Eindhoven University of Technology

MASTER

Interaction of a beam of metastable argon atoms and a diode laser beam

den Boer, A.P.

Award date:1993

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Eindhoven U niversity of Technólogy Department of Physics Group of Partiele Physics Atomie collisions and Spectroscopy

Interaction of a beam of metastable argon atoms and a diode laser beam

Anne den Boer

Thesis, october 1993 VDF /NO 93-22

Supervisors: dr. M. Hoogerland and dr. K.A.H. van Leeuwen Thesis advisor: prof.dr. H. Beijerinck

summary

In earlier work in the Atomie Collision and Spectroscopy group the interaction of two- level atoms with a quasi- resonant coherent light field has been studied, using an atomie beam setup in which the atoms interseet a laser beam almost perpendicularly. This configuration is particularly suited to study laser cooling, and the statistics of the fluorescent light.

Experimental information was obtained by measuring the one- dimensional deflection and broadening of the atomie beam as a function of the velocity component in the laser beam direction, which is selected by means of a collimating slit just before the interaction region, approximately 2 meter from the source. The profile of the deflected beam was measured using a scanning slit in front of a large- area detector, approximately 2 meter from the interaction region. The accuracy and flexibility of these measurements were, however , severely hampered by the low average count rates inherent to the scanning procedure.

In this work, preliminary experiments with a vastly improved setup are reported. The scanning slit- detection has been replaced by a large- area position sensitive detector register­ing arrival time and position of each metastable atom in the beam. This results in an im­provement of a factor 40 in average count rate, with a corresponding decrease in measurement time. Furthermore the detector allows the beam profile to he measured in two dimensions. This will allow a complete new range of phenomena to he stuclied in later experiments.

As a two- level system, the { 4s} J =2 metastable level of argon to the { 4p} J =3 excited level is used . Owing to the magnetic degeneration of these levels, sub- Doppler cooling mechanisms can occur , as in neon, which was used for the earlier experiments .

The wavelength of this argon transition is 811.531 nm. To obtain this wavelength, a diode laser system with grating feedback has been built . With the feedback, the linewidth of the laser is reduced to below the natural linewidth of the argon transition. Also , the grating enables easy tuning of the wavelength over a continuous range of 10 nm. Using saturated absorption in a gas discharge cell, the laser frequency can he actively locked to a range of frequencies around the transition frequency. The laser system proves to he stable enough to stay in loek for several hours.

Preliminary results show that with this equipment the deflection measurements can he performed. A calibration of the sensitivity and the resolution of the detector has been ob­tained .

1

Contents

1 introd u ct ion 1.1 quanturn opties 1. 2 laser cooling . . 1.3 history of looptijd II 1.4 this thesis . . . . . .

2 theory 2.1 general . ......... ......... ... .

2.1.1 two-level atoms and resonant light .. . 2.1.2 absorptionjspontaneous emission cycles 2.1.3 absorption/ stimulated emission cycles 2.1.4 calculating the light force .... 2.1.5 polarisation and atomie sublevels

2.2 sub-Poisson photon statistics .. 2.2.1 introduetion ........... . 2.2.2 the statisties parameter Q ... . 2.2.3 measuring Q with multilevel atoms .

2.3 sub-Doppier ............... .. . 2.3.1 Doppier cooling revisited ..... . 2.3.2 sub-Doppier cooling; overcoming the Doppier limit 2.3.3 Sisyphus cooling 2.3.4 a+ a- cooling

3 experimental 3.1 the atom. 3.2 the laser ..... .

3.2.1 diode lasers 3.2.2 reducing the linewidth with external feedback . 3.2.3 locking the laser to an atomie resonance frequency 3.2.4 using the laser in the experiment

3.3 the vacuum setup .... .. ... . 3.3.1 overview ..... .... .... . 3.3.2 the metastable atom souree .. . 3.3.3 the chopper; time of fiight technique 3.3.4 the interaction chamber . . . 3.3.5 the metastable atom detector .. ..

2

5 5 5 6 7

8 8 8 8

11 13 15 16 16 17 19 19 19 20 21 23

25 25 25 27 29 34 37 39 39 41 41 42 42

3.3.6 collecting data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

4 results 4.1 nulling the magnetic field in the interaction region 4.2 testing the detector .......... . 4.3 atomie beam profiles with the laser on

4.3.1 scanning the laser angle

5 conclusions

3

45 45 45 48 49

52

symbols

light field symbols atomie symbols x laser beam direction z atomie beam direction E field strength g ground level WL laser frequency e excited level s intensity parameter I/ Io T lifetime excited state n number of photons r ljT Q statistics parameter h Lorentzian lineshape

k wave vector ne excited state population Ë polarisation vector p density matrix

wo resonance frequency V atomie velocity

J.L dipale operator

interaction 8 WL -Wo

WD Doppler shift kv n Rabi frequency no Rabi frequency at resonance FD Doppler force

lift= Hint el. dipale interaction operator Tp pumping time TD lower limit temperature of Doppler cooling

V cap capture range f non-adiabaticity parameter

4

Chapter 1

introduetion

1.1 quanturn opties

In the Atomie Collision and Spectroscopy group (AOW), collisions between atomie beams, and of atomie beams with photons, are stuclied experimentally. The interaction of atomie beams with light is both of interest for its application to atomie callision experiments and intrinsically. As to its application, (laser) light beams can he used to collimate, intensify and slow atomie beams. These possibilities to manipulate atomie beams offer many new opportunities for callision experiments which have so far been impossible.

As for its intrinsic interest, the interaction of light with atoms is the subject of the field of quanturn opties [LOU73]. The kinetic effects of the interaction on the atoms, as used in the mentioned applications, have been only relatively recently stuclied extensively in theory and experiment. In fact, the theoretica! interest hàs been largely stimulated by the ( sametimes accidental) discovery of the applications.

1.2 laser cooling

Collimating atomie beams can more generally he seen as a two-dimensional cooling of the atoms, since the kinetic energy is diminished. The idea that atoms can he cooled by light dates back to Einstein. However, only the existence of powerful tunable lasers made a practical implementation possible. This implementation was suggested by Hänsch and Schawlow in 1975 [HAN75], and realised for the first time in 1985 by Chu et al. [CHU85].

Cooling requires a friction force, that is a force inversely proportional to the atomie ve­locity. The original laser cooling scheme depends on the Doppier effect for moving two-level atoms in a standing light wave. The Doppier effect causes a velocity-dependent imbalance in the absorption of photons ( and thus momenturn) from the two counterpropagating light beams forming the standing wave. This leads to an effective friction-like force on the atoms.

While investigating this cooling scheme, a whole new class of cooling mechanisms was dis­covered, leading, under certain conditions, to much lower temperatures than Doppier cooling. These mechanisms are all based on the complicated interplay between optical pumping and light shifts for atoms with a magnetically degenerated lower level. Generally, the sub-Doppier cooling forces are only operative for very small values of the atomie velocity ( ~1 m/s).

Theoretically, sub-Doppier cooling mechanisms have been stuclied extensively. Exper­iments have thus far been primarily oriented towards the demontration of the mechanisms

5

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and applications like the production of extremely cold (pK range) and dense samples of atoms. In the group AOW, the application of laser caoling to atomie callision experiments is

stuclied in several experimental setups. Furthermore, a separate continuing effort is aimed at the study of the kin et ie effects of light on atoms at a fundamentalleveL Thus far, the relation between radiation pressure of a laser beam on atoms and spontaueaus emission has been used to determine experimentally the statistkal properties of resonance fluorescence. Also the temperature limit of one-dimensional sub-Doppier caoling has been determined. In the most ambitious experiment, the sub-Doppier caoling force has been measured as a function of the atomie velocity, for the first time ever. The setup which has been used for all these experiments is an atomie beam setup called Looptijd II. In the next paragraphit is described how this setup evolved from a callision setup into its present farm.

1.3 history of looptijd 11

The looptijd II has a rich history going back to 1971, when plans were made to build a time of flight machine to study elastic collisions between ground state noble gas atoms. Atomie beam techniques were developing at this beginning of the 'ground state age' in atomie callision physics. In 1974, the vacuum setup consisted of a souree chamber, a chopper chamber to enable time aLflight measurements, an interaction chamber in which two atomie beams collide, and a UHV detection chamber containing a mass spectrometer. At the end of this year, the first measurements were clone.

Between 1976 and 1980, a plasma souree was installed to create a superthermal atomie beam. These sourees also produce excited atoms. Two of the three first excited substates are metastable, and live a few seconds. On these the callision experiments could also he performed, so with the plasma souree the setup entered the metastable age.

To detect metastable atoms another technique than mass speetrometry is needed. The setup was enriched with a metastable atom detector chamber, and from 1981 to 1985 elastic collisions between all kinds of noble gas metastable atoms and ground state atoms were studied.

Then in 1986 another revolution took place when the optical age set in. Cook had pro­posed a methad for experimentally confirming sub-Poissonian photon statistics in resonance fluorescence by observing atomie beam deflection and broadening due to interaction with a laser beam. The mass spectrometer chamber was removed and instead a windowed chamber to allow a laser beam was added.

