ofthe production rate, i.e. R �H�T� / T

�P, has been assumed,where T is the e� temperature. Assuming that the disap-

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FIG. 3 (color). Onset of �H production upon heat off at t � 0.(a) The data with �T � 870 meV (error bars). Green curve: thee� temperature evolution with �e � 0:48 s. Red curve: a repre-sentative fit to Eq. (1), giving R �H / T

�1:2. Dashed red curve:exponential fit. Blue: the case with R �H / T

�4:5. (b) The data andrepresentative fits for different �T. Fit time windows (indicatedby solid curves) were set with Tlow � 1 meV (see text). The datasets (which are vertically displaced for clarity) were taken withbetween 0:7–1:6� 105 �p.

0 1 2 3 4 5

log

( f

(t)

- f

)

22

0

-1

-2

-3

Time (s)

0

FIG. 2 (color). Measurements of e� plasma cooling time.Plotted are f�t�2 � f2

0 (proportional to �T) versus time afterRF removal. RF amplitudes of 25 mV (red), 13 mV (green), and5 mV (black) were applied.

PRL 101, 053401 (2008) P H Y S I C A L R E V I E W L E T T E R S week ending1 AUGUST 2008

053401-3

pearance of the �p is dominated by �H production over thetime scale of interest (< a few seconds), the observed �pannihilation rate ��t� can be written as

��t� � A�

�T exp��t�e

�� T0

��P� Bk; (1)

for t > 0, and ��t� � A�T � T0�P � Bk for t < 0. T0

(base temperature), A (normalization) and Bk (back-ground), as well as P, are the fit parameters. In this model,in the limit of T0 ! 0 and no background, the slope of theonset of �H production in a logarithmic plot represents thepower scaling P. Our data show indications of such scal-ing, especially at intermediate time where the effects of T0

and Bk are small. Increasing �T results in delayed onset of�H production as expected, since it takes longer for the e�

plasma to cool down.Representative fits are illustrated by the curves in Fig. 3.

The red curve in (a) is a fit to the �T � 870 meV data,resulting in the scaling P � 1:2� 0:2, and an effectivebase temperature of T0 � 180� 50 K, where the errorsare statistical only. The green curve shows the e� tempera-ture evolution, where T0 is taken from the fit above. Theblue curve is the case where the conventional three-bodyrecombination scaling P � 4:5 [6] is assumed. Here theonset of the �H production would be much delayed, ascenario which is clearly incompatible with the data.Similar fits to the data with different �T are given in curvesin Fig. 3(b). The fit time windows (indicated with solidcurves) were taken to be �2< t < ��e ln��T=Tlow�� s,where the effective low temperature cut off Tlow is set to1 meV here.

We observe that the fitted base temperatures T0 obtainedare typically higher than the nominal trap temperature of15 K. In our model [Eq. (1)], deviation from power scalingat low temperatures as implied by [22], would be ac-counted for by a higher value of T0 [29]. In order to avoidthe influence of the possible nonpower scaling at lowtemperatures, we make alternative fits, limited to thehigh temperature region, assuming the form: ��t� �A�T exp��t=�e�

�P � Bk, for t > 0. An example ofsuch fit is depicted as Exp fit in Fig. 3(a), giving P � 0:8�0:2 with Tlow � 35 meV.

Figure 4 illustrates consistency of the derived scalingparameters over the range of �T (a), and over the 70 smixing time (b). The emphasis here is on the relativeconsistency among the data, as the absolute value of Pmay shift due to the input parameters. In both figures, thestandard fits and the exponential fits are compared.

Given the simplicity of our model, overall agreementwith the data is very good. We have carefully investigatedsystematic uncertainties by performing a number of fits byvarying, e.g., �e, and Tlow. The exponential fits tend to giveslightly lower P than the standard fits.

