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Cold free-radical molecules in the laboratory frame J. R. Bochinski, Eric R. Hudson, H. J. Lewandowski, and Jun Ye JILA, National Institute of Standards and Technology and Department of Physics, University of Colorado, Boulder, Colorado 80309-0440, USA (Received 25 March 2004; published 19 October 2004) A special class of molecules that are important to many subfields in molecular dynamics and chemical physics, namely free-radical molecules, now enjoy a significant degree of center-of-mass motion control in the laboratory frame. The example reported in this paper concerns the hydroxyl radical sOHd, which, after the internal degrees of freedom are cooled in a supersonic expansion, has been bunched, accelerated, and slowed using time-varying inhomogeneous electric fields. In situ observations of laser-induced fluorescence along the beam propagation path allows for detailed characterization of the longitudinal phase-space manipulation of OH molecules by the electric fields. The creation of a pulse containing 10 3 –10 6 molecules possessing a longitu- dinal velocity spread from 2 to 80 m / s around a mean laboratory velocity variable from 550 m / s to rest with only a few mm spatial extent represents an exciting and useful experimental capability for exploring free- radical dynamics. DOI: 10.1103/PhysRevA.70.043410 PACS number(s): 33.80.Ps, 33.55.Be, 39.10.1j I. INTRODUCTION Efforts to create, study, and utilize samples of cold mol- ecules are at the forefront of experimental atomic and mo- lecular physics [1–5]. Scientific explorations of cold molecu- lar samples will allow spectroscopy to be performed at the fundamental level where vibrational relaxation can be di- rectly revealed and extremely weak interactions can be in- vestigated. Metrological applications will surely follow. The long interrogation times that cold molecules will provide is critical to a number of precision measurement projects such as the search for the permanent electron electric dipole mo- ment [6,7] and improved values of fundamental constants like the fine structure a. At low translational energies, mo- lecular orientation will play an important role in novel cold collisions [8–12] and ultracold molecular dynamics [13]. Ob- servations of cold atom–molecule interactions may also re- veal different regimes in physical chemistry [14]. Further, there has been a proposed application in quantum computing [15] for trapped ultracold polar molecules. Heteronuclear molecules possess permanent electric di- pole moments that create interesting opportunities for control of intermolecular interactions. While a number of research groups are actively pursuing experiments to form ultracold polar molecules utilizing photoassociation techniques to cre- ate weakly bound, vibrationally excited molecules from double-species magneto-optical traps of cold atoms [16–18], some other groups have focused on ground-state molecules that are manipulated by buffer gas cooling [1,19,20] or Stark deceleration [21–25]. In this paper we focus on a particular species of stable molecules, namely the diatomic hydroxyl radical sOHd. We note that, as with most molecular systems, at this time it is not technically practical to create cold OH samples using the above-mentioned cold atom approach. Nevertheless, while alternate techniques must be employed to produce the cooled sample, neutral free radicals remain an extremely attractive and significant class of particles for cold molecule research [26]. Historically important as a focal point of study in physical chemistry [27,28], astrophysics [29,30], atmospheric, [31] and combustion physics [32–34], these chemically reactive molecules typically possess large electric and magnetic dipole moments, thus supporting a va- riety of interactions. In the low-temperature regime, these interactions may create interesting effects; for example, at temperatures of ,1 mK, the translational energy becomes less than the intermolecular electric dipole-dipole interaction energy. Considering that the relative orientation of these di- poles determines whether the interaction is attractive or re- pulsive, these polar molecules can easily influence each oth- er’s trajectory and lead to complex dynamics. In principle, an external electric field can then be used to guide collisions and perhaps even to exert a different means for management of chemical reactions. Interestingly, this mechanism repre- sents a profoundly different type of control over collisions than the usual resonant scattering between cold atoms ex- erted by a magnetic field. The relatively strong dipolar inter- action should also open different analogies to condensed- matter systems, particularly those systems that interact by strong spin-dependent forces [35]. It may even be possible that the cold molecules could form a “dipolar crystal,” in analogy with an ionic crystal formed in ion traps [36]. Fi- nally, we note that experimental conditions under which both electric and magnetic fields simultaneously interact with the cold molecules may naturally provide even more useful and interesting dynamics to investigate [37]. Hence production of a large collection of neutral free- radical molecules populating a single quantum state and hav- ing a small center-of-mass motion in the laboratory frame represents a critical first step towards realizing these poten- tial cold molecule experiments. We employ the technique of Stark deceleration to prepare cold packets of the OH mol- ecules. Molecules produced at low temperatures by the Stark slowing process will be in their rovibrational ground states, and therefore do not suffer from rovibration-changing colli- sion losses. However, at low-temperature limit and under certain external electric fields and sufficient densities, the molecules in a weak-field seeking state can still experience PHYSICAL REVIEW A 70, 043410 (2004) 1050-2947/2004/70(4)/043410(18)/$22.50 ©2004 The American Physical Society 70 043410-1

Cold free-radical molecules in the laboratory framejila.colorado.edu/~junye/yelabsOLD/pubs/scienceArticles/... · 2008. 9. 18. · lecular orientation will play an important role

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  • Cold free-radical molecules in the laboratory frame

    J. R. Bochinski, Eric R. Hudson, H. J. Lewandowski, and Jun YeJILA, National Institute of Standards and Technology and Department of Physics, University of Colorado,

    Boulder, Colorado 80309-0440, USA(Received 25 March 2004; published 19 October 2004)

    A special class of molecules that are important to many subfields in molecular dynamics and chemicalphysics, namely free-radical molecules, now enjoy a significant degree of center-of-mass motion control in thelaboratory frame. The example reported in this paper concerns the hydroxyl radicalsOHd, which, after theinternal degrees of freedom are cooled in a supersonic expansion, has been bunched, accelerated, and slowedusing time-varying inhomogeneous electric fields.In situ observations of laser-induced fluorescence along thebeam propagation path allows for detailed characterization of the longitudinal phase-space manipulation of OHmolecules by the electric fields. The creation of a pulse containing 103–106 molecules possessing a longitu-dinal velocity spread from 2 to 80 m/s around a mean laboratory velocity variable from 550 m/s to rest withonly a few mm spatial extent represents an exciting and useful experimental capability for exploring free-radical dynamics.

    DOI: 10.1103/PhysRevA.70.043410 PACS number(s): 33.80.Ps, 33.55.Be, 39.10.1j

    I. INTRODUCTION

    Efforts to create, study, and utilize samples of cold mol-ecules are at the forefront of experimental atomic and mo-lecular physics[1–5]. Scientific explorations of cold molecu-lar samples will allow spectroscopy to be performed at thefundamental level where vibrational relaxation can be di-rectly revealed and extremely weak interactions can be in-vestigated. Metrological applications will surely follow. Thelong interrogation times that cold molecules will provide iscritical to a number of precision measurement projects suchas the search for the permanent electron electric dipole mo-ment [6,7] and improved values of fundamental constantslike the fine structurea. At low translational energies, mo-lecular orientation will play an important role in novel coldcollisions[8–12] and ultracold molecular dynamics[13]. Ob-servations of cold atom–molecule interactions may also re-veal different regimes in physical chemistry[14]. Further,there has been a proposed application in quantum computing[15] for trapped ultracold polar molecules.

    Heteronuclear molecules possess permanent electric di-pole moments that create interesting opportunities for controlof intermolecular interactions. While a number of researchgroups are actively pursuing experiments to form ultracoldpolar molecules utilizing photoassociation techniques to cre-ate weakly bound, vibrationally excited molecules fromdouble-species magneto-optical traps of cold atoms[16–18],some other groups have focused on ground-state moleculesthat are manipulated by buffer gas cooling[1,19,20] or Starkdeceleration[21–25]. In this paper we focus on a particularspecies of stable molecules, namely the diatomic hydroxylradicalsOHd. We note that, as with most molecular systems,at this time it is not technically practical to create cold OHsamples using the above-mentioned cold atom approach.Nevertheless, while alternate techniques must be employedto produce the cooled sample, neutral free radicals remain anextremely attractive and significant class of particles for coldmolecule research[26]. Historically important as a focal

    point of study in physical chemistry[27,28], astrophysics[29,30], atmospheric,[31] and combustion physics[32–34],these chemically reactive molecules typically possess largeelectric and magnetic dipole moments, thus supporting a va-riety of interactions. In the low-temperature regime, theseinteractions may create interesting effects; for example, attemperatures of,1 mK, the translational energy becomesless than the intermolecular electric dipole-dipole interactionenergy. Considering that the relative orientation of these di-poles determines whether the interaction is attractive or re-pulsive, these polar molecules can easily influence each oth-er’s trajectory and lead to complex dynamics. In principle, anexternal electric field can then be used to guide collisionsand perhaps even to exert a different means for managementof chemical reactions. Interestingly, this mechanism repre-sents a profoundly different type of control over collisionsthan the usual resonant scattering between cold atoms ex-erted by a magnetic field. The relatively strong dipolar inter-action should also open different analogies to condensed-matter systems, particularly those systems that interact bystrong spin-dependent forces[35]. It may even be possiblethat the cold molecules could form a “dipolar crystal,” inanalogy with an ionic crystal formed in ion traps[36]. Fi-nally, we note that experimental conditions under which bothelectric and magnetic fields simultaneously interact with thecold molecules may naturally provide even more useful andinteresting dynamics to investigate[37].