The deflection and broadening had to he stuclied as a function of the atomie velocity component in the laser beam direction. Toselect this velocity, a slit for the atoms was inserted in the interaction chamber, and a one meter long vacuum drift tube to make the deflection detectable. At this time the set up got its name 'looptijd II', because the metastable atoms have an exhausting three meter to run through the setup.

The looptijd II had only just begun to fruitfully produce sub-Poisson results when it entered the glacial age of laser caoling. In 1990 another laser interaction chamber was inserted just past the metastable souree to cool the atomie beam almast to the recoillimit.

Then in 1991 it was realised that with its velocity-selecting slit looptijd 11 is the first, and still the only, machine with which the cooling farces can he stuclied velocity-selective. Mea­surements have been done, with the drift tube extended another meter for better resolution, on three types of sub-Doppier cooling farces on neon, yielding excellent agreement with the

6

theory.

1.4 this thesis

The work described in this thesis is aimed at a drastic impravement in the setup. A new position sensitive metastable atom detector has been installed, which increases the average signal count rate with a factor of 40. At the same time, this detector prepares the way for the next evolutionary step of looptijd II: extension to measuring in two dimensions.

For flexibility, the dye-laser used in previous experiments has been replaced by a diode laser system, specially built for this experiment. This enables the experiments to he performed with different atoms (i.e. argon and krypton), and makes the experiment independent of the dye laser system, which is time shared between different experiments.

Originally, performing a new series of measurements on photon statistics and cooling farces was planned as well. This goal turned out to he nat feasible, mainly because of experimental set-backs due to failing vacuum pumps, vacuum gauges, cryo generators and electranies (mostly because of old age). Still, the diode laser system and the detector have been built, installed and tested. This workis described in this thesis tagether with the theory bebind the experiments. The first results of the atomie beam interading with the laser beam are shown. These results show puzzling and so far unexplained results.

7

Chapter 2

theory

2.1 general

2 .1.1 two-level atoms and resonant light

In this work, the interaction between resonant light and an ensemble of two-level atoms is stuclied by letting an atomie beam interseet an almast perpendicular either running or standing (laser) light wave. During the interaction, energy and momenturn will be exchanged between the two systems. This will affect the atomie velocity component in the direction of the laser beam, a quantity that can be measured. Details about the experiment can be found in chapter 2; In this chapter a theoretica! description of the interaction is given.

If only single photon interactions are considered, absorption of a photon by an atom must be foliowed either by spontaneous or stimulated emission. In the first case the emitted photon has a random direction and phase and can be considered to be lost for further interaction. In the second case the photon is returned into the laser beam. Thus the first interaction cycle, absorption-spontaneous emission, drains energy irreversibly from the combined system of light and atoms, while the other cycle represents reversible energy exchange within the combined system.

So three energy reservoirs can be distinguished :

• the laser, storing the number of photons times TiwL

• the atoms, storing the number of excited atoms times 1iw0

• the vacuum, acting as a photon dump for spontaneously emitted photons.

The two mentioned interaction cycles will be treated as independent, first separately in the following two paragraphs, then together. The characteristic time constants will be discussed, and an expression for the force that the laser exerts on the atoms is discussed.

2.1.2 absorptionjspontaneous emission cycles

moment urn and energy transfer

We start by consiclering the interaction between one photon and one atom. The photon has an energy of TiwL, and for the time being WL is considered equal to w0.

8

~· b

/ • ._

Figure 2.1: An absorption-spontaneous emission cycle. When the atom absorbs a photon (a), it takes over the photon momenturn (b). With spontaneons emission ( c), it gets another momenturn change, this time in the random emission direction.

In a rather classica! picture, the atom and the photon are represented as point masses, and absorption as an inelastic collision. As indicated in fig. 2.1, the (excited) atom has gained the momenturn hk of the photon. When later the spontaneons emission takes place as the atom returns to its ground level, the at om gains a recoil - hk', this time in a random direction, with k' the wavevector of the spontaneously emitted photon.

When the a torn interacts in this way with an ensemble of n photons with identical wavevec­tor k, the recoils will average out and the atom gains a net momenturn of nhk. Thus a force in the direction of the light is exerted on the atom. This force is commonly called radiation pressure.

first time constant: lifetime of the excited atomie state

The force can he calculated if it is known how many interactions take place per time unit. For this, the atomie transition needs to he investigated a bit further.

The mean time that the atom stays in the excited state befare spontaneons emission is called the lifetime of the excited state, T. Due to this fini te time, the transition freqnency has an finite uncertainty of ~E = hr, with r = 1/T.

The lineshape, which is the relation between absorption probability and driving frequency, is thus nat a delta peak at w = w0 , but a normalised Lorentzian peak with a width of r:

f/27r h(w) = (wo- w)2 + (r /2)2 (2.1)

The difference between the laser freqnency WL and the atomie frequency w0 will from here on he called the de tuning b:

WL- Wo= b. (2.2)

Since the decay takes on average a time T, one wonld expect that r interactions can take place per second and that the maximum resulting force is given by nkf. But the atom can spend no more than half of the time in the excited state if driven by a laser. This will be explained in section 2.1.3. So the maximum force that a laser beam can exert on an atom is tnfr. For an ensemble of atoms, the mean number of atoms in the excited state is denoted

as ne, and the force is given by nenkr.

9

Figure 2.2: Lorentz lineshape of an atomie level with fini te lifetime T. The linewidth r is equal to 1/r.

intensity dependenee

If the laser frequency differs from the atomie transition frequency, absorption becomes less probable. The mean number of atoms in the excited state drops, and with it the resulting force. The detuning and intensity dependenee of the excited state population is expressed in a resonant intensity parameter s = I/ Io,

s ne = 2

2(s + 1 + ~2 ) (2.3)

The parameters is chosen so that when s = 1 and 8 = 0, ne is 1/4. For small s, ne is linear in the intensity, but for large s it approaches asymptotieally the value 1/2. At ne = 1/2 the ensemble of atoms is saturated and can absorb no more photons.

With this expression, the frequency dependent force becomes:

- - s F(w)=nkf 452 • 2(s + 1 + f2)

(2.4)

It should he noted that this is an expression for an atom at rest. If the atom has a velocity component Vx in the direction of the laser beam, it will see the laser frequency Doppler shifted by an amount of -vxk, to he called WD. 8 + WD is the frequency that should appear in expression 2.4, leading to the final expression

- - s F(w, v) = nkf (4ó-vxk) 2 ,

2( s + 1 + f2 ) (2.5)

which is atomie velocity-dependent. The force curve has its maximum at the value of vx for which 8 = -WD, i.e. Vx = 8/k.

an example: Doppier cooling

The fact that the above discussed force is dependent on the atomie velocity leads to an application called Doppier cooling. The idea is to create a friction force for the atoms, that is a force linear in the velocity, and opposite in direction,

F = -ctiJ. (2.6)

10

i\ . \',

+ : \'-. \ ..

Figure 2.3: The Doppler cooling force. An atomie beam is collimated by two counterrunning transverse laser beams, bath detuned below resonance. The sum of the radiation pressures they exert ( dashed lines) is a friction force for the atoms, linear in the velocity around v=O.

With such a force an atomie beam can be collimated, as pictured in fig. 2.3. The friction force is realised by using two laser beams, coming from opposite sicles as

indicated in fig. 2.3, and bath detuned below resonance. The beam coming from the left exerts a force F+ to the right, and the other beam a similar force F- to the left, in which only the term -vxk must be replaced by +vxk. The sum of these farces is, in the limit of small intensity and around v = 0, a friction force as defined above:

F+ + F- = 8nks8 v k 1 r x (s+1)2+8(s+1)62+~:!2k2 +16(62-~~2k2)2

(2.7)

The two force curves this yields are given in fig. 2.3, as well as their sum. One can see that the force is linear, and for negative detuning opposite to the atomie velocity, around v = 0.

Cooling farces will be treated more extensively in section 2.3.

2.1.3 absorption/stimulated emission cycles

In this section the interaction of an atom with a monochromatic electromagnetic field is considered while neglecting spontaueaus emissions. The intuitive approach shows that with a single laser beam this interaction does nat lead to a force: the stimulated emitted photon has the same direction and frequency as the absorbed, and the momenturn change of the atom with absorption is cancelled by the recoil of the emission. When several laser beams are used, as in our case the standing light wave, a photon absorbed from one of the beams can be emitted in another beam. This does lead to a momenturn change of the atom.

To calculate the momenturn change, the intuitive approach offers no help. But since the interaction consists purely of reversible energy exchange between the atom and the coherent field, Hamiltonian theory can be used.

11

The atom is treated quantummechanically. lts free Hamiltonian Îl0 has as eigenfunctions the two energy levels 19) and Ie).

The monochromatic light wave is described classically as the electric field

(2.8)

The interaction is described as electric dipale interaction. The atomie dipale operator can he split in a raising part, descrihing excitation, and alowering part for deexcitation. They will he indicated with up and down arrows.