Taking into account these systematic effects, we obtainthe scaling parameter of P � 1:1� 0:5, i.e., R �H /T�1:1�0:5. The result is consistent with our earlier continu-ous heating measurements [22], but the present work sub-stantially extends the measurements in the 100 meV to1.5 eV range, and provides evidence for the power lawbehavior at these temperatures. Since the full range of thetemperatures is probed during a single pulsing cycle, thepresent method should be less sensitive to some of thepossible systematics, such as normalization errors.However, our determination of P is highly correlatedwith �e, and hence relies on the validity of the plasmamodel [27] used to extract it.

Because of the high rate of �H production [3], three-bodyrecombination [6] is considered to be dominant in ourexperiment. However, our observed scaling is not consis-tent with the theoretical prediction of R �H / T

�4:5 [6],which pertains for thermal equilibrium in an infiniteplasma [30]. Deviation from this scaling can be qualita-tively explained by the finite size of the e� plasma, forwhich nonequilibrium processes are important [8]. Suchprocesses can produce �H with larger velocities [10,23],which in turn has implications for its trapping in a mag-netic trap [5]. Calculations in Ref. [8] suggest P� 1:4between 15 and 30 K, though extrapolation of this to theeV region requires caution. On the other hand, the consis-tency in Fig. 4(b) implies, within our experimental sensi-tivity, that the mechanism responsible for �H formation doesnot change over the time scale of 10 to 70 s in theseexperimental conditions. While the quantum state of theproduced �H and its subsequent cascades is a subject of on-going studies, a significant fraction of the produced �H

Initial heating temperature ∆T (meV) Time after start of mixing (s)

Tem

pera

ture

sca

ling

P

0 500 1000 1500 0 10 20 30 40 50 60 700.0

0.5

1.0

1.5

2.0(a) (b) FIG. 4 (color online). Dependence of

P on (a) �T and on (b) the time afterstart of the mixing for the �T �870 meV data set. Open squares andcircles are with the standard fits toEq. (1), while filled ones are with theexponential fits. For the standard fits in(b), T0 was fixed (to 150 K here) toachieve convergence. The plotted errorsare statistical only.

PRL 101, 053401 (2008) P H Y S I C A L R E V I E W L E T T E R S week ending1 AUGUST 2008

053401-4

seems to reach deeper binding states in times shorter thanour typical pulsing time [7,10,11]. Note that although theobserved rise time of �1 s is rather modest, it could bereduced with a higher B field, since �e scales scale as 1=B2.

Finally, we remark on the possible applications of modu-lated �H production. First, the temperature scaling analysisreported here can be extended to a variety of plasma andfield conditions, including nonuniform B fields that are ofinterest for �H trapping [5]. Second, temporal modulationcan be used as a corroborating signature for �H produc-tion in future experiments where standard direct detectionmay be difficult [31]. Third, it can be applied to low-yieldand/or low-duty-cycle measurements, such as investiga-tions of laser or microwave transitions, to give a phase-sensitive signal enhancement. Furthermore, controlledmodulation of �H production may be combined with devel-opments in cold atom manipulation (e.g., [32]), opening upfuture new possibilities.

This work was supported in part by CNPq (Brazil),NSERC, NRC/TRIUMF (Canada), SNF (Denmark),MEXT, RIKEN (Japan), INFN (Italy), SNF(Switzerland), and the EPSRC (UK).

*Makoto.Fujiwara@triumf.ca[1] M. Amoretti et al., Nature (London) 419, 456 (2002).[2] G. Gabrielse et al., Phys. Rev. Lett. 89, 213401 (2002).[3] M. Amoretti et al., Phys. Lett. B 578, 23 (2004).[4] G. Kilgus et al., Phys. Rev. A 46, 5730 (1992); H. Gao

et al., J. Phys. B 30, L499 (1997).[5] G. Andresen et al., Phys. Rev. Lett. 98, 023402 (2007);

G. Gabrielse et al. ibid. 98, 113002 (2007).[6] M. E. Glinsky and T. M. O’Neil, Phys. Fluids B 3, 1279

(1991).

[7] E. M. Bass and D. H. E. Dubin, Phys. Plasmas 11, 1240(2004).

[8] F. Robicheaux, Phys. Rev. A 70, 022510 (2004).[9] B. Zygelman, J. Phys. B 38, S387 (2005).