    Hence production of a large collection of neutral free-radical molecules populating a single quantum state and hav-ing a small center-of-mass motion in the laboratory framerepresents a critical first step towards realizing these poten-tial cold molecule experiments. We employ the technique ofStark deceleration to prepare cold packets of the OH mol-ecules. Molecules produced at low temperatures by the Starkslowing process will be in their rovibrational ground states,and therefore do not suffer from rovibration-changing colli-sion losses. However, at low-temperature limit and undercertain external electric fields and sufficient densities, themolecules in a weak-field seeking state can still experience

    PHYSICAL REVIEW A 70, 043410(2004)

    1050-2947/2004/70(4)/043410(18)/$22.50 ©2004 The American Physical Society70 043410-1

  • non-negligible inelastic scattering losses to strong-field seek-ing states[9]. The Stark deceleration approach[21–25,38]has worked effectively with molecules such as CO, ND3,OH, and YbF, resulting in experimental observations ofslowing and trapping. Our previous work[24] demonstrateddeceleration of stable packets of OH, with a minimum trans-lational velocity in the laboratory frame of 140 m/s and avelocity spread less than 2.7 m/s. In the present work, wereport further progress along this research direction, culmi-nating with the present capability to produce phase stablepackets of molecules with a molecular-frame temperaturefrom ,1 K to ,tens of mK around a mean laboratory ve-locity variable from 550 m/s to essentially zero. We alsodocument detailed technical approaches at various stages ofour cold molecule machine.

    The complex structure of the molecular states and theassociated energy levels of OH will be described in the nextsection. The Stark shift of the relevant molecular states dueto an external electric field is also introduced, along with themolecular detection scheme based on sensitive, laser-inducedfluorescence(LIF) measurement. Section III gives a generaldescription of the entire experimental setup, with a brief dis-cussion regarding construction of the supersonically cooledOH beam source, which combines an interesting dischargeapparatus with a pulsed supersonic expansion valve. Armedwith the understanding of the Stark effect of OH, we de-scribe in Sec. IV beam propagation into the acceptance ap-erture of the decelerator. This process is aided by an electrichexapole-based molecular lens that provides initial-state se-lection and focusing. Section V provides underlying prin-ciples and mechanisms responsible for the Stark decelerationprocess. Theoretical descriptions of the longitudinal phase-space evolution and comprehensive numerical simulationsusing realistic molecular parameters and modeled spatial dis-tributions of inhomogeneous electric fields are presented.Practical information concerning the design, fabrication,construction, and preparation of the Stark decelerator isgiven in Sec. VI. The simulation model presented in Sec. Vgenerates results that provide excellent agreement to the ex-perimental observations reported in Sec. VII. Thein situ LIFdetection enables detailed characterization of the experimen-tal phase-space evolution of the molecular packets at variousstages along the entire decelerator and within the quadrupoleelectrostatic trap region. These observations demonstrate athorough understanding and control of the molecular slowingprocess and reveal that the present experimental system isfully functional for ongoing research in molecular trappingand cold molecule collisions. Finally, in Sec. VIII we discussfuture directions of the experiment involving improved elec-trostatic and magnetic trapping, limited laser cooling, as wellas collision experiments between trapped atomic and mo-lecular samples.

    II. STRUCTURE OF OH

    The neutral hydroxyl free-radicalsOHd, though extremelychemically reactive, is a stable, diatomic molecule. Becausethe basic molecular energy structure is well understood, herewe will discuss only the states relevant to the current experi-

    ment. For low rotation levels, the angular momentum cou-pling of the2p electronic ground state of the OH molecule issufficiently described by Hund’s case(a) [39]. Under thisinteraction scheme, both the electron orbital angular momen-tum L and electron spinS are coupled to the intramolecularaxis, leading to the definition of the total electron angularmomentum asV=L+S, where uLu=1 sS=1/2d representsthe projection ofL sSd onto this axis. This coupling results intwo spin-orbit states, where the2P3/2 state lies,126 cm

    −1

    below the2P3/2 state as shown in Fig. 1. Strong spin-orbitcoupling sASO=−139 cm−1d is responsible for the observedlarge splitting between the twoV branches. The molecularangular momentumJ in the laboratory frame is defined asJ=L +S+R, whereR represents the nuclear rotation angularmomentum. The allowed values ofJ in the laboratory frameare given asJ=V, V+1, V+2, . . .. Therelatively large en-ergy splitting betweenJ states is due to the small moment ofinertia of the molecule and subsequent large rotational con-stant. The coupling between the nuclear rotation and theelectron angular momentum(projection ofL along the inter-nuclear axis) results in lambda-type splitting(l doubling) ofeach state, denoted asf and e states. In the figure, theseenergy separations are exaggerated for clarity. For16OH withan intrinsic nuclear spinI of 1/2, the free-radical molecule isa boson. The total angular momentum is given byF= I +J.Eachl-doublet component is split into hyperfine states thatare characterized by a symmetry indexp that defines thestate’s paritys±d. The hyperfine energy separations have alsobeen exaggerated for clarity of presentation.

    The 2S first electronic excited state of the OH moleculehas an electron spin of 1/2 but no electron angular momen-tum; thus the appropriate couplings are well described byHund’s case(b). For this angular momentum configuration,the only important interaction is between the nuclear rotation

    FIG. 1. Relevant energy-level structure of OH, showing the firstelectronically excited state and the first two vibrational levels in theelectronic ground state.e indicates symmetry(“e” and “f ” states)from l doubling andp indicates overall parity. The transition(solidarrow) and decay(wavy, dotted arrow) pathways used for laserinduced fluorescence detection of OH are also indicated.

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  • of the moleculeR and the electron spinS— so-calledrdoubling. This coupling separates everyJ state that has nonzeroR into two states of the same parity. Figure 1 shows theimportant energy levels and schematically depicts the exci-tation and detection pathways, as described in detail below.

    Because thel-doublet states possess opposite parity andsmall energy separations, adjacent levels of the ground-stateOH readily mix under the interaction of the molecule’s per-manent electric dipole(1.67 D[40]) with an external electricfield. The energy of these mixed states increases(weak-fieldseeking states) or decreases(strong-field seeking states) as afunction of the electric field strength, as shown for the rovi-brational ground state of OH in Fig. 2(a). The Stark energyshift evolves from quadratic to linear when the energychange due to the applied field exceeds thel-doublet split-ting value of 0.055 cm−1. The ground-state shift is unaffectedby the next higher rotational state due to the large energyseparation of,84 cm−1. In the high electric-field regime, thecomplex energy levels depicted in Fig. 2(a) emerge as fourdistinct families. As shown in Fig. 2(b), for the Stark slowingexperiment discussed here, the weak-field seeking states aremost relevant, with the2P F=2, umFu=2, 1 states experienc-ing approximately three times the Stark energy shift of the2P3/2 F=2, umFu=0, and

    2P3/2 F=1, umFu=0,1 states. We notemolecules in strong-field seeking states do not survive thefirst state-selection device, namely the hexapole acting as amolecular focusing lens, and therefore do not contribute toany observed signals thereafter.

    Optical detection via fluorescence measurement is a pow-erful tool in atomic and molecular physics experiments. Arelatively favorable branching ratio, a large difference be-tween the excitation and decay wavelengths, and a reason-able quantum efficiency in fluorescence detection make laserinduced fluorescence(LIF) a versatile approach for measur-ing the hydroxyl radical. The excitation source is tuned reso-nant with theX 2P3/2 sv=0d→A2 S+ sv=1d electronic tran-sition at 282 nm for subsequent detection of the red-shiftedradiative decay around 313 nmA 2S+ sv=1d→X 2P3/2 sv=1d, as shown in Fig. 1. The separation in wavelength allowseffective optical filtering to reduce the background scatter-ing, as discussed in detail in the next section. The character-istic fluorescence 750-ns decay lifetime provides a distinc-tive signature of the presence of OH molecules.

    III. OH BEAM SOURCE AND DETECTION

    Supersonic expansion in molecular beam experiments is awidely used technique. Under proper operating conditions,rotational and vibrational temperatures are significantly low-ered along with the benefit of a reduced translational velocityspread in the molecular frame. Within the present experi-ment, collisions during the expansion represent the only truecooling mechanism. The maximum phase-space densityachievable in the experiment is determined at this stage sinceduring the subsequent deceleration process the phase-spacedistribution of the molecules undergoes conservative rotationwithout any enhancement in density. Therefore, as long asthe relatively large translational speed of the molecular beamcan be compensated for by the slowing capability of the

    Stark decelerator, a supersonic expansion provides a veryuseful initial source for creation and experimentation of coldmolecules.

    Figure 3 illustrates the overall experimental setup, show-ing the discharge and the pulsed valve configuration, alongwith the subsequent skimmer, hexapole, decelerator stages,and the electrostatic quadrupole trap. The experiment utilizesa seeded, pulsed supersonic beam combined with electricdischarge to realize an efficient free-radical source. The

    FIG. 2. (a) The Stark energy shift for ground-state OH mol-ecules in low electric fields. The initialesfd state is shown in thelower (upper) panel, where the hyperfine levels are indicated next tothe traces.(b) The Stark shift for ground state OH molecules in highelectric fields. The vertical dotted line indicates the regime wherethe Stark decelerator operates; the dashed horizontal line denoteszero energy.