(2.9)

The interaction Hamiltonian, or n times the Rabi operator, is formed as

(2.10)

the first term representing absorp.ion of a photon, and the second emission. Non-resonant processes, like transition to the excited state while emitting a photon, are considered toa unlikely, and are left out. This is called the rotating wave approximation in analogy to the approximation made in magnetic resonance theory. Magnetic resonance is accomplished by making a magnetic dipale precess in a static field. Transitions are then caused by a field varying sinusoidally with the precession frequency, but only the Fourier component that rotates with the precession needs to he considered, and the other component is left out of the equations. If a transformation is made to a frame that rotates with the precession frequency, the ac field becomes statie.

Similarly, in our case the internal motion of the atom can he transformed to a frame rotat­ing with WL, where the Rabi operator is time independent. The atomie transition frequency is then 8 instead of wo.

another time constant; the Rabi frequency

With the interaction Hamiltonian as a time-dependent perturbation, the evolution of the internal state of the atom can he investigated [BAL 77]. The results will only he valid for interaction with a weak light field.

To find this time evolution, the time dependent Schrödinger equation

n a , , -i äti7,U(t)) =(Ho+ Hint)I7,U(t)), (2.11)

with 7,b( t) a linear combination of the eigenfunctions of the free Hamiltonian

(2.12)

is solved. The time evolution of the two constants Cg( t) and Ce( t) is found, and with them the time dependenee of the level populations, which are given by the square of the constants.

When at t = 0 the constants Cg and Ce are put 1 and 0 respectively, the upper level population varies sinusoidally as

(2.13)

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nis called the Rabi frequency, with n 0 , equal to ïf·E/n, the value at resonance. The relation between them is

(2.14)

At resonance the upper level population oscillates between 0 and 1. When the laser is detuned, the oscillating frequency increases, but the amplitude diminishes.

lightshift

The energy levels of the atom also undergo an energy shift. This is classically understandable as the energy a dipole gains when it is aligned to an electric field. Since in this case the electric field is time-varying, the shift is called dynamica! Stark effect. The time-averaged weak field approximation of this shift can be calculated in the rotating frame, using time-independent second order perturbation theory. Since in a weak field approximation the atom is mainly in the ground state, the ground state shift is calculated:

(2.15)

A more elaborate calculation [NIE91], taking into account spontaneons emissions, gives a value of the lightshift

(2.16)

Still, the above derived expression can serve as approximation for large detuning, which corresponds to dominating stimulated emission. In this limit the shift is linear in field intensity and the coupling strength between the two levels, and inversely proportional to detuning.

The magnitude of this shift can, for any strength of the field, be calculated in the exact method, when the field is quantised and the Hamiltonian of the combined system of laser and atoms is diagonalised. The eigenfunctions then found are called dressed atom levels. The atom is in a superposition of the ground and the excited state [DAL85].

an example: channeling

The lightshift can he seen as a potential for the atoms, and the discussed interaction results in a force, commonly called the dipale force, equal to the gradient of this potential. Thus there will only be a force if there is spatial variation in lightshift.

This is the case in a standing light wave, where the intensity varies sinusoidally. The atom, crossing the laser beam at right angle, sees a potential landscape of hills and valleys, and will, for negative detuning, channel into the antinocles of the field. In fig. 2.4 the idea is pictured.

2.1.4 calculating the light force

steady state upper level population

Due to spontaneons emissions, the above discussed Rabi asciilation will damp out and the mean upper level population becomes a steady value, which is apparently never more than 1/2. This damping is understandable with the following argument: at t=O, when the field is switched on, the Rabi oscillation starts and all atoms are in phase. Another way to say this

13

Figure 2.4: Channeling. The sinusoidally varying intensity in a standing light wave creates a potentiallandscape of hills and valleys for the atoms that react with it.

is that the atomie coherence is maximaL Then at random moments atoms are returned to the starting point of the oscillation by a spontaneous emission, and the coherence decreases, until a steady state value of the atomie coherence is reached.

an expression for the force

Still in the same Hamiltonian calculus, an expression of the force operator on the atom is given by

( 2.1 7)

since the force on the atom equals its momenturn change. The expectation value of the force operator must he calculated by sandwiehing it between

atomie wavefunctions. An equivalent of this is tracing over the density matrix p.

F = (~IFI~) = Tr(pF). (2.18)

The density matrix is given by

(2.19)

with an expectation value of

_ ( Cg 2

Cg *Ce ) P- Ce*Cg Ce2 .

(2.20)

The advantage of using the density matrix is that the matrix elements have a clear physical meaning: the diagonal elements are the ground resp. excited level populations, and the off­diagonal elements, which are each others complex conjugates, represent the atomie coherence.

The time evolution of the density matrix, a very general case of the discussion of the Ra bi frequency in subsection 2.1.3, is described by so-called Optieal Bloch Equations, again in analogy to the Bloch equations used in magnetic resonance theory. It is rather straightforward to include in these equations not only spontaneous emission and detuning, but even Zeeman precession in the case of degenerate atomie levels, which will he discussed in the next section.

It has been shown that the coherence does not immediately adjust to changes in the light field. This complicates the evaluation of the force. Therefore, usually the adiabatic approach is made: one puts for the coherence the steady state value, assuming that the damping time

14

Figure 2.5: The transition probabilities fora J=1/2 to J=3/2 transition

is much smaller than the time scale with which the field varies. This applies for low intensities (n .c:t: f) and slow atomie motion (kv.c:t: f).

The general Bloch equations and a derivation of the resulting force in the adiabatic ap­proach, are presented in [NIE91]. Two types of force emerge: dissipative, resulting from spontaueaus emissions, and reactive, resulting from stimulated emissions. An example of the first type has been discussed in the treatment of Doppier cooling, where stimulated emission has been neglected. Channeling has been discussed as an example of a reactive force.

2.1.5 polarisation and atomie sublevels

So far only a pure two-level atom has been considered. These levels are now allowed to be magnetically degenerated. Only consiclering J to J + 1 transitions, the simplest example is an atom with a lower level angular momenturn of 1/2 and upper level angular momenturn of 3/2. The ground level has then two sublevels and the excited level four. The level scheme and transition probabilities, equal to the square of the Clebsch-Gordan coefficients, is shown in fig. 2.5.

The effect of polarisation can now be made clear. Linearly (1r) polarised light will induce a transition with ~m=O, which has so far been the only possibility. Circularly polarised light however, a-+ or o--, induces transitions with ~m=1 or -1, respectively.

third time constant: the pumping time

If the multilevel atom is driven by, for example, a-+ light, the ground state population will shift to the m=1/2 sublevel, until the m=-1/2 sublevel is emptied, and the only possible transitions are between the m=1/2 ground level to the m=3/2 excited level. An effective two level system is formed. The charaderistic time neerled to reach this situation is called the pumping time Tp, as the atoms are pumped into one subleveL

This pumping time is, for low values of s, proportional to 1/(sf). The exact value depends on the sublevel structure. For the simple example of the J=1/2 to J=3/2 transition, there is only one path from the m=-1/2 ground sublevel to the m=1/2 ground sublevel, which is via the m= 1/2 excited level. The two transition probabilities multiplied give the proportionality constant: Tp = ~ (s~).

lightshift

As was noted before, the lightshift of a level is linear in the coupling strength with the laser field. This means that the lightshifts of sublevels are proportional to the transition probabilities as given in fig. 2.5, to the relevant level. This leads to very different sublevel

15

., 0 ., -·2 -1

- m;=•3 - I I •2

·3

J 1

+1 ·2

I mJ=•3 ·3 0 -·2 ., -;-- ~ - T -;;--

I I 5 8 9 8 5 I I I l l I

1 3 6 10 15 I I I I I 0.04 0 0 0.04 - 0 - 0.24 ·2 -·2 c ~3 0.24 ·1 - 0 - - "'.i =•2 0 ·1 - t .o

0 +1 •1 -(a) fb\

m;=•2

Figure 2.6: lightshifts and steady state ground level populations for a J =2 to J =3 transition in linearly (a) and circularly (b) polarised light with negative detuning

lightshifts for different light polarisations. As an example the shifted levels for a J =2 to J =3 transition and for negative detuning are shown for 1r and a+ light in fig. 2.6.

In section 2.3 a type of cooling force that depends on these differences in lightshift will he discussed.

influence of a magnetic field; fourth time constant

The two effects caused by a magnetic field are Zeeman shift and Larmor precession. The first is present when the magnetic field is parallel to the quantisation axis. The energy of the sublevels shifts with an amount linear in the magnetic field and the value of m:

l!:!.E = mgf,lsB, (2.21)

with g the gyromagnetic constant and fLB the Bohr magneton. It follows that for a l!:!.m=Ü transition, the transition frequency does not change.