[10] T. Pohl et al., Phys. Rev. Lett. 97, 143401 (2006).[11] T. Topcu and F. Robicheaux, Phys. Rev. A 73, 043405

(2006).[12] S. X. Hu, Phys. Rev. Lett. 98, 133201 (2007).[13] M. Amoretti et al., Nucl. Instrum. Methods Phys. Res.,

Sect. A 518, 679 (2004).[14] L. V. Jørgensen et al., Phys. Rev. Lett. 95, 025002 (2005).[15] C. Regenfus, Nucl. Instrum. Methods Phys. Res., Sect. A

501, 65 (2003).[16] M. C. Fujiwara et al., Phys. Rev. Lett. 92, 065005 (2004).[17] M. C. Fujiwara and M. Marchesotti, Nucl. Instrum.

Methods Phys. Res., Sect. A 484, 162 (2002).[18] G. Gabrielse et al., Phys. Rev. Lett. 63, 1360 (1989).[19] C. M. Surko et al., Phys. Rev. Lett. 62, 901 (1989).[20] G. Gabrielse et al., Phys. Lett. A 129, 38 (1988).[21] M. Amoretti et al., Phys. Rev. Lett. 91, 055001 (2003);

Phys. Plasmas 10, 3056 (2003).[22] M. Amoretti et al., Phys. Lett. B 583, 59 (2004).[23] N. Madsen et al., Phys. Rev. Lett. 94, 033403 (2005).[24] N. Zurlo et al., Phys. Rev. Lett. 97, 153401 (2006).[25] B. R. Beck et al., Phys. Plasmas 3, 1250 (1996).[26] A. Mohri et al., Jpn. J. Appl. Phys. 37, 664 (1998).[27] D. H. E. Dubin, Phys. Rev. Lett. 66, 2076 (1991).[28] M. D. Tinkle et al., Phys. Rev. Lett. 72, 352 (1994).[29] We cannot, however, exclude from these data the possi-

blity of T0 > 15 K, due, e.g., to some plasma heatingprocesses, since we have no direct measurement of T0.

[30] In fact, from the scaling alone, we cannot rule out thecontribution from radiative recombination (R� T�0:6),although its predicted rate, assuming no magnetic field,is too small by at least an order of magnitude. See [22].

[31] E.g., M. C. Fujiwara, AIP Conf. Proc. 793, 111 (2005).[32] N. Vanhaecke et al., Phys. Rev. A 75, 031402(R) (2007);

E. Narevicius et al., Phys. Rev. Lett. 100, 093003 (2008).

PRL 101, 053401 (2008) P H Y S I C A L R E V I E W L E T T E R S week ending1 AUGUST 2008

053401-5

High-resolution laser spectroscopy on the negative osmium ion

U. Warring,1, ∗ M. Amoretti,1 C. Canali,1 A. Fischer,1 R. Heyne,1 J. O. Meier,1 Ch. Morhard,1 and A. Kellerbauer1, †1Max Planck Institute for Nuclear Physics, Saupfercheckweg 1, 69117 Heidelberg, Germany

(Dated: October 5, 2008)

We have applied the technique of electric-field detachment to excited negative atomic ions for thefirst time, resulting in an enhancement of the excited-state detection efficiency for spectroscopy bytwo orders of magnitude. Applying the new method, a measurement of the bound–bound electricdipole transition frequency in 192Os− was performed using collinear spectroscopy with a narrow-bandwidth cw laser. The transition frequency was found to be 257.831190(30) THz [wavelength1162.74706(14) nm; wavenumber 8600.3227(10) cm−1], in agreement with the only prior measure-ment, but with roughly 150-fold higher precision. Both two-photon detachment and one-photonexcitation followed by electric-field detachment were employed in an otherwise identical setup, thusallowing the first direct determination of the cross-section for the resonant excitation process.