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  • source apparatus creates an intense OH molecular beam, pos-sessing both narrow initial temporal width and small longi-tudinal velocity spread, primarily populating only the lowestrotational ground-state energy level. XenonsXed, due to itslarge mass, is employed as an inert carrier gas to minimizethe initial molecular velocity. At a stagnation pressure of,3 atm, Xe bubbles through a small reservoir of deionizeds.10 MV cmd, distilled water sH2Od. When the valveopens, the carrier gass,99%d and seeded H2O s,1%d ex-pand supersonically into the vacuum chamber. The0.5-mm-diameter exit nozzle valve is operated at a 5-Hz rep-etition rate, creating a molecular supersonic beam with a fullpulse width of,100 ms.

    We utilize an electric discharge to generate the hydroxylradical moleculesduring the supersonic expansion. Suchmethods have been used previously[41–43]. Our approach[44] contains several key ingredients, including the use of ahot filament to aid in discharge initiation, selected voltagepolarity for maximum discharge stability, geometry of thedischarge electrodes to ensurewhere the discharge createsmolecules is well defined, as well as utilization of ams-scalehigh voltage(HV) pulse to control preciselywhen the dis-charge occurs. These beneficial improvements over earlierwork lead to a dramatic reduction in the discharge heating ofthe molecules, resulting in the production of a rotationallyand longitudinally colder radical beam, well suited for thedeceleration experiment.

    For the most stable discharge operation, the voltage po-larity is selected such that electrons are accelerated againstthe propagation direction of the expanding supersonic jet.Application of sufficiently high voltage to the electrodes dur-ing the molecular supersonic expansion enables self-initiating of an electric discharge that produces the hydroxylradical sOHd by disassociating the H2O [45]. When the OHcreation occurs spatially near to the nozzle in the expansionregion, the diatomic molecule is subsequently cooled by col-lisions with the more abundant Xe atoms, resulting in rota-tionally cold free-radicals. Empirically, we learned that oper-ating the discharge voltage in a short duration, pulsedmanner significantly reduces undesirable heating of the mo-lecular beam by the discharge. Moreover, employing acurrent-driven filament within the vacuum chamber in addi-tion to the pulsed high voltage ignites the discharge at asignificantly lower voltage level, further minimizing heatingto molecules during the supersonic expansion. We utilize afast switch to pulse the high voltage(typically, for 2 ms at−1.4 kV), resulting in increased OH production, lower rota-

    tional temperature, narrower longitudinal velocity spread,and reduced mean longitudinal velocity. Under normal oper-ating conditions, the source produces a free-radical molecu-lar pulse having a mean speed around 385 m/s with a fullwidth at half maximum velocity spread of 16% at a rota-tional temperature of,25 K, corresponding to,98.5% ofthe molecules in theJ=3/2 lowest rotational state.

    The filament-assisted discharge can occur at virtually anymolecular density during the supersonic expansion. Hencethe narrow-pulsed HV discharge can selectively create OHover a broad range in time within the,100-ms-wide mo-lecular pulse envelope. As the discharge duration is muchshorter than the molecular pulse, OH molecules generated atdifferent times within the pulse reflect the different instanta-neous characteristics of the supersonic expansion at the mo-ment of their creation. This effect is most directly manifestedas the ability to tune the mean longitudinal velocity of themolecular pulse, as depicted in Fig. 4. In this figure, pulsesof rotationally cold OH are measured by LIF after they havepropagated from the source to just in front of the molecularbeam skimmer. The pulses were created using identical dis-charge voltage amplitudes and pulse widths but varying thedischarge initiation time within the molecular pulse. This ini-tial creation time difference has been normalized for the

    FIG. 3. System schematic of Stark decelerator, displaying the pulsed valve, the molecular beam skimmer, the electric hexapole, theelectrode stages, and the trap region. The electrode stages alternate orientation(vertical-horizontal) as shown in the figure. The spatiallocations indicated by arrows correspond to the measured data traces in Fig. 5.

    FIG. 4. Controlled tuning of the initial mean molecular speed;varying the discharge initiation time creates OH pulses with differ-ing mean speedssVmd, FWHM velocity widths sDVd, andamplitudes.

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  • three data traces where time zero represents the dischargeinitiation; the subsequent change in arrival time demonstratesthe differences in pulse mean velocity. As the discharge ini-tiation time is varied from earlier to later within the overallmolecular pulse envelope, the amplitude and mean speed ofthe OH signal decreases while the velocity width increases,consistent with sampling OH production within the diminish-ing supersonic expansion.

    Potentially, background-free resonance fluorescence is ahighly sensitive technique for detecting small numbers ofmolecules. In analytical chemistry and biology, resonancefluorescence is used extensively for efficient detection andidentification of single molecules[46]. The sensitivity of thefluorescence detection technique depends upon the character-istics of the decay channels of the excited states, namely thatthe radiative branching ratios are favorable and quenchingprocesses are not significant. Further, for maximum detectedsignal, the decay photons should be collected over as large asolid angle as possible; in our experiment, intravacuum op-tics provide solid angle efficiencies of 0.5–4.5%, dependingon the specific spatial location. With quantum efficiencies inthe range of 10% for the cathode surfaces of modern photo-multipliers, one then expects a photoelectron event for every,200 fluorescent decays. The dark current of the quantumdetector is a few to a few tens of counts per second. How-ever, various phenomena may degrade the signal-to-noise ra-tio. Even with careful baffling and shielding, the most severelimitation on the detection sensitivity in the present experi-ment is due to scattered excitation laser photons, whichdominate stray background light.

    A key benefit of utilizing fluorescence detection as op-posed to a spatially fixed ionization-based scheme is the abil-ity to detectin situ molecules at multiple locations, greatlyincreasing the experimental flexibility and level of under-standing. OH signals are measuredwithin the deceleratorduring the actual slowing process, giving insight into theactive longitudinal phase-space manipulation of the mol-ecules by the pulsed, inhomogeneous electric fields. Specifi-cally, in the experiment we employ LIF detection to monitorthe hydroxyl radicals after the discharge, observe the focus-ing effects of the hexapole on the molecules, measure themolecular packet spectra at various positions within theStark decelerator, and finally, detect the molecules within theelectrostatic trap region.

    Using a beta barium borate(BBO) crystal to frequencydouble a 564-nm dye laser output(,10 ns pulse duration)creates the ultraviolet(UV) excitation light at 282 nm withhigh peak intensity. The excitation laser is counterpropagatedto the molecular pulse traveling down the central axis of theStark decelerator. The spectrally broad light sources,2 GHzd encompasses any Doppler-induced frequencyshifts in the OH resonance as the molecular longitudinal ve-locity changes during the deceleration process. Reduction ofthe laser scatter is paramount for optimized signal collection.First, due to the separation of the excitation and fluorescencewavelengths, the carefully selected photomultiplier tube(PMT) has a photocathode responsivity that is severely re-duced at the laser wavelength versus the fluorescence wave-length. Next, an interference filter selectively inhibits the la-ser light (103 suppression) versus the fluorescent photons

    (,20% transmission coefficient). We also utilize aswitchedPMT whose dynode voltages are quickly arranged during thelaser pulse so as to actively repel photoelectrons liberated bythe scattered UV light on the cathode material. The first,third, and fifth dynodes are used rather than the photocathodeitself for improved switching speed, while the rest of theelements in the dynode chain remain at their normal volt-ages. The usual state of the PMT is “interrupted;” in order toobserve the OH molecular decay signal an externally appliedcontrol pulse rapidly turns the detector “on” for,5 ms withthe appropriate dynode voltage levels for normal PMT op-eration. In this manner, a,104 suppression of the measuredlaser intensity is achieved, at a small expense of a fast noisespike generated by the switching currents. This repeatablenoise feature caused by the PMT switching is subtracted offas a background signal. We note additionally, this systemalso works well using fewer switched dynodes. For example,utilizing only two dynodes(e.g., the first and fourth dynode)provides attenuation of laser scatter by,103.

    The OH molecular signal is measured as a function oftime at a particular spatial location in the following manner.First, immediately prior to the measurements,1 msd, allhigh voltage electrodes within the vacuum chamber aregrounded to avoid Stark shifting of the OH transition fre-quency. Subsequently, before the molecules have had an op-portunity to exit the specific detection region, the excitationlaser pulse fires, generating the OH fluorescence signal. Thedetected photoelectrons from the PMT are amplified, aver-aged 300 times, and displayed on a digital oscilloscope overa ,5-ms time window to fully encompass the appropriatestate decay lifetime. Next, a background spectrum consistingof an equal number of averaged traces with the source dis-charge voltage off(and thereby, solely consisting of laserscatter, switching, and other intrinsic noise contributions) issubtracted from the measured signal, resulting in the cor-rected molecular fluorescence spectrum. This spectrum isthen integrated by the oscilloscope, giving a value directlyproportional to the number of OH molecules present in thedetection area at that time. The laser is stepped later in timerelative to when the valve opens, and the entire measurementis repeated. In this iterative manner, a spectrum consisting ofthe OH signal as a function of time is generated.