The second effect, Larmor precession, is classically a precession of the atomie magnetic moment around the magnetic field. Quantummechanically, the effect is present when the magnetic field is perpendicular to the quantisation axis, causing redistribution among the sublevels. The characteristic frequency is given by the classica! Larmor frequency:

(2.22)

In section 2.3.4 a cooling mechanism based on competition between this frequency and the inverse pumping time will he discussed.

2.2 sub-Poisson pboton statistics

2.2.1 introduetion

All results have so far been derived semiclassically, treating the atom quantummechanically, but the light field classically as a monochromatic coherent electromagnetic wave. Spontaneons emission has been taken into account phenomenologically. The 'photons' that have been

16

rnentioned, must be seen as a fancy name for the counts that a photoelectric detector would give. The operation of the detector is based on absorption in the detector rnaterial, and the discreteness of the signal can be explained by the quanturn character of this rnaterial, without quantisation of the light field.

Classica! theory prediets that in the limit of complete coherence, the counts must have Poissonian statistics, which rneans that the spread in the nurnber of detected 'photons' in a given time interval is the square root of this nurnber. A loss of coherence implies a larger spread, so that classically the spread can never be lower than the Poissonian value.

A quantity that describes the statistics is p(n,t,t+ T), the probability of detecting exactly n photons in a time T. This quantity is closely related to the cornbined chance of detecting a photon at time t, and detecting another at time t+Llt, which is called the second order coherence g(2l(t,t+Llt). Already in 1956 [HAN74] it was found that for therrnallight the maximurn of this cornbined probability lies at Llt = 0. The photons tend to be ernitted in bunches, so the effect is called photon bunching. The statistkal spread in the nurnber of detected photons is large.

This is very different for our two-level a torn being driven by a laser, when only spontaneous ernissions are considered. After having ernitted a photon, it will on the average take a delay time Texc "' 1/!1 befare the atorn is excited back to the upper level, and can ernit a photon again. So the cornbined probability decreases for Llt < Texc, and is zero for Llt = 0. This effect is called antibunching.

For very weak driving intensity, the spontaneous decay time T of the a torn can be neglected and the fluorescence light follows approxirnately the statistics of the driving field. For very strong intensity the excitation delay time can be neglected and the statistics correspond to the Poissonian statistics of the spontaneous decay time. However, for moderate intensity the ernitted photons will be very regularly spaeed in time. It can be suspected that such regular light should have a srnall statistkal spread.

In 1976 Mandel published a full quanturn theory of the fluorescent light frorn a two­level atorn driven by a coherent electrornagnetic field, with as result a value for the spread in photon nurnber that is smaller than the Poissonian value. A rneasurernent of this sub­Poissonian statistics can be regarcled as 'proof' of the quanturn character of light.

2.2.2 the statistics parameter Q

To characterise the statistkal spread, Mandel introduced the parameter Q, defined as

Q _ ((Lln?)- (n) - (n) . (2.23)

Q characterises the deviation of the spread in photon nurnber of the Poissonian value. He derives a sirnple analytica! expression for resonant excitation

(2.24)

valid only in the limit of long interaction time. A logical methad to rneasure Q seerns to be to use a photon detector, for exarnple a

photornultiplier, and directly register the photoelectric counts. This kind of experiment has been perforrned, and yielded sub-Poissonian values of Q that agreed with the theory. However, the lirnited quanturn efficiency of photornultipliers and lirnitations on the opties collecting the

17

fiuorescence photons put a low upper limit to the detection efficiency. It can he shown that the measured value of Q will he proportional to this detection efficiency, and thus hardly discernable from Poissonian statistics.

In 1980, Cook published an artiele [C0080] in which he treated fiuorescence statistics using the theory of atomie motion in a running light wave. In the case of an atomie beam intersecting a transverse laser beam, the atomie beam will he defiected due to radiation pressure (see subsection 2.1.2). Since an atom gains on average a momenturn hk with each absorption-spontaneous emission cycle, the defiection of the atomie beam is a direct measure for the average number of scattered photons per atom. From the braaderring of the beam, the spread in number of emitted photons can he deduced. Braaderring is caused by fiuctuations in the pressure, stemming for a two-level atom from two different origins:

• fiuctuations due to the random direction of spontaneously emitted photons

• fiuctuations in the number of emitted photons per time unit.

The second contribution represents the statistkal information we need, the first can he calculated from the angular distribution of the spontaneously emitted photons.

So, defining the average initial momenturn of the atomie beam in x-direction (Po), and the initial divergence ((.6.P) 2 ) 0 , the experimental value of ((.6.n?) can he deduced from

(P) = (Po)+ hk(n), (2.25)

and (2.26)

with (P) the final average momenturn in x-direction, and ((.6.P) 2 ) the final divergence. The term 215 ( n) represents the angular distri bution of fiuorescence photons for a two-level a torn.

Converting these expressions to the defiection angle ( 0), according to ( 0) = ( Px) I Pz and ((.6.0)2) = ((.6.Px)2) I Pz 2, the experimental value of Q is given by

(2.27)

Atomie motion theory gives the theoretica! values for ((.6.n)2 ) and (n). The atoms should interact with the light long enough to permit a description of their

motion with a Fokker-Planck equation (2.29), so that defiection and broadening appear as two distinct terms in the description.

The resulting theoretica! expression for Q is

s( 462 lf2 - 3) Q = (1 + 8 + 462 lf2)2 '

(2.28)

including the effect of detuning. The detection efficiency f3 can he taken 1 in the defiection experiment, and hence does nat enter the expression.

At resonance Q is always negative. However, for detunings larger than /I_ r, Q becomes positive, implying super-Poissonian statistics. So far only sub-Poissonian valnes have been measured with the setup.

Below (fig. 2. 7) the theoretically predicted dependenee of Q on the de tuning is pictured fors = 1 and s = 10. For larger intensity the super-Poissonian statistics are more pronounced.

18

0.50 r-----------,

Q

0.00 ~/

-0.50 ~;

/"---L- ---

4

otr

-s=l - s=IO

6

Figure 2.7: theoretica! dependenee of Q on detuning for two different intensities.

2.2.3 measuring Q with multilevel atoms

The theory can also be applied in the case of multilevel atoms as discussed in subsection 2.1.5, with only some adaptions. For the J=2 to J=3 transition in linearly polarised light, for example, one only has to change the factor 2/5 in equation 2.26 into 16/45. In circularly polarised light the transition becomes eventually a pure two-level transition, but for small intensity the time needed to reach this state can be very long in comparison to the interaction time in the above discussed case.

It can be expected that this behaviour can be influenced using a magnetic field. Investi­gating this influence is one of the future plans for this project.

2.3 sub-Doppier

2.3.1 Doppier cooling revisited

In this section some charaderistics of cooling forces will be explained. In section 2.1.2, a one­dimensional friction force has been derived occurring in a standing laser wave. This force, if exerted perpendicular to the direction of an atomie beam, can be used to narrow the velocity distribution of the atomie beam, i.e. to collimate the beam. For this process, the term 'one­dimensional Doppier cooling' is used. The velocity distribution could also be narrowed by letting the beam pass through a narrow slit, but then the beam loses intensity, whereas with Doppler cooling the intensity is conserved.

Because the force is linear in the velocity, the transverse velocity distribution stays Gaussian (provided it started as Gaussian), and a temperature can be defined according to !m( V x 2 ) = kBTx. A temperature in one direction is not at all a st range idea if one realises that the force could as well be produced in all directions, yielding the same temperature, which is in fact a common practice already [ASP92].

In general cooling forces work only for a certain range of veloeities around v = 0. The range of veloeities for which a force is appreciable is called the capture range. This capture range is related to the time constant with which the atom reacts to the applied field, in this case the natural lifetime T. For Doppier cooling this is obvious, since the process is based

19

on radiation pressure, a force with a capture range of ~v = rIk. The friction coefficient is maximal when 8 = -f 12.

diffusion; a lower limit to the temperature

Broadening of the atomie beam due to fiuctuations in the force has been mentioned before. These fiuctuations can be presented in the form of a diffusion coefficient D in the Fokker~ Planck equation descrihing the evolution of anatomie velocity distribution W(v):

(2.29)

With M the atomie mass. While the cooling force tends to narrow the velocity distribution, the diffusion tends to widen it. This determines the equilibrium temperature that is reached, given by

(2.30)

For a two-level atom there are fiuctuations in the number and direction of spontaneous emissions. Secondly, there are fiuctuations in the reactive force, due to fluctuations in the number of scattered photons into the different laser beams by stimulated emission. Both contribute to the diffusion coefficient, and both terms are linear in intensity.

Since for Doppler cooling the friction coefficient is also linear in intensity, the equilib­rium temperature DI a is independent of intensity, as long as stimulated emission does not dominate. In this case, kBTD = nf 12.

For an atom with degenerate levels an extra term, also linear in intensity, comes in for fiuctuations in the polarisation of the spontaneously emitted photon. For polarisation gradient cooling, discussed below, the friction coefficient is however independent of intensity, so that the equilibrium temperature of this cooling mechanism goes down linearly in intensity. This can he understood in a more formal way in termsof atomie response times, as will be discussed in the next prargraph.