PACS numbers: 32.80.Gc, 32.30.Bv, 32.70.Cs, 37.10.Rs

The potential experienced by the valence electron of anegative atomic ion is both shallow and short-ranged [1].Hence, in stark contrast to neutral atoms or positiveions, only a limited number of bound states (if any) aresupported. Their binding energies are typically aboutan order of magnitude smaller than in atoms or posi-tive ions. Bound excited states exist in only a minorityof elements that form negative ions [2]. Among these,those cases where bound states of both odd and even par-ity are present are of particular interest. Since electric-dipole transitions between such states are allowed, theyare more amenable to experimental study using standardatomic-physics techniques, such as laser spectroscopy andfluorescence detection. Furthermore, such an electric-dipole transition could be used to laser-cool a sample ofconfined negative ions [3]. In this context, the resonantcross-section of the transition and the excited-state life-time are of major interest, because they determine therequired laser power, the expected two-photon detach-ment loss rate and the total cooling time.

Opposite-parity bound states have been predicted forthe anions of some lanthanides and actinides [4–7] andfor cesium [8–10], but for cesium and lanthanum theirexistence was later ruled out experimentally [11, 12].Some years ago, a survey of the negative osmium ionusing infrared (IR) laser photodetachment spectroscopy(by two-photon absorption) with a pulsed dye laser led tothe discovery of a strong resonant transition just belowthe photodetachment threshold [13]. This experimentalevidence, combined with theoretical calculations on theground state configuration [14], yields the energy leveldiagram shown in Fig. 1.

In this Letter, we report on the results of high-resolution laser spectroscopy on the relevant electric-dipole transition between the 4Fe ground and 6Do boundexcited states in the negative osmium ion. The exper-imental precision of the transition frequency was im-proved by more than two orders of magnitude, as com-pared with the only previous measurement. A high-

0.000

50

100

150

200

250

0.25

0.50

0.75

1.00

(eV)(THz)

J = 7/2

Jg = 9/2

6Do

4Fe

J = 5/2J = 3/2

Je

detachmentthreshold

1162

.75

nmFIG. 1: Energy level diagram for 192Os−. The wiggly arrowshows the explored transition from the Jg = 9/2 (ground)state to the Je (excited) state.

precision determination of the transition frequency re-quired the use of a continuous-wave (cw) laser. Whilesuch narrow-bandwidth light sources yield narrower res-onances as well as larger observed cross-sections thanpulsed lasers, they cannot deliver the high instantaneousintensities which characterize pulsed lasers. Therefore,we applied the technique of electric-field detachment, firstconceived almost 50 years ago [15], to excited negativeions for the first time. In this way, the detection efficiencywas increased by two orders of magnitude compared withtwo-photon detachment. Furthermore, we were able tomeasure the cross-section of the transition directly, with-out resorting to theoretical models of the combined res-onant and non-resonant processes.

The setup (see Fig. 2) with which the present mea-surements were performed is installed at the Max PlanckInstitute for Nuclear Physics (MPIK) in Heidelberg, Ger-many. The negative ions are produced with a Middleton-type sputter negative-ion source [16]. They are extractedand accelerated to form a beam whose energy can be set

2

500 mm

einzel lens electrostaticquadrupole

negativeion source

electrostaticquadrupole

electrostaticbender

Faradaycup

Faradaycup

massseparator

laser beamcw OPO

wavemeterfeedbackloop

F-cupMCP

CCDcamera

aperture

ionizerdeflector

192Os-

beam

electric-fielddetachment

V-

V+

192Os

192Os-

photo-detachment

photo-excitation

FIG. 2: Sketch of the experimental setup for the collinear laserspectroscopy. The inset is an enlarged sketch of the spectrom-eter section which illustrates the two possible mechanisms forelectron detachment.