    Figure 5 shows time-of-flight(TOF) LIF measurements ofOH molecules at different spatial locations in the experimentas indicated in Fig. 3. Figure 5 trace(a) shows OH signalsdetected just before the skimmer(1.58 cm in height, 1.5-mm-diameter central aperture) tip. The peak amplitude ofFig. 5(a) corresponds,33106 molecules at a density of,109 cm−3, with an total pulse population,33107 mol-ecules. With no voltages present on the molecular focuser,the OH packet traverses the skimmer and hexapole region asshown in Fig. 5 trace(b). The approximate two orders ofmagnitude signal loss is due to transverse spreading of theOH beam. Operating the pulsed hexapole with high voltagesprovides state selection and transverse focusing, leading toenhanced signal sizes after the hexapole. Measurements aremade further downstream when the hexapole is in operation,as well as with constant voltages applied to all electrodestages. These unswitched voltages result in no net longitudi-nal velocity change but provide transverse confinement to

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  • the molecular pulse as it propagates down the slower; werefer to this mode of operation as “transverse guidance.” Fig-ure 5, traces(c)–(e) are observed OH signals as the pulsepropagates before the 23rd stage, the 51st stage, and into thecenter of the electrostatic trap region. The increase in mo-lecular pulse width corresponds to the expected “stretching”in the longitudinal direction that occurs under free flight asfaster molecules move ahead and slower molecules lag be-hind. Integration of measured peak areas at different obser-vation points reveal transverse loss of molecules within theslower, as discussed in more detail in Sec. VII[see Fig.10(d)].

    IV. ELECTRIC HEXAPOLE AS A MOLECULAR FOCUSER

    Electrostatic hexapoles have been widely used in beamexperiments to perform state-selected focusing[47–51] andspatial orientation[52–56] of weak-field seeking, Stark-sensitive molecules. In contrast to those experiments, thehexapole utilized here is quite short in length and functionsto increase the OH beam flux by matching molecules fromthe source into the acceptance aperture of the Stark decelera-tor. The hexapole is formed by six, hardened steel, 3.175-mm-diameter, 50-mm-long cylindrical shaped rods, set every60° at a center-to-center radius of 4.39 mm, mounted to aninsulated macor support disk. The rods are mechanically pol-ished and the ends are rounded to a smooth curvature. Alter-nate rods are electrically connected, thus forming two sets ofthree rods. Each set is charged to equal magnitude but oppo-site polarity high voltage. The hexapolar field distribution inthe transverse plane allows a weak-field-seeking molecule tobe confined and even focused in this plane, leading to trans-verse phase-space “mode matching” between the supersonicnozzle and the Stark decelerator.

    The electric fielduEW u of an ideal hexapole is given as[57]

    uEW u =3Vor

    2

    ro3 , s1d

    where Vo is the absolute value of the symmetric, oppositepolarity voltages applied to each set of rods,ro is the radius

    of the hexapole(from the center of the hexapole to the inneredge of the rods), and r is the radial spatial coordinate. Aweak-field seeking molecule will thus experience Stark po-tential energy asW«= umef fEu. We define an “effective” dipolemoment of the molecule asmeff=mkcosul, wherem is themagnitude of the electric dipole moment,u the angle be-tween the moment and the electric-field direction, andkcosul represents quantum-angular mechanical averagingover all angles. The radial forceFW is written as

    FW = − S6Vormeffro

    3 Dr̂ . s2dThis linear restoring force results in radial harmonic motionof the weak-field seeking molecules inside the hexapole fieldregion. Thus, in analogy to ray tracing in optics, it is possibleto define the focal lengthf of the hexapole in the thin-lenslimit (for l →0 asÎ6Vomef f/mro3sl /vd remains constant) as

    f = S ro36mef f

    DSmv2Vol

    D , s3dwhere l is the longitudinal length of the hexapole,n is themolecule’s longitudinal velocity, andm is the molecularmass. Equation(3) demonstrates the focusing strength of agiven hexapole linearly increases(decreases) with appliedvoltage(molecule kinetic energy). For a “real world” hexa-pole, the finite size of the rods can lead to deviation from Eq.(1) [58]. Accounting for this effect, as well as the full Starkshift as illustrated in Fig. 2(a), detailed numerical simula-tions of the hexapole focusing effect are shown in Fig. 6. Thetrajectory simulations deterministically map an initial vol-ume in phase space to a final volume, which is then matchedto the corresponding experimental data by proper weightingof initial molecular numbers. The figure shows three sets offocusing curves consisting of OH signals measured directly

    FIG. 5. TOF LIF measurements of the propagation of an OHmolecular pulse(a) before skimmer,(b) after hexapole,(c) beforethe 23rd stage,(d) before the 51st stage, and(e) in the trap region.Traces(c), (d), and (e) are taken with the hexapole energized andconstant, transverse guidance voltages applied to the slower.

    FIG. 6. Hexapole focusing curve for different OH molecularvelocities. The symbols represent the data points for molecules withvelocities of 350 m/s(squares), 385 m/s(diamonds), and 415 m/s(triangles), while the solid lines represent the corresponding simu-lation result. The inset depicts the contribution of the2P3/2 F=2,umFu=2, 1 states and the

    2P3/2 F=2, umFu=0 and2P3/2 F=1, umFu

    =0, 1 states to the observed signals for the 385 m/s trace.

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  • after the hexapole, under conditions where the applied hexa-pole voltage has been pulsed to match to the correspondinginput molecules’ velocity. Operating the hexapole in such aswitched manner is designed to give maximum benefit to aparticular velocity class, wherein the hexapole voltages arecontrolled by fast switches that rapidly charge the rods whenthe selected molecules enter—and then terminate the volt-ages to ground when the molecules exit—the hexapole re-gion. Thus molecules with speeds significantly different thanthe targeted velocity class experience less focusing power ofthe hexapole, minimizing the aberration effect from the dis-tribution of velocities in the molecular pulse. From compari-son of the simulations to the hexapole focusing data, thetransverse temperature of the OH beam is determined to be,4 K, consistent with a supersonically cooled molecularbeam. The upper inset in the figure depicts the contributionsfrom the two weak-field seeking states to the 385 m/s trace[see Fig. 2(b)], where molecules in the2P3/2 F=2, umF=0uand 2P3/2 F=1, umFu =0,1 states are marginally focused bythe hexapole fields, in contrast to the strong effect experi-enced by molecules populating the2P3/2 F=2, umFu =2,1states. The two weak-field seeking states are included in thesimulations with equal weighting.

    This figure demonstrates the powerful molecular-focusingcapability of the electric hexapole, as the OH molecules areobserved only a few millimeters past the end of the hexapolerods. However, for the deceleration experiment, the hexapoleis operated only to provide efficient molecular coupling intothe physical opening of the slower. This task requires simplymatching the transverse velocity and spatial spreads with thedecelerator cross-sectional acceptance and the subsequentrequisite focal length is thus longer than that needed to bringthe molecules to a sharp spatial focus. Experimentally, wefind utilizing ,7–9 kV applied voltages results in sufficienttransverse coupling. This empirical result agrees well withcomputer simulations of the process. Unless otherwise speci-fied, all subsequent data traces shown in this paper are takenwith operating the hexapole in this pulsed manner.

    V. THEORY AND SIMULATIONS OF THE STARKDECELERATOR

    An initial, well characterized, and relatively high phase-space density source of molecules in the ground state is criti-cal for the most efficient use of Stark deceleration. Super-sonic expansion provides a direct and convenient approachto meeting this goal. The conservative reduction of thepulse’s mean velocity is accomplished by exploiting theStark effect associated with weak-field-seeking molecules.As such a polar molecule moves from a low electric-fieldinto a high electric-field region, its internal energy increasesat the expense of its kinetic energy; thus itslows downas itclimbs the potential energy hill created by the increasingelectric field. If the electric field is rapidly extinguished, themolecule will lose this Stark potential energy. This proceduremay be repeated as many times as necessary to lower mol-ecule’s speed to any arbitrary final velocity. Critical param-eters associated with the deceleration process, such as thenumber of molecules and the associated velocity spread at

    the end of deceleration can be determined from a detailedunderstanding of the deceleration process and the related ex-perimental conditions.

    To understand the decelerator, it is necessary to examinethe electric-field distribution produced by the spatiallyalternating-oriented electrode stages(see Fig. 3). First, con-sidering the plane perpendicular to the molecular propaga-tion direction, there is a local minimum of the transverseelectric field in between a pair of slowing electrodes. Sinceneighboring stages alternate in their respective orientations,the transverse minimum similarly alternates. Thus the elec-trode geometry results in a stage-to-stage, transverse guidingof weak-field seeking molecules, simultaneously as their lon-gitudinal velocity is modified by interaction with the inho-mogeneous electric fields. Second, in order to minimize therequired number of expensive, fast high voltage switches, allthe horizontal(vertical) electrodes of the same polarity areconnected to a single switch, thus allowing four switches intotal to operate the entire 69 stages of the slower. A conse-quence of this practical switch minimization is that when thehigh voltage at a particular slowing stage is removed andsimultaneously turned on at the following(and preceding)stage, the local electric field does not go to zero but rather toa value generated by the now active set of electrodes. Whilethis effect reduces the amount of energy per stage that can beextracted by the decelerator, it beneficially maintains thequantum-mechanical state identity of the molecules, as thehydroxyl radicals are phase-stably slowed.