2.3.2 sub-Doppier cooling; overcoming the Doppier limit

Cohen-Tannoudji points out [COH92] that not only the capture range, but also the final temperature of a cooling mechanism is inversely proportional to the internal time constant Tint with which the atom reacts to the light field. In the case of Doppler cooling this constant is the naturallifetime 7. He introduces the non-adiabaticity parameterf = kvTint, which is relevant because it determines how much, due to the finite reaction time, the internal state of a rnaving atom lags behind its steady state in the light field. The force is linear in this parameter, as long as f < 1.

A mechanism with a larger internal time would give the same force strength at a smaller velocity, and thus a larger friction coefficient, which leads to a lower final temperature. This is called sub-Doppler cooling.

An internal time that is available is the pumping time Tp = TI s for atoms with degenerate ground level (see section 2.1.5), which grows larger with decreasing light intensity. The final temperature can go down, as long as the interaction time is much larger than the pumping time, until the Fokker-Planck equation is no langer a valid description. This is the case when v is of the order of magnitude of the recoil velocity due to spontaneous emission, so that the velocity can no langer be considered to change in a continuous way, but instead varies with

20

discrete steps of lik. Therefore the lowest temperature that can be reached is the recoillimit temperature, in which case the atom hops back and forth around zero velocity,

(2.31)

with M the atomie mass. In any mechanism which depends on the requirement that a rnaving atom has to update its

internal state by pumping among its sublevels, the polarisation of the light must be spatially varying. Therefore sub-Doppier cooling is also called polarisation gradient cooling. Two examples will be discussed below [DAL89}. For both examples it can be shown that the friction coefficient a is independent of Tp and hence of s, whereas the diffusion coefficient decreases linearly with s, showing again that the final temperature of these mechanisms will go down linearly with the laser intensity.

2.3.3 Sisyphus cooling

The idea of a timelag Tp in the reaction of the atom on changes in the light field is very clear in the Sisyphus cooling mechanism. The basic idea is to make use of the difference in sublevel lightshifts for different light polarisations (see section 2.1.5). For e.g. a multilevel atom in circular light, the difference in lightshift is maximal between the two outer sublevels, and the atom is always pumped into the substate with the largest lightshift, which for negative detuning means the lowest energy. Fora+ light this is the substate with the highest m value, and for a- light the lowest.

So, if an atom were adjusted to a+ light and suddenly (meaning here: in a time shorter than the pumping time) put in a- light, its potential energy is raised and thus its kinetic energy must diminish; the a torn is cooled. However, the potential energy picture can only be used when the atom interacts with a static field. Therefore, the light field in which the atom can lose kinetic energy in the way described above must be spatially varying from one a type to the other and back. This is realised in a standing laser beam, created from two coun­terpropagating laser beams with perpendicular linear polarisations (lin l_ lin configuration). The two beams are described as

E- E - -ikx-wt = oEze '

E- E - ikx-wt = oEye ,

respectively, and the superposition yields

- ~Ëy+fz Ëy-Ëz ·t E = Eov2[ ..j2 coskx- i ..j2 sinkx]e-tw

(2.32)

(2.33)

(2.34)

What this formula represents is depicted in fig. 2.8. One sees that every 1/2 À the polarisation changes from one a type to the other and back. In between the light is linearly polarised.

Also the lightshifts for negative detuning of the example at om with a J = 1/2 ground state are indicated. They vary sinusoidally with x. If an atom is at rest in this light field, its population depends on x, varying with x from one sublevel into the other and back.

Now a rnaving atom is considered. Beginning at a point where the light is a- polarised and the atom is pumped in the m=-1/2 sublevel, the atom will move towards a+ light, which means climbing a potential hill and losing kinetic energy. Meanwhile, as soon as the other sublevel is lower in energy, the atom will start pumping into the other sublevel, but for any

21

}x z

+1/2 -112

Figure 2.8: In the lin .l lin standing wave (top), the polarisation varies from a+ to a- and back. The lightshifts of the sublevels of a J=l/2 state vary accordingly (middle), and since the atom is, for negative detuning, always pumped into the sublevel with lowest energy, these have the highest steady state population (indicated by dots ). A rnaving atom in this state (bottom) will he pumped into the level with lowest energy aft er a time lag, so that on the average it is climbing potential hills.

22

-0.2

J,= 1 ~J.=2

J,=2_,J.=3

J,=3_,J.=4

-0.1 0 0.1 reduced velocity w

0.2

Figure 2.9: Calculated sub-Doppler force in the lin l_ lin configuration for a few different transitions.

Figure 2.10: The a+a- standing light wave. Because the polarisation is linear everywhere and the intensity does not vary, the lightshift is independent of x.

velocity smaller than V x = -41 ~, the capture range for this cooling force, it will on the average

Tp

only climb hills. A typical example of the resulting force as a function of velocity, calculated in the formal­

ismof Nienhuis mentioned insection 2.1.4, is shown in fig. 2.9, with b = -1.5f. The reduced force and reduced velocity are scaled with the intensity, according to <P = 2 /i~ks and w = ;~. Qualitatively, the curves are similar to the Doppler cooling curve of fig. 2.3, but bath the magnitude of the force and the capture range are much smaller.

2.3.4 er+ er- cooling

When a standing wave is created with a a+ and a a- beam, another type of polarisation gradient is formed, according to

Ë(x) = Eo[(?ycoskx + Ëzsinkx)]e-iwt. (2.35)

A picture is given in fig. 2.10. The polarisation is linear everywhere, but the direction varies as a helix with pitch À. For our J = 1/2 ground state a torn, there is no difference in lightshift of the ground state sublevels. Therefore, the example here is a J=1 to J=2 transition. Of this atom, the lightshifts of the ground state sublevels are indicated in the picture. In steady state, the populations of the sublevels lg1), lgo) and lg-1) are respectively 4/17, 9/17 and 4/17.

A rnaving a torn sees a polarisation rotating with kv. To give a better understanding of how the atom reacts to this, a transformation is made to a rotating frame in which the light

23

polarisation is constant. Unlike the rotating wave approximation, this is a transformation of the external variables of the atom. For the atom, the rotating frame acts as a magnetic field that causes Larmor precession among the sublevels.

Due to this precession the atomie sublevels become mixed up. In [DAL89] it is shown that a difference in population of the g1 and g_ 1 levels arises, according to

40kv n -n ------

91 9-1 - 17 "E ' u ls,l9o)

(2.36)

with ~Eis,l9o) the light shift of the m=O ground level. In the case of negative detuning, and atom travelling towards the a+ beam will get an

overpopulation in its m=l sublevel, which makes absorption of a a+ photon more probable than of a a- photon. For the other direction goes the opposite; the atom always absorbs more photons from the counterpropagating beam than from the copropagating. Thus, in a sense the mechanism is equivalent to the Doppier cooling mechanism, except that the capture range is inversely proportional to the pumping time, as for Sisyphus cooling.

24

Chapter 3

experiment al

3.1 the atom

The transition between the metastable 3 P2 level and the 3 D3 level of the next excited contig­uration in noble gas atoms forms an effective two-level system. The lower level is forbidden to decay to the ground state because of the selection rule b..J = ±1 or 0, and because of the same selection rule, the upper level can only decay back to the 3 P2 metastable level. Thus a closed system is formed.

Fig. 3.1 shows the relevant part of the spectrum of argon. So far experiments have been performed with neon, using a dyelaser to drive the transition [H0093]. Recently a diode laser system has been built ( see section 2.2) to drive the argon transition, which with the experiments in this work will he performed. Thus, from hereon only argon will he discussed.

The wavelengthof the transition is 811.5311 nm [WIE69]. The lifetime of the upper state is 27 ns, so that the linewidth in frequency units, 2

;, is 5.8 MHz. The lower level has five magnetic substates, the upper level seven. Fig. 3.2 shows the transition probabilities.

Finally the sealing intensity Io in the case of a transition probability of unity is calculated for argon, using the relation

nwo3 Io = '

127l"TC2 (3.1)

to be 13.5 J.LW/mm2•

3.2 the laser

From the farmer paragraph one can conclude that the laser should he stably tunable to the 3 P2 - 3 D 3 transition frequency of argon, and with a linewidth and stability well below the natural linewidth of the transition. There should also be the possibility to tune the laser several times this linewidth off resonance. The intensity need not be very large; a few milliWatts will suffice to reach several times the sealing intensity, since the interaction region will only be a few millimeters wide (see section 2.3).

It will appear that these demands can be met by using a diode laser. This kind of laser can be mass-fabricated using microchip technology, and thus the price of the laser is, in comparison toother lasers, very low [WIE91].