to E = 2.5. . . 6.5 keV, before being mass-separated in alarge (R = 500 mm) dipole magnet with a typical resolv-ing power of 180. After the mass separation, the 50 nAion beam consists of over 90% of 192Os−, with low impu-rities of 190OsH− and 192OsH−. An electrostatic benderguides the negative ions into the spectrometer section,which consists of an entrance diaphragm, a set of ioniz-ing diaphragms, a deflector, a micro-channel plate detec-tor (MCP) and a Faraday cup. All diaphragms have adiameter of 7.5 mm, and the overall interaction region is520 mm long. In the so-called ionizer the beam passesa longitudinal electric field of up to 2 × 106 Vm−1. Theionizer is built as a sandwich of three apertures coveredby copper meshes (transparency 70%). To the centralaperture a voltage of up to ± 6.5 kV can be applied. Adeflector leads the ions into a Faraday cup, at which 10%(5 nA) of the mass-seperated beam typically arrive. Inforward direction the MCP counts neutralized particleswhich are not deflected.

The light is produced by a cw optical parametric oscil-lator (OPO) system custom-built for this experiment (Xi-ton Photonics), which is pumped by a frequency-doubledNd:YAG laser. The pump beam at 532 nm wavelength isfocused into the periodically poled lithium niobate crys-tal (PPLN), which is embedded in a bow-tie cavity. Theoptical amplification yields a signal of 980 nm and anidler wave of 1163 nm fulfilling the quasi-phase-matchingcondition. The resonator oscillates on the idler wave, al-lowing roughly 4% of it to be coupled out and used forthe experiment. The laser beam has a bandwidth belowΓlas ≤ 5 MHz, and at a pumping power of 2 W morethan 170 mW of infrared light is provided.

νcenter - 257892166 (MHz)-75 -50 -25 0 25

two-photondetachment (×10)

electric-fielddetachment

50 750

10000

20000

30000

40000

50000

num

ber o

f det

ecte

d pa

rticl

es

FIG. 3: Typical resonance of the dipole transition at an ionbeam energy of 5 keV. It also shows the efficiency gain due tothe field-detachment process in comparison to the two-photonprocess.

The wavelength is determined and stabilized via awavemeter (HighFinesse WSU-30 IR), which is calibratedby a stabilized diode laser. The calibration laser is lockedto the D2 line in 6Li via Doppler-free-spectroscopy. Theabsolute accuracy of 30 MHz of the wavemeter limits thefinal uncertainty of our experiment. Since the MCP canbe moved out of the beam axis, the collimated laser beam(≈ 1 mm diameter) can be projected through the entirespectrometer arm and aligned with the help of a CCDcamera (DAT TaperCamD). It is a well-known advan-tage of collinear spectroscopy that the effect of velocitybunching reduces the Doppler width of the resonance (seefor example [17]). For our typical operating parameters,an ion temperature of T ≈ 1500 K and an accelerationvoltage of 5 kV, a reduction of about a factor ten withrespect to the transverse case is achieved.

During data taking the OPO frequency can be sweptcontinuously over a range of 1.5 GHz. For high-resolutionmeasurements, the laser is scanned over a smaller regionaround the resonance. If an ion in the interaction zoneis excited, it is either photo-detached by a second pho-ton, as in the work of Bilodeau and Haugen [13], or willbe detached by the electric field of the ionizer (see insetof Fig. 2). In both cases the neutral atom will be de-tected by the MCP, with a detection efficiency of about40%. In order to subtract background events, a chop-per is introduced into the laser beam. Figure 3 showsa typical resonance recorded at 5 keV beam energy. Itclearly shows the dramatic enhancement effect due to theionizer. The peak width of Γres = 45 MHz is dominatedby the Doppler width of the ion beam, and the shape iscompatible with a Gaussian line profile except for a slightasymmetry, which is due to a corresponding asymmetryin the velocity distribution of the ions.