    Figure 7(a) shows the longitudinal potential energy distri-bution experienced by OH molecules with our present ex-perimental electrode geometry, generated under normal op-erating conditions of ±12.5 kV. Figure 7(b) demonstrateshow switching the electric field between the successivestages leads to a change in the molecular kinetic energy perslowing stage that depends critically on the position of themolecules at the switching time. This dependence is conve-niently characterized by utilizing a spatial coordinatew,called the phase angle, which is defined at the instant ofelectric-field switching and written as

    w =z

    L180 ° , s4d

    wherez is the longitudinal position of the molecule andL isthe stage-to-stage separation. We definez=0 sw=0°d as thepoint midway between two adjacent stages. To analyze thenet effect of deceleration on a spatially distributed pulse ofmolecules, it is useful to define thesynchronous moleculeasone that is atexactlythe same phase anglewo at the momentof each switching of the electric fields; thus losing an iden-tical amount of energy per stage[59,60]. While the region0,w0,180° does lead to deceleration of the synchronousmolecule, only operating in the range 0,w0,90° results inphasestabledeceleration of a molecular packet. This can beseen in Fig. 7(b), that on the positive slope of the potentialhill do molecules which are slightly ahead(i.e., faster) orbehind(i.e., slower) the synchronous molecules experience anet restoring force towards the synchronous molecule posi-tion. Detrimentally, operating on the negative slope of the

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  • hill (i.e., in the range 90øw0,180°) results in faster(slower) molecules becoming progressively faster(slower)relative to the synchronous molecule. By similar arguments,phase stableaccelerationof a molecular packet is only pos-sible on the positive slope of the potential hill in the range0.w0.−90°. The phase stable ranges are indicated by theshaded portions in Fig. 7(b). This restoring force experiencedby nonsynchronous molecules when the slower is operated inthe proper regime is the underlying mechanism for the phasestability of the molecular packet trapped in moving potentialwells. For example, given that the spacing between the suc-cessive stages is uniform in the decelerator, if the electric-field switching time is also uniform, then the position of thesynchronous molecule will bew0=0°, leading to the so-called “bunched” molecular packet traveling at a constantspeed down the slower. Forw0.0°, the proper switchingperiod of the electrodes systematically lengthens from at thebeginning of the slower to at the end of the slower.

    Defining the excursion of a nonsynchronous moleculefrom the synchronous molecule position asDw=w−wo andwith the help of a sine function fit to the change of kinetic

    energy per stage, it is straightforward to write the time evo-lution of Df, as

    d2Dw

    dt2+

    Wmaxp

    mL2fsinsDw + wod − sinswodg = 0, s5d

    whereWmax is the maximum work done by a slowing stageon a molecule andm is the molecular mass. This equation isthe same as the one describing an oscillating pendulum, withan offset equilibrium positionsw0d. The longitudinal phase-space distribution of the nonsynchronous molecules will thusrotate inside an asymmetric oscillator potential. From nu-merical integrations of Eq.(5), solutions for the stable re-gions of phase space are shown as a function of the synchro-nous molecule phase anglew0 in Fig. 8(a). The most relevantfeature of this figure is the rapidly decreasing area of stableevolution, defined as the area inside the separatrix. This de-crease in phase stable area is easily understood by analogy toa pendulum driven by a constant torque. As the torque in-creases, the amplitude of stable oscillation decreases. Thiseffect results in an asymmetric oscillator potential for non-synchronous molecules as shown in Fig. 8(b). As the originalphase-space distribution of the molecular source before thedecelerator populates the phase stable area forw0=0, then asw0 increases, the stable phase-space area decreases, whichtranslates into a decrease in the velocity spread of the mo-

    FIG. 7. Phase stable operation of the decelerator.(a) Longitudi-nal Stark energy potentials generated by the two sets of electrodes,where the solid(dotted) line represents the potential from the active(grounded) set of electrodes.(b) Kinetic energy loss per stagesDKEd experienced by molecules from switching between the twopotentials given above. Solid(dashed) line corresponds to a numeri-cal calculation(sine function fit).

    FIG. 8. (a) Phase stable area(separatrix area) versus phase anglefor w0=0°, 30°, and 60°. As the phase angle is increased, the stablearea is reduced; equivalently, the stable longitudinal velocity widthnarrows, decreasing the numbers of molecules in the phase stablepacket.(b) Longitudinal traveling potential wells at various phaseangles ofw0=0°, 30°, and 60°.

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  • lecular packet as well as the number of slowed molecules,setting a practical, observable limit to the ultimate tempera-ture of the molecular packet.

    From Fig. 7(b), it is seen that for molecules ahead of thesynchronous molecule the maximum stable excursion, i.e.,the separatrix upper spatial bound, is given as

    Dwmax,+= 180 ° − 2wo, s6d

    since molecules withwo,w,180°−2wo will be slowedmore than the synchronous molecule. A molecule with zerovelocity at this position(i.e., atw=wo+Dfmax) will have themaximum stable velocity at thew0 position, thus the longi-tudinal acceptance of the slower in velocity as a function ofw0 is given as

    Dvmaxswod = 2ÎWmaxmp cosswod − Sp2 − woDsinswod. s7dFigure 9 usefully summarizes the results of the calculationgiven above, giving an intuitive expectation of performanceunder different modes of slower operation. The solid squaresymbols represent stable areas,A, in phase space, plotted asa function of slowing phase anglew0 and normalized to thatof the bunching casesA0d. The open circles are plotted alongthe right axis and depict the maximum longitudinal velocityspread of the phase stable packet. As seen in the figure, op-eration at increasing phase angles results in fewer but alsocooler molecules in the phase stable packet. Hence, with aneye toward experimental goals, a careful balance between therequired number of molecules in the phase stable packet andthe desired longitudinal temperature must be consideredwhen using the Stark decelerator. While Eq.(7) allows forthe estimation of the longitudinal temperature of the stablemolecular packet, the dependence of the transported mol-ecule number onw0 must be determined. For an initial ve-locity distribution ofDvFWHM (full width at half maximum),the number of molecules successfully loaded into the phase

    stable bucketNsw0d, normalized to that for the bunchingcase, is shown to be

    Nswod < S1 − wop/2

    D erfSDvmaxswodÎlns2d

    DvFWHM/2D

    erfS 2DvFWHM/2

    ÎWmaxlns2dmp

    D , s8dwhere erf is the error function. In the above derivation, thearea inside the separatrix is approximated as square since weare only concerned with variation relative to molecularbunching. Also, we assume that at the input of the decelera-tor there is no spatial variation of the molecular packet overthe dimension of one slowing stage separation, as well asignore any convolution of the input distribution due to freeflight from the creation region. A more limiting assumptionmade for the sake of a closed-form solution is that the lowerseparatrix bound relative towo varies in the same manner asthe upper bound(i.e., Dfmax,−=−Dmax,+). Nonetheless, theresults of Eq.(8) are in good agreement with the measuredmolecule number as seen in Fig. 15, where a more detailednumerical solution for Eq.(8) that accounts for the propervariation ofDfmax,− is also shown, along with the results ofa full Monte Carlo simulation of the slowing process.

    The Monte Carlo simulations are performed not only forcomparison of the expected stable molecule number, but alsofor assessment of the detailed TOF spectra observed, and toaid in the understanding of the deceleration process. Fromthe geometrical and electrical properties(sizes, distances,and applied voltages) of the decelerator, a three-dimensionalelectric field map of the slower is constructed, which whencoupled with an understanding of the OH energy structure,gives complete information on the forces experienced byradical molecules within the decelerator. The initial inputdistribution parameters are determined from both experimen-tal dimensions(spatial parameters) and measurements onhexapole-focused, transversely guided molecular pulses(ve-locity parameters). The trajectories of four-million molecules(with equal weighting of the two weak-field seeking states)sampled from the initial distribution are calculated for theappropriate Stark manipulation process(i.e., bunching, slow-ing, or accelerating), starting from the skimmer entrance,then traversing the focusing hexapole and decelerator, andfinally reaching the appropriate detection region. All simula-tion curves displayed in this paper are generated with inputparameters of an initial velocity of 385±50 m/s, a transversespread of ±32 m/s, and a longitudinal spatial extent of1.25 cm at the input of the skimmer. We point out the impor-tance of including the lower weak-field seeking state(2P3/2F=2, umFu =0 and

    2P3/2 F=1, umFu =0,1 levels) to properlyreproduce the measured spectra. While its contribution to thesignal observed after the hexapole is small(because the mo-lecular focuser more dominantly affects radicals in the2P3/2F=2, umFu =2,1 states; i.e., see Fig. 6), as molecules withlarge transverse velocities are progressively lost from thephase stable packet during propagation down the slower, thepercentage contribution of the lower weak-field seeking stateto the observed signals increases since the molecules in this

    FIG. 9. Phase stable area(separatrix area) A vs slowing phaseanglesw0, normalized to the phase stable area under bunching op-eration A0. The subsequent maximum allowed velocity spread ofthe phase stable packetDVmax is shown with respect to the rightaxis.