25

14.0

11.0 1=0 1=1 1=2 1=3

Figure 3.1: The energy levels belonging to the 4s (lowest four levels) and the 4p configuration of Argon. The transition 3 P2 - 3 D3, indicated by the arrow, forms a two-level system.

m=-3 m=1 m=2 m=3

~ T 1/3 1

1~ m=-1 m=O m=2

Figure 3.2: The transition probabilities for a J =2 to J =3 transition

26

Buried heterostructure (index-guided slripe geometry)

Oxide---r--'w.-­n-GoAs

(octive layer)-+--+--r-n-GaAIAs -t----J---J

J_y ~

n-GoAs

conduction bend

Heterojunctions

t - flow af electron• óE" r_L f .... ,,, F, E,., Z

r "'' \ ---. I' ',~~~-

Figure 3.3: A cross-section of an index-guided diode laser, and band structure across the laser

3.2.1 diode lasers

Fig. 3.3 shows an cross-section of an index-guided laser. Essential for laseraction is a medium that can amplify the laser light by stimulated emission, and a cavity in which the light can resonate. Stimulated emission can dominate over absorption if there is population inversion, which means that the upper level of the desired transition is more occupied than the lower level.

In diode lasers, the transition frequency is the bandgap of the semiconductor materiaL Fig. 3.3 makes clear how a population-inversion can be created: The active layer lies between n-doted and p-doted material, so that energy harriers are created. When a current, typically tens of milliAmperes, is applied in the z direction, electrans and holes amass at their energy harriers, and can be reccmbined by spontaneons or stimulated emission of a photon with the bandgap energy. At a certain value of the current, the threshold value, population inversion is realised and stimulated emission dominates.

The light propagates in the x direction. The endfacetsof the semiconductor material form 30% reflective mirrors because of the difference in refractive index between the semiconductor material and air, thus creating a cavity. In the y and z direction the active layer is sandwiched between material with a higher refractive index, so that diverging light is reflected back in the active layer. Thus, a waveguide for the laserlight is formed, and this is why the laser is called index-guided.

The laser output is linearly polarised, and typically a few tens of milliWatts. The diver­gence angle of the outcoming light is typically 15 degrees, which is rather large. Therefore a collimating lens is required to make a parallel beam.

tuning the wavelength, cavity pulling and modehops

As has been made clear, the wavelength of the laser depends on the bandgap energy of the semiconductor materiaL The band structure results in a gain curve with a parabalie maximum. From this curve, the wavelengths that can resonate in the cavity are selected. The condition for this is that the wavelength fits ~n times in the cavity. Since the diode laser cavity is so small, the resonant wavelengths are far apart and only one wavelength is selected; the laser works single-mode.

The cavity length, and with it the resonant wavelengths, can be varied by changing the temperature of the laser, but this influences also the bandgap energy. As showed in fig. 3.4, the gain curve shifts faster than the resonance wavelengths. Fora while the wavelength follows the cavity ( cavity pulling), until another mode is allowed for which the gain is higher. The

27

a------

b --c -- /

/

~---······----/ .. ········

/· .... ··

~-

temperature

Figure 3.4: Wavelength dependenee on temperature of a diode laser ( c ). Changing the tem­perature changes the cavity length and thus the resonating wavelength (a), but shifts the gain curve faster (b ). This results in gaps in the tuning characteristic.

laser modehops to the new mode and skips a band of frequencies, as indicated in the figure. Changing the current through the laser also inftuences its wavelength, because the current

inftuences the laser temperature. Furthermore the refractive index of the material is changed, thus changing the optical path length.

Based on these two tuning possibilities, a diode laser housing has been developed in the group AOW. It consistsof an alnminurn black box with a watercaoled baseplate. On this the laser is mounted in an alnminurn holder on a Peltier element. A NTC near the laser registers temperature changes, which are then corrected by the Peltier element. The laser current is supplied by a stabilised power supply. Same characteristics of this system are listed in the table below.

gain curve shifting cavity length change current dependenee stabilisation up to

0.5 nm/K 0.06 nm/K 0.012 nm/mA 1 mK and 5 J.LA

Thus, in between two modehops, the demand of tunability seems to he met. The laser we use is specified to have a maximum output of 30 m W, which also should he sufficient.

linewidth

If only stimulated emission were present in the laser, the light would he of exactly one wave­length. However, spontaneons emissions still occur, introducing random phase photons per­turbing the light field in the cavity. This causes the laser output to contain a band of frequen­cies around the lasing frequency. The ratio between stimulated and spontaneons emissions determines the width of this band, called the linewidth of the laser output.

Various factors contribute to this ratio. The most important is the residence time of photons in the cavity. The residence time is determined by the length of the cavity and the finesse, which is the number of times the photon is reftected befare it leaves the cavity. Both constants are not in favour of a diode laser. The cavity length is only a few 100 J.Lm and the

28

Figure 3.5: weak feedback using a Fabry Perot in the V-mode.

finesse is at most 2. So it can he expected that the linewidth will he much larger than that of, e.g. a He-Ne laser with a cavity length of 30 cm and a finesse of 100. In fact, estimates of this linewidth give valnes on the order of 50 MHz, toa large for the experiment.

3.2.2 reducing the linewidth with external feedback

weak feedback with a Fabry-Perot

The obvious way to rednee the linewidth is to create an enlarged cavity by putting a mirror at some distance of the laser and reflect part of the light back, thus enlarging the average residence time of photons in the cavity. However, the laser will then tend to become unstable and even cease to emit coherent light (the 'coherence collapse' ).

A way to approach the problem is nat to include the laser in an enlarged cavity, but to couple it weakly to an external cavity, which can he made of arbitrary length and finesse. This idea has been carried out [CON92] using a Fabry-Perot resonator in the V-mode as external cavity (see fig. 3.5). One of the outgoing beams is reflected back in the laser, the others are left for output. The linewidth of this system has been measured to he less than 100kHz, which shows that the idea is succesful in reducing the linewidth. However, tuning the wavelength in this system has become an elaborate affair: The laser, the external cavity and the distance between them needs to he adjusted. This is typical for weak feedback: bath cavities have an equally strong influence on the wavelength, and these need to he carefully balanced.

strong feedback with a blazed grating

lt would he more desirabie to make the external cavity completely dominant, because in this limit even the coherence collapse is overruled. For this strong feedback is needed, but the more light is reflected back in the laser, the less is left for output. Therefore st rong feedback is only a realistic option if one has a laser, with one facet coated for 90% reflectance and the other for 10%, as available for wavelengtbs between 800 an 850 nm. An external mirror will effectively dominate the latter facet if it reflects about 30% of the light back in the laser [TKA86]. Putting this mirror at 2 cm from the laser, an enlarged cavity is created with a much greater length than the diode laser. This should also rednee the linewidth, but offer a more easily tunable system.

If the enlarged cavity is completely dominant, the cavity length is nat a good wavelength

29

e,. \. ........ ... ·· \.._

~EJ;

Figure 3.6: A diode laser with grating feedback. The blazed grating reflects the first order back into the laser.

selector anymore, because the resonant modes are too closely spaeed to select one wavelength from the laser gain curve. A lot of modes can he expected to coexist.

A way to· control the wavelength in this system would he to use a dispersive element as external reflector, such as a prism or a grating. This provides a narrow 'external gain curve'. Our choice was to use a blazed grating. Fig. 3.6 shows the principle; the first order is coupled back and the zeroth order is used as output. The possible modes belonging to one cavity length can now he selected by changing the grating angle. Independently, by varying the cavity length, the position of the individual modes can he shifted. Thus this system offers a wide and continuons tuning range.

Because a blazed grating reflects most of the intensity in the first order, at least 50% of the light is available for feedback. This makes sure that the system will work for a comparatively wide range of grating angles, which corresponds to a range of lasing wavelengths.

Fig. 3.7 shows the system as it has been built. The drawings were copied from an artiele by Wieman et al. [McAD92], in which the details of this system are described.

The only difference in our case is that we use the temperature stabilisation which was already available. Now the Peltier element has to control the temperature of the alnminurn housing of the laser and the grating, instead of only the laser housing. It appears that the accuracy of the temperature stabilisation stays the same, only its response to temperature changes becomes slower. Some characteristics mentioned in the artiele are listed in table 3.1. The output power of the system is only about one third of the originallaser output, but this will still he sufReient for the experiment.

operating the grating feedback system

How to align the collimating lens and the gratingis described in [McAD92]. The system was fi.rst investigated with a small monochromator, with a resolution of 0.5 nm, not enough to notice any modehops. At a constant temperature a tuning range of 10 nm was found (fig. 3.8). This is indeed a wide range, because for a free laser the temperature must he varied over 40°C to get this range.

The treshold current, predicted to he lower for the coupled system [WYA83], was also

30

Figure 3.7: grating feedback system overview. DL = diode laser, C = collimating lens, G = grating. The grating can he coarse aligned with the micrometers H and V, and fine with the piezo disc P. The temperature of the system is controlled by a water caoled Peltier element, and monitored by the NTC T near the laser.

cavitylength modehop micrometer tuning piezo tuning temperature tuning tuning range

0.02 m 16 pm (8 GHz) 5000 GHz/turn 1 GHz/V 7 GHzjK 20 to 30 nm

Table 3.1: some charaderistics of the grating feedback system discussed in [McAD92]

31

6 70

4

""' 00 60 5

<:i < > "' 5 '" :î 0 Ë

""' t: § ::l

u

""' :sa ""

0

.5 "'

~

"' -2 50 " .a -5 o.> 1!. -c 1!. E "' 1!.