Since in a parallel collinear setup all measuredfrequencies are blue-shifted, data points at different

3

ion beam energy (keV)

257.900

257.895

257.890

257.885

257.880

257.875

257.870

3 4 5 6

dopp

ler s

hift

frequ

ency

(TH

z)

b)

a)

c)resi

dual

s(M

Hz)

0

-60

60

FIG. 4: a) Blue-shifted resonance frequencies as a functionof the ion beam energy. The error bars are too small to bevisible. The solid curve is the resulting fit for the Dopplershift. b) For illustration the function is shown over the wholerange (without explicit scales). c) Residuals of the fit areshown to illustrate the fit quality.

beam energies were taken (see Fig. 4) to extract therest frame resonance frequency from fitting the datawith the simple function for the Doppler shift ν =ν0

√[c + v(E + ΔE)]/[c − v(E + ΔE)]. In addition to

the un-shifted transition frequency ν0, a possible offsetof the beam energy ΔE was allowed for in the fit. Thequality of the fit is illustrated by the residuals shownin Fig. 4(c). The resulting ν0 = 257.831190(30) THzis consistent with the previous experimental value of257.8341(46) THz [13] (deviation 0.6σ), but more thantwo orders of magnitude more precise. The statistical un-certainty is 2.6 MHz, and the total uncertainty is limitedby the frequency measurement with the wavemeter.

With the combination of laser excitation and fielddetachment, it is possible to measure the binding en-ergy of the excited state directly. For this purpose,the laser was stabilized to the center of the resonancewithin 5 MHz and the electric field was scanned from 0up to 2 × 106 Vm−1. Saturation of detached ions oc-cured at an electric field of 6 × 105 Vm−1. After mod-eling the resulting saturation data with a theoretical de-scription for field detachment [18, 19], the binding energywas extracted and found to be 11(2) meV, in agreementwith, but less precise than the indirect determinationby laser photo-detachment spectroscopy, which yielded11.48(12) meV [13].

For a determination of the resonant cross-section, it isuseful to consider the time evolution of the ground andexcited state populations in the beam, as well as the neu-tralized atoms, for different laser intensities, on resonanceand at constant ion beam energy. In order to describe thecombined processes of photo-excitation and electric-fielddetachment of the excited state while also taking into ac-count the sequential two-photon detachment, a system of

standard rate equations is introduced:

dNg(t)dt

= − σ0φNg(t) + (σ0φ + τ−1) Ne(t) (1a)

dNe(t)dt

= σ0φNg(t) − (σ0φ + τ−1 + σdφ) Ne(t) (1b)

dNd(t)dt

= σdφNe(t), (1c)

where Ng and Ne are the ground and excited state (laterfield-detached) populations and Nd is the number ofphoto-detached atoms, respectively. τ is the lifetime ofthe excited (Je) state into the ground (Jg) state and φis the photon flux. In this model a possible decay intothe intermediate (J = 7/2 and 5/2) states is neglectedbecause the partial lifetimes, which scale as ν−3, are ex-pected to be 8 times longer into those channels.

The set of differential equations (1a)–(1c) can be solvedanalytically and rearranged to express the populationNe(t) and Nd(t) (where t is the time of flight of the ionswithin the laser beam) as a function of φ. The pho-ton flux is modeled to have a spatial Gaussian profile,in line with observations from the beam profile CCDcamera. Finally, the number of neutralized particlesNneut(σ0, τ, σd, N0, Plas) =

∫Ne(t)+Nd(t)dt is a function

of the average laser power and has three independent pa-rameters: The resonant and non-resonant cross-sectionsσ0 and σd and the number of ions within the overlap re-gion N0. A fourth parameter is the lifetime τ of the ex-cited state, which is however related to the cross-sectionσ0 via

τ = c2/(4π2σ0ν20Γres) (2)

when neglecting alternative decay channels as indicatedabove. For the purpose of this analysis, τ was neverthe-less treated as an independent parameter of the function.It is important to point out that this analysis does notrely on a precise knowledge of the MCP detection effi-ciency, provided it is constant during the course of themeasurement. The function Nneut is very sensitive to theparameter of interest, σ0, and much less sensitive to allother parameters, with the exception of N0, which corre-sponds to the asymptotic value of the function.