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  • level entering the decelerator have smaller transverse veloc-ity spread.

    VI. PRACTICAL CONSTRUCTION AND OPERATION OFTHE SLOWER

    A particularly important practical issue is the stable op-eration of high voltagess,25 kVd between electrodesspaced only a couple of millimeters apart inside the decel-erator and the electrostatic trap. Discharge between elec-trodes will not only disrupt normal operations of the decel-erator, but could also inflict permanent damage to theelectrodes. A high vacuum system is helpful in terms of en-hancing the threshold for unwanted discharges in the appa-ratus. Additionally, high vacuum is also useful for reducingOH background collision events. The skimmer acts as aneffective differential pumping hole that separates the super-sonic expansion source chamber from the decelerator cham-ber. During quiescence, the source(slower) chamber reaches,10−8 Torr s,10−9 Torrd s1 Torr=13.3 Pad. Under activeconditions, the source(slower) chamber is at,10−4 Torrs,10−7 Torrd.

    High voltage components are fabricated from 304L stain-less steel, or hardened steel, and subsequently mechanicallypolished and then electropolished(for 304L) for the bestpossible surface finish. These high voltage elements aremounted on insulating materials(macor, alumina, or boronnitride) in such a manner to avoid close proximity to groundor opposite high voltage polarities. When opposite polarityvoltage elements are attached to the same insulating support,grooves were fabricated into the insulating surface in orderto create longer surface path lengths to minimize currentleakage between the components. Once under vacuum, theelectrodes are subject to a sequence of high voltage condi-tioning sessions to ensure stable operation. The conditioningconsists of two related but distinct methods: dc current andglow-discharge modes[61], both of which essentially create“microdischarge” events that help clean the surfaces and pre-pare the electrodes for HV operation. Under dc current con-ditioning, all electrodes are gradually brought up to 1.2–2times their nominal operating level in incremental voltagesteps. A limiting resistors,0.1 GVd in series with the HVpower supplies limits the possible discharging current tosmall values. The series current can be actively monitored bya floating digital voltmeter and also via the chamber vacuumpressure where higher pressure indicates increased discharg-ing. It was empirically discovered that the Bayard-Alpert-type ionization gauge that actively monitored the chamberpressure was also inducing low-level discharging during theconditioning process. UV lamps have also been utilized topurposefully create these beneficial microdischarges duringthe current conditioning process. When the apparatus fails todc current condition to satisfaction, we utilize a sparkingglow discharge technique. The chamber is backfilled with afew tens of milliTorr of helium gas, and a Tesla coil is usedto spark a discharge between the relevant electrodes for ap-proximately ten minutes. The system is then vented and thisprocedure repeated with a backfill of nitrogen gas. Subse-quently, the system is dc current conditioned with significantimprovements.

    Successful operation of the Stark decelerator relies onthorough knowledge of the initial position and velocity dis-tribution of the OH, and temporally accurate control of theinhomogeneous electric fields in order to ensure stable ma-nipulation. We rely on machining precision in the manufac-ture of slower components(,±50 mm stated tolerance) toensure that any physical discrepancies from the specified di-mensions are minimized. The applied electric fields arepulsed using commercially available, fast high voltageswitches with a specified,10−8-s rise time. External currentlimiting resistors are used both to protect the switches fromexcessive current and to slow down the rise time to,1 ms tominimize the generated electromagnetic interference(EMI).The molecules are insensitive to the switching speed reduc-tion, as even on thems-time scale, the fastest-moving mol-ecules in the system are almost stationary. We note the im-portance of reduction of the overall EMI from the systemwhen high voltages are being switched actively.

    Two HV power supplies(one devoted to each polarity)generate the requisite high voltage for the slowing stages.Each individual power supply output is coupled in parallelwith a ,2-mF high voltage capacitor on the input side of thefast switch in order to provide the large currents(21-A peakcurrent) required for the rapid charging of the slowing elec-trodes. A similar arrangement generates the slightly lowerhigh voltage and current used for the pulsed electric hexa-pole operation and for the electrostatic trap. A digital delaygenerator(DDG) acts as the master clock for the experiment,controlling the firing of the pulsed laser, and triggering acomputer-based timing board. The timing board repetitivelygenerates user-defined timing signals to subsequently drivethe fast HV switches that control the OH-generating dis-charge, hexapole, slowing stages, and trap elements. Thetiming pattern incorporated into the timing board is derivedfrom computer simulations of the deceleration process asdiscussed in Sec. V.

    VII. PHASE-SPACE MANIPULATIONS OF THE OHMOLECULES: EXPERIMENTAL RESULTS

    In situ experimental observations of OH molecules under-going longitudinal phase-space manipulation inside the prop-erly timed decelerator provide firm confirmation to the theo-retical understanding. TOF spectra from three representativeand distinct spatial locations — before 23 stages, before 51stages, and in the electrostatic quadrupole trap region — areselected to demonstrate the evolving character of the phasestable molecular packet. Where present in all data figuresthat follow, a downward-pointing arrow indicates the loca-tion of the phase stable molecular packet.

    Figure 10 depicts the OH TOF spectra when the decelera-tor is operated under a phase anglew0=0°; i.e., the net lon-gitudinal velocity of phase stable molecules is not changedbut the molecular packet maintains tight spatial confinementdue to bunching. Unlike the transverse guiding effect shownin Fig. 5, spectra generated under properly timed and pulsedelectric fields exhibit peak and valley structures, demonstrat-ing the velocity and spatial selectivity of the inhomogeneouselectric fields acting on the evolving molecular packet. Fig-

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  • ure 10(a) shows the spectra before 23 stages of bunchingsw0=0°d. With such few stages of interaction, longitudinallyphase unstable molecules are still dominantly present anddetected by the LIF technique, generating the side peak fea-tures and contributing to the broad pedestal that the centralpeak sits on. By the time the molecular pulse has propagatedin front of the 51st stage under the same experimental con-ditions, the phase stable packet has become the only distinctfeature remaining, as shown in Fig. 10(b). The moleculesthat correspond to untrapped orbits in phase space generatethe small, broad background on top of which the phase stablepeak sits. Similarly, the bunched, phase stable packet domi-nates the spectrum in Fig. 10(c), where the molecules haveexited the slower, propagated a short free-flight distance, andpassed through the center of the electrostatic trap regionwhere they are detected.

    In principle, all molecules within the selected phase stablepacket are transported without loss down the decelerator; thedifference in peak amplitude between Figs. 10(b) and 10(c)is a result of molecular loss due to molecules with too hightransverse velocities being progressively removed from themolecular pulse, inefficient coupling between the deceleratorand trap region, and scattering from background gas. Figure10(d) depicts the bunched packet peak areas at different spa-tial locations from both experimental data and simulations,normalized to the peak before the 23rd stage. This figure,along with the understanding gained from simulations, dem-onstrates that the apparent loss of signal is primarily due tothe “boiling” away of longitudinal phase unstable moleculesas they propagate down the slower, as well as moleculespossessing transverse velocitiesù5 m/s slowly escapesfrom the phase stable packet throughout the deceleration pro-cess. Essentially, the focusing power of the hexapole isboosting the initial total number of molecules coupled intothe slower. However, many of these molecules are ultimatelynot useful because they do not enhance the population of thephase stable packet and are subsequently lost. The simulation

    results provide excellent agreement with the observed spec-tra, confirming good understanding and control of the decel-erator.

    We gain more insight into the slowing process by exam-ining in detail the TOF spectra obtained at a single specificspatial location as the phase angle is varied. Figure 11 fo-cuses on LIF measurements made before the 23rd stage. Fig-ure 11(a) shows the expected broad, basically featurelesspeak as the packet spreads longitudinally while being trans-versely guided down the central axis of decelerator understeady-state high voltages applied to all slowing stages. Fig-ure 11(b) depicts the spectra under bunching operationsw0=0°d, creating the multipeaked structure, as also shown inFig. 10(a), wherein the spatial periodicity of the high voltagestages is imprinted onto the OH pulse. The phase anglew0 isthen increased to 20°, 40°, 60°, 67°, and 80° in Figs.11(c)–11(g), respectively.

    Careful examination of the data traces reveals smallchanges in amplitudes and subtle time shifts in the locationof the peaks asw0 increases. However, the basic structure ofthe spectrum at this spatial location is mostly unchanged, asthe signals from phase unstable molecules dominate thespectra. The downward-pointing arrow indicates the locationof the phase stable packet—however, its presence is substan-tially masked by the signal from unstable molecules. Thiseffect is expected and clearly seen in Fig. 12, where theresults of a 3D Monte Carlo simulation after 22 stages ofdeceleration(i.e., in front of the 23rd stage) are shown forbunching and slowing withw0=60°. Figure 12 represents asnapshot of the longitudinal phase-space distribution of themolecular packet, with each dot corresponding to the longi-tudinal position and velocity of a simulated molecule. Alongthe horizontal(vertical) axis is shown the spatial(velocity)projection of the distribution, and a horizontal(vertical)dashed line represents the expected position(velocity) of thephase stable pulse at this instant. Figure 12(a) shows theresult of bunching to the 23rd stage, revealing that phase

    FIG. 10. OH LIF TOF spectra under bunchingsw0=0°d decelerator operation(a) before the 23rdstage,(b) before the 51st stage, and(d) within theelectrostatic trap region. The data points aredrawn as squares, circles, and triangles while thesimulation results are shown as solid lines, with avertical offset for viewing clarity. Figure 10(d)shows both experimental and simulation resultson bunched peak areas, normalized to the 23rdstage; the reduction in peak height with positionis due to longitudinally phase unstable moleculesas well molecules with radial velocitiesù5 m/sbeing lost from the packet.