+ -4 1!. 1!. +

1!.

1!. "' "' 1!.

-6 40 20 30 40 50

micrometer position (a.u.)

Figure 3.8: measured tuning range and threshold current of the grating feedback system

measured. It was seen to increase at the edges of the tuning range, and to return to the free threshold current at the point where the coupling is lost, and the wavelength jumps back to the free wavelength_

modehops in the grating feedback system

The fine tuning characteristics were investigated with a Michelson interferometer accurate to 1 pm. On this scale the modehops of the feedback system can be made visible. About the same tuning range between two modehops as in the Wieman artiele was found: Wieman found 16 pm, we found 12 pm. Remarkable is the fact that when changing the wavelength by turning the grating, the laser modehops backwards to the starting frequency.

Also forward modehops of 0.3 nm were found, just like in a free laser. Still, with a combination of grating and temperature tuning, the tuning range is effectively continuous.

To explain this complicated tuning behaviour, three factors that determine the wavelength must be considered; the 'external gain curve', and cavity pulling by both the external and the internal cavity. The internal gain curve is much wider than the external gain curve, so its infl.uence can be neglected.

As is shown in fig. 3.9, turning the grating to shift the external gain curve changes the external cavity length as well. The internal cavity length can be varied independently by changing the temperature. For the moment it is considered fixed.

The dependenee of the maximum of the external gain curve, )..9 , on the grating angle is given by

d)..g- )..

d0 tan(0) (3.2)

This formula is found when the condition for a wavelength to be refl.ected back in the first order,

)..9 = 2asin(0), (3-3)

is differentiated. a is the spacing between the grating lines, 8.10-7 m in this case.

32

Ll

\ .... ·· \._

e

Figure 3.9: Turning the gratingin the configuration of 3.6.

The wavelength change of the external cavity modes caused by the according displacement of the grating is given by

(3.4)

With (3.5)

this results in dÀc L2À

d0 - L 1 cos 0. (3.6)

With 0 = 30°, L1 = 20 mm and L2 = 35 mm, the variations of À9 and Àc are 1.4 nm/mrad and 1.6 nm/mrad, respectively, which is almost the same. The internal cavity length does not change. lts influence on the wavelength is schematically depicted in fig 3.10 I. Pulled back by the internal cavity, the gain curve shifts effectively much slower, until a forward hop is made as the wavelength pulls towards the next internal cavity mode.

The lasing wavelength does not, however, actually shift according to this dependence, but is at any moment equal to the highest gain mode of the external cavity. The external modes shift according to 3.6, much faster than the effective gain curve shifts. In this way, the small backwards modehops with the external cavity separation of 12 pm are formed. Thus a tuning behaviour as in fig. 3.10 II is predicted, which corresponds with the observation. In this case the gaps in the tuning range can be overcome by changing the temperature to shift the internal cavity modes.

tuning to a specific wavelength

The tuning range at constant temperature is not quite continuous. So to find a specific wavelength, the grating should be coarse tuned with the micrometer, after which the black box can be closed and the temperature adjusted until the desired wavelength can be reached using the fine tuning piezo's. A great help in this process is the 1 pm accurate Michelsou interferometer of AOW, which is discussed in [MOR89], since one can not only measure the wavelength, but from the photodiode signal one can also see clearly if the laser is single-mode or not, without having to align an extra Fabry-Perot interferometer.

33

II

I

wavelength

/ /

grating angle

a-­b -----C-

Figure 3.10: I: Cavity pulling by the internal cavity in the grating feedback system. a = external gain curve, b = internal cavity resonance profile. The scale is too coarse to show the resonance profile of the external cavity. II: Tuning characteristic of the grating feedback system. a = dependenee of the wavelength of the grating angle, b = a, pulled by the internal cavity, c = b, pulled back by the external cavity.

3.2.3 locking the laser to an atomie resonance frequency

saturated absorption

To see if the laser is on the correct argon transition frequency, an absorption cell is used. This cell is depicted in fig. 3.11. A plasma is formed in the cell to create the metastable atoms. In the picture is also indicated what happens if the frequency is below the exact resonance frequency: metastable atoms having a velocity component towards the laser beam will see the frequency Doppler shifted to the blue, and so the light will still be absorbed. This effect causes the absorption curve to be approximately 1 GHz wide (Doppler broadening), much more than the naturallinewidth of 5.8 MHz.

Figure 3.11: In an glass cell filled with argon gas, a plasma is created by a de discharge. The metastable atoms created in this plasma absorb the depicted laser beam, even if it is off resonance; due to the Doppler shift, moving atoms will see aresonant beam.

34

_________________________________ ~a_t~r_ap99 _______ _

5

l

frequency

Figure 3.12: The absorption cell of fig. 3.11, now with the laser beam reflected back. If it is off resonance, the atoms absorbing the first beam are not the same as the ones absorbing the reflected beam. They are only if the laser is resonant. If further the first laser beam saturates the atoms, only at resonance the ~eflected beam is passed through.

To abserve a narrow peak, the technique of saturated absorption is used [STE85]. Fig. 3.12 shows the method: after having passed through the absorption cell, the laser beam is reflected back and passes the cell again. When the laser beam is off resonance, it will in the first pass he absorbed by metastable atoms with a certain velocity component Vx, and on the way back by those with the opposite velocity component -Vx. These are different metastable atoms for any value of Vx, except when Vx = 0, which is the case for resonant light. Furthermore the intensity is chosen so that on the first pass the transition for atoms in this velocity class is saturated. When Vx = 0, the probe beam will find the meatstable state population partially depleted because of the saturation caused by the ingoing beam. Thus, its absorption is diminished, and the saturated absorption curve in fig. 3.12 is formed, with a tiny dip in the middle with a width of the order of the naturallinewidth.

reducing frequency fluctuations

The laser does not of itself stay on the resonance frequency. The frequency fluctuations can roughly he divided in two parts:

• slow drifting due to temperature fluctuations, at most a few MHz per minute,

• fluctuations at acoustic frequencies around 1 kHz, with an amplitude on the order of the naturallinewidth.

The fluctuations can he made visible using a Fabry-Perot interferometer tuned so that the laser frequency is on the flank of a transmission peak. That way a small change in frequency causes a large change in transmitted intensity. A dominant frequency of about 1 kHz could clearly he distinguished, as well as an increase of the amplitude as a reaction to speech.

The souree of this resonance was quickly found to he in the piezodisks, since these disks are also used in loudspeakers and are designed to resonate around these frequencies. The resonance frequency was measured to he 1.2 kHz. This resonance must he damped in some way, since the laser has to he used in a noisy laboratory (vacuum pumps, etc.).

35

Loek in amplifier

Figure 3.13: Locking the laser to the resonance frequency. The photodiode detects the satu­rated absorption peak. The lock~in amplifier modulates the resonance frequency, so that it can determine the derivative of the peak, which can serve as an error voltage to feed back to the grating position. a= glass plate, b = 1/4 lambda plate, c = absorption cell, d = coil, e =mirror, f = photodiode

First it was tried to prevent sound waves from propagating in the black box by pumping the air out of it, but this appeared to have no visible effect. The acoustic noise must he mainly transmitted by the aluminum structure. Therefore it was tried to damp these vibrations by applying putty at several critical points in the construction. The piezo disks are still free to flex, but not to vibrate. This had a very satisfying effect; no more reaction to speech was observed, nor to vacuum pump noise. The 1 kHz noise had changed into two new components:

• fluctuations of the same amplitude, but of a frequency of a few 100 Hz,

• fluctuations of very high frequency and of negligible amplitude.

The first component, and also any slower drifting, will he actively correctedusinga lock~in technique with a modulation at 1.025 kHz, as described below.

the lock-in amplifier; principle

The signal of a photodiode registering the transmitted probe beam is used as input for the lock~in amplifier. When the laser frequency is modulated at the lock~in reference frequency, the lock~in essentially takes the first derivative of the saturated~absorption peak. The output signal around zero can then he fed back as an error signal, in this case to the piezo disks, locking the centrallaser frequency to the zero of the derivative at the center of the saturated absorption signal. (see fig. 3.13)

However, actually modulating the laser wavelength would make the laser useless for the experiment. As an alternative, the absorption frequency in the gas cell is modulated in the following way [LIP91]:

36

Dlll

d

Figure 3.14: The diode laser system in the atomie beam experiment. a= saturated absorption branch, b = outlining mirrors, c = telescope, d = polariser, e = optional1/4lambda plate, f is vacuum setup.

First, between the laser and the gas cell a ~À plate is positioned to produce circularly polarised light, thus ensuring that in the gas cell only L1m = 1 transitions are induced, or even, supposing the atoms are all pumped into the m=2 sublevel, only m=2 to m=3 transitions.