The number of neutral atoms detected on the MCPwas recorded for beam energies ranging from 2.5 keV to5.5 keV as a function of the laser intensity, which wasvaried via a polarizing beam splitter from 0 to 160 mW,without changing other laser beam characteristics. Fig-ure 5 shows a typical measurement at E = 2.5 keV,along with a fit according to the rate equation model.Ion-optical simulations have shown that the beam diver-gence between the diaphragms is 1.5◦. This effectivelyreduces the interaction region by 30%, but has otherwise

4

laser power (mW)

num

ber o

f det

ecte

d pa

rticl

es

25 50 75 100 125 150

2000

6000

10000

14000

FIG. 5: Number of detected atoms vs. laser intensity at theresonance frequency at fixed ion beam energy. The solid curveis a fit to the data according to Eqs. (1a)–(1c), which yieldsthe cross-section σ0 for the transition.

no consequences for the parameteres obtained from thefit. The weighted mean of 10 such measurements yields afinal value of σ0 = 2.5(7) × 10−15 cm2, where the uncer-tainty includes a contribution which is equal in magni-tude to the beam divergence correction. While great carewas taken to exclude other effects which can mimic theasymptotic behavior of the data, in particular the MCPresponse cannot be ruled out completely. Such an effectwould make the cross-section appear larger than the truevalue. The fit to the data is not sufficiently sensitive tothe parameter τ , the lifetime of the excited state, to yielda definite value. Therefore, it was only possible to infer alower limit of τ ≥ 30 μs. Similarly, the fit result does notconstrain the photo-detachment cross-section very well,and only a rough estimate of σd ≈ 10−17 cm2 was ob-tained, in line with the expected value for a non-resonantprocess. As pointed out above, the mean lifetime canalso be deduced from the cross-section via Eq. (2), usingΓres = 45 MHz, which represents the experimental widthof the resonance. In this way, a value of τ = 3(1) ms isobtained, in agreement with the limit from the fit.

The measured observed cross-section and correspond-ing Einstein coefficient A ≈ 330 s−1 confirm that theresonance is due to an electric-dipole transition. The Ein-stein coefficient is, however, at the lower end of the scalefor E1 transitions, but not unusual for a spin-forbiddenresonance. Our measurements indicate that the naturallinewidth is even narrower than suggested by the resultof Bilodeau and Haugen, who found A ≈ 104 s−1 [13]. Asconcerns the prospect of laser cooling with this transition,the achievable Doppler temperature will in the foresee-able future be limited by the laser bandwidth. With ourlaser and at a detuning of δ = Γlas/2 the cooling rate maybe as low as 50 Hz and cooling times from 80 K to theDoppler temperature prohibitively long. Therefore, pre-cooling to liquid-helium temperature may be required,

resulting in a cooling time of roughly 5 minutes.In conclusion, the only known bound–bound transi-

tion between states of opposite parity in an atomic anionhas been studied by high-resolution laser spectroscopyand its transition frequency determined to 10−7 preci-sion. This is the most precise study of any atomic transi-tion in negative ions. While the Einstein A coefficient ofthe relevant transition is lower than previously found, ourwork confirms that laser cooling of Os− should be feasi-ble. If demonstrated to work, this technique will allowthe preparation of ultra-cold samples of any negative ion,ranging from elementary particles to molecular anions.

This work was supported by the German ResearchFoundation (DFG) within the Emmy Noether programunder Contract No. KE1369/1-1. We thank the MPIKaccelerator group and workshop, in particular M. Konig,V. Mallinger and M. Beckmann, for their invaluable sup-port. The assistance of the group of S. Jochim for thewavemeter calibration is gratefully acknowledged Finally,we are indebted to D. Beck (Michigan Technological Uni-versity), R. C. Bilodeau (Lawrence Berkeley NationalLaboratory) and J. Walz (University of Mainz) for theircomments on the manuscript.

∗ To whom correspondence should be addressed; Electronicaddress: u.warring@mpi-hd.mpg.de

† Electronic address: a.kellerbauer@mpi-hd.mpg.de

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(1989).[11] A. M. Covington et al., J. Phys. B 31, L855 (1998).[12] M. Scheer et al., Phys. Rev. Lett. 80, 684 (1998).[13] R. C. Bilodeau and H. K. Haugen, Phys. Rev. Lett. 85,

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