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  • unstable molecules are “boiling” away symmetrically aroundthe stable molecule bunch. On the other hand, whenw0=60°, Fig. 12(b) demonstrates that unstable molecules arelost in only one direction as the phase stable packet is pulledto lower velocities[consistent with the nonsynchronous mol-ecule potentials shown in Fig. 8(b)]. These phase unstablemolecules lead to dramatic effects in the observed TOF spec-tra of Fig. 11. In the bunching case[Fig. 11(b)], because theunstable molecules are lost symmetrically the bunched peakis only broadened. However, in the case of slowing or accel-eration[Figs. 11(c) through(h)], the molecular loss is direc-tional and the center of the observed peak is shifted andbroadened from the expected location. From the projectiononto the horizontal axis it is evident that a peak does indeed

    FIG. 12. 3D Monte Carlo simulation of the OH packet in frontof the 23rd stage under the bunching and slowings60°d conditions.Molecules are shown in longitudinal phase space as dots. Projec-tions along the longitudinal spatial and velocity coordinates areboth shown.

    FIG. 11. OH packet of mol-ecules in front of the 23rd stageunder(a) transverse guidance,(b)w0=0° (385 m/s), (c) w0=20° s365 m/sd, (d) w0=40° s344 m/sd, (e) w0=60° s323 m/sd, (f) w0=67° s317 m/sd, (g) w0=80° s309 m/sd, and (h) w0=−45° s424 m/sd, where thenumber in parenthesis indicatesthe mean velocity of the phasestable packet. At this spatial loca-tion, under all operating condi-tions the spectra are dominated bysignals from still present phase-unstable molecules.

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  • occur at the spatial location expected for the phase stablemolecule packet. However, because of convolution with thedetection window this peak is unresolved in the large centralpeak in the TOF data. Also in Fig. 12(b) the manipulation ofthe input velocity distribution (Vm=385 m/s, DvFWHM,75 m/s) is beginning to become evident as molecules aremoved from the central regions385 m/sd towards smallervelocities. The stable moleculeshave been incrementallyslowed from the initial 385 m/s[Fig. 11(b)] to 309 m/s[Fig. 11(g)], although this corresponds to only a,40-msshift in the peak location at this position. We point out thatthe spectrum is simpler than previously observed(i.e., Fig. 2in Ref. [24]) at this spatial location, when only 14 stages ofslowing were utilized, coupled with an additional 9 stages oftransverse guidance. Generally speaking, the more stagesused, the more straightforward the interpretation of the spec-trum will be, as contributions from the interesting thoughcomplicated dynamics of the longitudinally phase unstablemolecules will be reduced. For display purposes, Fig. 11(g)shows similar characteristics as we selectw0=80°. At thisaggressive slowing phase angle, the selected molecules willactually come to rest before the end of the 69-stage Starkdecelerator. Finally, demonstrating the flexibility of this ex-

    perimental technique, phase stableaccelerationis depictedin Fig. 11(h), where a negative phase angle is utilizedsw0=−45°d. The OH molecules have been accelerated from 385 to424 m/s. However, similar to the slowing data traces, theacceleration spectrum is complicated by signals from mol-ecules with open trajectories(not contained inside the sepa-ratrix) in longitudinal phase space.

    We next observe molecular packets after 50 stages of op-eration. Similar to above, Fig. 13(a) shows the TOF spectrumsolely under continuous, transverse guidance fields. FromFig. 14 it is clear that after 50 stages of operation(i.e., ob-served in front of the 51st stage) essentially all of the phaseunstable molecules have boiled out of the phase stable re-gion. This simplifies the interpretation of TOF spectra sinceonly the well-characterized stable molecules remain in thepeak of interest. Indeed, under bunching operation experi-mentally (i.e., w0=0), Fig. 13(b) shows a single tall centralpeak representing the phase stable molecules that are main-tained together with their net longitudinal velocity un-changed. The much smaller, lower-lying broad feature againarises from the phase unstable molecules. As the slowingphase angle is further increased, the behavior of the deceler-ated packet becomes manifestly clear in the data at this spa-

    FIG. 13. TOF LIF measurements of OH mol-ecules before the 51st stage under(a) transverseguidance, (b) w0=0°s385 m/sd, (c) w0=20°s337 m/sd, (d) w0=40°s283 m/sd, (e) w0=60°s220 m/sd, (f) w0=67°s198 m/sd, (g) w0=80°s168 m/sd, and (h) w0=−45°s470 m/sd,where the number in parenthesis indicates themean velocity of the phase stable packet.

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  • tial location unlike after 22 stages. The slowed peak corre-sponding to the phase stable packet evolves towards laterarrival times, demonstrating its steadily decreasing velocity.In Figs. 13(c)–13(g), the slowed peak appears at later timepositions as the velocity of the OH molecules is reduced to337, 283, 220, 198, and 168 m/s, respectively. As expected,the peak amplitude decreases as the phase angle gets larger,reflecting the reduced stable area in phase space. Again, fromFig. 14(b) for w0=60°, we see this expected behavior in thesnapshot projections of the longitudinal phase space distribu-tion. In the horizontal projection we observe a single phasestable peak that has been moved towards the rear of themolecule pulse, while in the velocity projection we see thatthe input velocity has been significantly modified, resultingin a single packet of decelerated molecules traversing theslower.

    Interestingly, there are distinctly different spectra featuresgenerated under bunching versus slowing conditions at thisspatial location. In contrast to in front of the 23rd stagewhere the spectra maintain essentially the same characteris-tics at all operating phase angles, after the 50th stage at anynonzero phase angle, the spectrum changes from a singlepeak to a distinct triplet of peaks, where one of these struc-tures corresponds to the phase stable packet of moleculesthat shifts to later(earlier) times for stable deceleration(ac-celeration) in the TOF observation. Within the presented da-ta’s time resolution, the other two peaks remain essentially atthe same temporal locations for the same sign of phase angle,but these positions undergo a large time shift for oppositesign phase angles, as seen by comparison with Fig. 13(h).These structures may result from phase unstable moleculeshopping around neighboring traveling potential wells.

    We now examine OH signals observed beyond the final(69th) stage of the decelerator and moving within the trapregion. The electrostatic trap consists of three elementswhich produce a quadrupole-configuration confinement fieldin order to spatially contain sufficiently slowed, Stark-sensitive molecules in three dimensions. A stainless steel ringwith two pairs of orthogonally oriented 3-mm holes for fluo-rescence detection forms the central axis of the trap, located,14 mm from the middle of the final slowing stage. Twoidentical end cups with 2-mm apertures along the deceleratorbeam axis create the symmetric end caps of the trap. The trap

    element surfaces — the inner ring and inner end-cap sides—are machined to a specific curvature from 304L stainlesssteel and held in precise orientation and separation by insu-lating support rods. The three pieces are electrically isolatedboth from earth ground and each other, enabling voltages tobe applied independently for user-defined, precisely timed,molecular loading and trapping sequences. In order to pro-vide high-efficiency molecular fluorescence detection withinthe trap region, an in-vacuum, 25.4-mm-diameter lens ismounted one focal length awaysf =35 mmd from the trapcenter, axially aligned to one pair of the ring element aper-tures. A second identical relay lens is mounted 2f aways70 mmd to transport the fluorescence photons, forming animage of the trap central region at the photocathode of anexternal PMT for molecular detection. While the back endcap is always grounded, high voltage of −12.5s−9.0d kV isapplied to the central ring(front end cap) during the loadingsequence. Subsequently, the front end cap is terminated toground, resulting in an eventual trap volume confinement of,1 mm3.

    While we have recently observed signatures indicatingthat OH radicals slowed to,27±3 m/s are successfullyloaded into the trap, and spatially confined by the high elec-tric fields, this topic is beyond the scope of the present paperand will be presented in a future publication. We present hereadditional TOF spectra of OH molecules observed movingwith varying velocities through the trap region after the de-celerator, which is operated under various conditions. Whereappropriate, the simulation results are plotted as lines thathave been offset vertically from the data trace for viewingclarity. Figure 15(a) shows the transversely guided pulse ofOH molecules in the trap region with a mean pulse velocityof 385 m/s. Under bunching conditions selected for thismean velocity, the expected narrow, single, phase stablepacket shows up as a single large peak depicted in Fig. 15(b),arriving at 1.37 ms. In Fig. 15(c) at a phase anglew0=45°,the slowed peak arrives later in time as the molecular speedis further slowed to 210 m/s. In fact, the peak has beenmoved completely off of the residual signals from phase un-stable molecules that form the broad pedestal in Fig. 15(b).This complete separation occurs at a smaller value ofw0 thanthat for 51 stages since the entire 69 stages of decelerator areutilized for kinetic energy extraction. Finally, phase stableacceleration is shown in Fig. 15(d). Here the molecularpacket is accelerated to 541 m/s, arrives correspondinglyearlier in the TOF spectrum and creates the narrow peak at1.19 ms. Interestingly, similar to the observations after the51st stage, at nonzero phase angles, the double peak structureappears to persist in the data even after an additional 18stages of high electric-field manipulation. Above the datatraces, simulation spectra with higher temporal resolution areplotted. Consistency between simulation and measurement isquite good, with locations of the phase stable packet andrelative peak heights demonstrating excellent agreement.

    We now focus with higher temporal resolution on measur-ing solely the phase stable packets generated by the decel-erator moving through the trap region. Successful operationof the decelerator relies on precise knowledge of the molecu-lar packet’s velocity and location in order to be able to stablyslow the packet. Hence we can easily predict when the pulse

    FIG. 14. 3D Monte Carlo simulation of the OH packet in frontof the 51st stage under the bunching and slowings60°d conditions.Molecules are shown in longitudinal phase space as dots. Projec-tions along the longitudinal spatial and velocity coordinates areboth shown.

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    043410-14

  • of molecules will arrive in the trap region after it exits thedecelerator. We note that at low phase angles, when the ve-locity change of the molecules is not that large, the analyticexpression(i.e., sine fit) to the potential energy hill presentedin Fig. 7(b) enables sufficient accuracy to predict the peakarrival times. However, at higher phase angles, the deviationbetween the analytical calculation and the actual shape of thepotential becomes a significant factor such that a numericaldetermination of the potential must be used to generate theproper time sequence to operate the decelerator. In fact, bothsimulations and measurements demonstrate that the molecu-lar packet actually becomes phase unstable oncew0 becomesgreater than 40°, unless the more accurate calculation of thetime sequence is used. Finally, as a minor detail, when themolecules are exiting the decelerator through the last stage,the voltage on the last electrodes is switched off, while thevoltage on the preceding stage is turned on. The presence ofthis nonzero electric field results in a small accelerating forceto the molecules. This effect needs to be taken into accountto determine accurately how the molecules propagate fromthe last decelerator stage through the essentially field-freeregion into the trap.

    In Fig. 16, we detect the molecules with 2.5-ms timingresolution per point. Phase stable packets are measured overa broad range of operating parameters, both in acceleration,bunching, and slowing for −70øw0ø65°. Figure 16 traces(a)–(d) represent OH radicals that have been acceleratedfrom an initial velocity of 385 m/s to a maximum speed of545 m/s. The phase stable molecules arrive earlier in timerelative to the bunched peak[Fig. 16 trace(e)] and create theobserved increasingly narrow structures. The bunched packetcorresponds to,104 molecules at a density of,106 cm−3.Traces(f)–(m) show phase stable OH packets which havebeen decelerated to correspondingly lower velocities, as in-dicated in the figure. As the molecular packet is increasinglyslowed, the molecules arrive progressively later in time. Forw0.40°, the slowed peak is completely separated from thebroad background signals produced by residual phase un-

    stable molecules. In contrast to the accelerated molecules,the slowed, stable molecular packets broaden as the phaseangle increases, due the reduced molecular speed.

    As the molecules slow down towards rest, there is anartifact in estimating molecular numbers due to the finitespatial size of the detection window. Basically, slow mol-ecules are counted multiple times as they move through thedetection region where the LIF light pulses are shifted in finetime steps to obtain high-resolution TOF spectra. When thiseffect is properly deconvolved from the actual underlyingsignal size, the numbersNd of OH molecules in a phasestable packet as a function of phase angle can be determined.The measured results, normalized to the bunching peak num-ber N0 are plotted in Fig. 17. In addition, points generated

    FIG. 15. Observations of OH molecules mov-ing through the trap region under(a) transverseguidance,(b) bunching(w0=0°, v=385 m/s), (c)slowing (w0=45°,v=210 m/s), and(d) accelera-tion (w0=−67°, v=541 m/s). Monte Carlo simu-lation traces are plotted above the data.

    FIG. 16. Slowed, accelerated, and bunched molecular packagestraversing the trap region at varying phase angles. Here, thedownward-pointing arrow indicates solely the position of thebunched[trace (e) w0=0°] packet, as all observed peaks are theresult of phase stable packets. Molecular peaks arriving earlier intime result from accelerated OH packets with corresponding nega-tive phase angles as denoted in the figure. Peaks arriving later intime are similarly the result of slowed molecules, generated byusing positive phase angles.

    COLD FREE-RADICAL MOLECULES IN THE… PHYSICAL REVIEW A 70, 043410(2004)

    043410-15

  • under Monte Carlo simulations and theory curves from thesimple analytic expression of Eq.(8) and the more accuratenumerical calculation are shown. The agreement between ex-perimental results and simulation is quite good. The mainsources of error are peak reproducibility and accurate esti-mation of the peak area of the bunched packet as it is tem-porally coincident with signals from phase unstable mol-ecules. Disagreement between the measured data points andthe simulation results are within experimental error. Devia-tion of the data points under acceleration conditionssw0,0°d are primarily due to insufficient time resolution inthe data points, making peak area estimates difficult.

    VIII. CONCLUSIONS, FUTURE DIRECTIONS, ANDOTHER DISCUSSIONS

    The work reported in this paper has centered on creatingcold hydroxyl radicals through the use of the Stark decelera-tion of a supersonic beam. Specifically, our work from bothexperimental and modeling perspectives has been focused onuncovering the complex dynamics, that govern the evolutionof the molecules within the decelerator, and efficiently pro-duce molecules for trapping and subsequent study. In ourcurrent experiments we accelerate/decelerate a supersonicbeam of free radicals to a mean speed that is adjustable be-tween 550 m/s and rest, with a translational temperature tun-able from tens of mK to 1 K. These velocity-manipulatedpackets contain 103–6 molecules(depending on the transla-tional temperature) at a density of,104–6 cm−3 inside themoving potential wells.

    Improvements will come from several different fronts.One of the most important future developments is to enhance

    the number and phase-space density of the initial supersonicbeam expansion source. Since a Stark decelerator cannot en-hance the phase-space density, progress along this line willbe particularly important to push the low-temperature limitof the cold molecular samples. We will explore improve-ments to the existing system as well as alternative techniquessuch as photolysis to attempt to produce colder and moreintense OH beams.

    Of course, one of the most effective, demonstrated ap-proaches to enhance the phase-space density is to laser coolthe sample, especially when the sample density is not suffi-ciently high or the ratio of elastic versus inelastic collisionrates is not favorable to afford direct evaporative cooling.For OH radicals, it will be interesting to explore laser cool-ing effects through specific, relatively radiatively closedelectronically excited pathways. For example, due to thelarge Franck-Condon overlapping factor, OH molecules ex-cited from thev9=0 level in the ground electronic state to thev8=0 level in the first electronic state will return to the sameground state at,99.3% branching ratio. The cooling forceassociated with this electronically allowed transition is com-parable to laser cooling of alkali-metal atoms. Within this0–0 transition band, with strict selection rules(DJ=0, ±1;DJ=0, ±1; and +↔− for parity operation), the slowed andtrapped molecules in the(J=3/2, “f ”, F=2) state wouldneed only two independent repumping lasers, in addition tothe cooling laser, to close the cooling cycle. There are actu-ally five leakage states, however, small frequency gaps be-tween hyperfine levels can be bridged using electro-opticalmodulators. Although we still have a 0.7% unrepumped leak-age to other vibration levels, when the molecules are alreadyprepared at a few tens of mK temperature, noticeable coolingeffects should take place.

    Because of the existence of an unpaired electron, the OHmolecule also possesses a large magnetic moments,1.4 mBd and is suitable for magnetic trapping. We are ex-ploring a hybrid trap configuration combining both electro-static and magnetic fields for trapping of cold OH. Such atrap will provide an ideal environment to study cold, inter-molecular interactions with a varying electric field to influ-ence the molecular dipoles, as well as cold collisions be-tween atomic and molecular samples.

    ACKNOWLEDGMENTS

    We are grateful to H. L. Bethlem and Gerard Meijer forfruitful interactions and technical advice. We also thank C.Lineberger, S. Leone, and J. Daily for generous equipmentloans, and J. Bohn and D. Nesbitt for useful discussions. Weacknowledge important help we have received from A. Pat-tee and T. van Leeuwen. This research work was supportedby the Keck Foundation, NSF, and NIST. H.J.L. acknowl-edges support from the N.R.C.

    FIG. 17. Observations within the trap region: numbers of mol-ecules in the phase stable packetN relative to the number in thebunched packetN0, for varying slowing and accelerating phaseangles. Data points(solid circles) and three-dimensional MonteCarlo simulations(open diamonds) are shown. For comparison,theory traces generated from the simple analytic expression[Eq.(8), solid line] and the numerical calculation(dotted line) for stableareas in phase space are shown.

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