This transition frequency can he Zeeman shifted with a magnetic field along the laser beam axis, allowing modulation of the transition frequency by amplifying the lock-in reference voltage output and letting it drive a current through a coil around the gas cell.

To he able to loek the laser to a detuned frequency, another coil is wound around the gas cell, through which a de current can he sent, introducing an offset magnetic field.

results

The remairring frequency fluctuations can indeed he controlled in this way. The system has been observed to stay in loek for several hours, even in noisy surroundings.

The second coil used for detuning has been calibrated using a Fabry Perot, giving a resonance frequency shift of 30 MHz detuning per Ampere. Since the free speetral range of the Fabry Perot is 2.5 GHz, this number is not very accurate. Another calibration of the detuning will he done ( see section 4.1) by measuring the radiation pressure as function of the current through the second coil.

3.2.4 using the laser in the experiment

The complete configuration as used for the experiment is given in fig. 3.14. The output of the laser system is 12.5 mW. First a small part of the laser beam is split off for the saturated absorption branch. Then via a set of mirrors the beam is directed onto a positive lens, a

37

~<--~3' oE:-------~~(;---~)

2f

Figure 3.15: Creating an image of a slit. The laser light falls undisturbed through the slit, except for diffraction on the sides. Because of this, the lenses are needed to farm the image.

pinhole and another positive lens, forming a spatial filter and a telescape to broaden the beam. The outgoing beam has a Gaussian profile with a FWHM of 4 mm. The total power is at this point 3m W. The loss of intensity is primarily caused by the dirty spatial properties of the diode laser beam, sa that the spatial filter only passes a small part of the beam.

This beam is polarised and directed into the vacuum interaction chamber through a win­dow coated for non-refiectivity. In the vacuum the beam passes a slit of 1 mm wide. The atomie beam passes at a few times 100 1-Lm of this slit, where the intensity profile should have a clean square profile. Several components as a polariser or a 1/4 lambda plate can he put between the third mirror and the vacuum chamber.

a square profile standing light wave

To create a standing wave with an square intensity profile, it would nat suffice to reileet the beam back with a mirror. At the edges of the slit the beam suffers diffraction, which deforms the square profile visibly already at less than 500 1-Lm from the slit.

Therefore animaging lens is positioned at its focal distance from the slit, and the mirror another focal distance away. The idea is that the central beam through the slit passes undis­turbed, while the sicles of the slit are more like point sourees of the diffracted light. So at the first pass through the lens the central beam is focused, and the diffracted light is made parallel. On the way back, the reverse happens, and at the slit the square profile is restored.

This idea has been tried out first [PEN92], with the mirror replaced by a second lens at twice the focal distance, and a CCD array to monitor the image (fig. 3.15). We will call this setup a monitoring branch. The image, from here called monitoring image, is made visible on an oscilloscope. After careful adjustment, making sure the lenses are clean and perfectly perpendicular to the laser beam, and all the distances are right, the desired square profile was detected.

With the mirror placed between the two lenses, an image should he formed in the same way upon the slit itself. This image we will call the 'standing wave image'. To he able to monitor this image, a more elaborate setup is needed. The system is depicted in fig. 3.16.

A beamsplitter befare the slit refiects to the left in the picture the light that returns from the mirror, into a monitoring branch. The monitoring image in this branch will only have the right square profile if the standing wave image is formed correctly. With this setup it is possible to create a standing light wave with an square intensity profile.

38

Figure 3.16: creating a standing wave with square intensity profile, using the imaging tech­nique explained in fig. 3.15. The beamsplitter and the extra imaging setup are needed to see if the first image is formed correctly.

3.3 the vacuum setup

3.3.1 overview

An overview of the setup is given in fig. 3.17. The Looptijd II is an atomie beam setup of more than four meters long. On their way from

souree to detector, the metastable atoms pass several components that make it possible to calculate their axial and transverse velocity from the position where they strike the detector.

Directly bebind the souree is the first collimating slit of 50 pm wide and 500 pm high. 773 mm from the souree is a chopper, whieh passes small bunches of the atomie beam, and also generates a trigger signal every time a bunch is transmitted. The detection electranies registers, for every metastable atom that is detected, the arrival time as counted from this trigger signal, so that the axial velocity Vax can be computed.

2219 mm from the souree is a second slit for the atoms, which can he moved in the x­direction. lts position is indicated with Xsiit· This slit serves to select a specific transverse atomie velocity Vtrans· This velocity can be calculated from the incidence position at the detector Xdet, the axial velocity and the axial distances, according to

Vtrans X det - X s/it (3. 7)

with L2 = 2562 mm. In a similar way, the width of the beam fraction that passes the second slit gives the initial spread in velocity.

So far, the laser has been left out of the discussion. If it is switched on, a transverse velocity change of the selected beam will result from the interaction, as well as an increase in width. These changes are the important parameters of the experiment. From the velocity change the light force is calculated, and from the broadening the fluctuation in this force.

39

Lt

z

\ : J : J

: _____ \ ______ _

Figure 3.17: Overview of Looptijd II. In a detail the form of the chopper slot is shown

IGP ODP

Figure 3.18: The vacuum system of Looptijd II. TP = turbopump, ODP = oil diffusion pump, IGP = ion getter pump, CB = cryobody. The cryobody lowers the pressure from 10-6 to w-8 Torr, but only in the left half of the setup.

vacuum

In order to obtain a mean free path that is larger than the length of the setup, a pressure of lower than 10-6 Torr is needed. Since all the metastable atoms travel in the same direction, collisions between them can be neglected. The most important pressure effect will be a loss of atomie beam intensity.

The vacuum system that is used is depicted in fig. 3.18. The setup has a series of 7 high vacuum pumps, as well as three differential pumping stages, separated by narrow openings between the vacuum chambers. With this equipment a pressure of 2.10-6 Torr is reached. The pressure is further lowered by means of a cryobody, which is kept at a temperature of 20 K by an external cryo generator. Residual gas freezes to this body, lowering the pressure further to 2.10-8 Torr in this part of the setup. The interaction chamber and drift tube to the detector, however, are not cryopumped and the pressure in this part of the setup is back to the 10-6 level.

40

-::::::::-

Figure 3.19: A souree that creates an atomie beam containing metastable atoms. On the left, argon is let in with a pressure of about 10 Torr. Where the atoms leave the source, a discharge is made in which the metastable atoms are created.

Tests under these pressure conditions show that the atomie beam intensity is such that in one minute an atomie beam profile for one slit position can be measured (see paragraph 4.2). Still, because the detector's lifetime decreases with increasing pressure, it would be advisable to increase the pumping speed at this end of the setup to lower the pressure.

The metastable atom detector is in a chamber that is always closed when it is not used. Anion getter pump keeps this chamber at a pressure of 10-8 Torr, toproteet the detector. During measurements this pump must be switched off, because it produces ions which are attracted by the negative potential of the detector, causing a huge background of about 50 kHz counts.

3.3.2 the metastable atom souree

The beam of metastable atoms is created in a discharge, discharge current typically 10 mA, and released in a supersonic expansion. A picture of the souree is given in fig. 3.19. A pressure of about 10 Torris supplied; the metastable atom production has been measured to increase almost linearly with decreasing pressure, until below a certain pressure the discharge extinguishes. The anode of the discharge is formed by the first collimating slit of 50 f-Lm wide. The velocity of the outgoing beam is centered round 800 mjs, and has a speed ratio of approximately 4.

The metastable atomie beam consists in case of thermal equilibrium of 1/6 part 3 Po, and 5/6 3 P2 metastable atoms.

3.3.3 the chopper; time of ftight technique

To enable time of fiight velocity detection, a chopper with an open fraction of 1/50 and a frequency of about 150 Hz is inserted in the atomie beam. With an atomie beam velocity of 800 m/s and a travelling distance to the detector of about 3m, the travel time is 3 ms, so the chopper frequency must be below 330 Hz.

The chopper has the form of a disk with slots on opposite sides. In fig. 3.17, in a detail it is shown that the slots consist of a wide opening and two narrow ones. The two narrow openings can transmit the atomie beam with either small or large velocity spread, the wide opening transmits a light signal, which supplies the trigger pulse for the measuring interface.

The detector registers ultraviolet light, which is produced in the discharge by excited atoms decaying to the ground state, as well as metastable atoms. The UV light is, of course,

41

detected immediately when the chopper opens. Some time later the peloton of atoms arrives.

3.3.4 the interaction chamber

In the interaction chamber a second slit of 50 11m wide is positioned. This one can be moved in the x-direction, to select the x-component of the velocity. The light slit is attached to the slit for the atoms, so that the atoms always passes at the same distance of it, and always sees the same intensity profile.

The slit assembly is moved with a stepper motor driven translator. In the case of a standing wave, the imaging lens plus mirror outside the vacuum are moved synchronously with a second translator, in order to maintain the correct distance between the lense-mirror assembly and the slit.

3.3.5 the metastable atom detector

At the end of the set up, the beam profile must be measured. U ntil now this has been done by point-for-point scanning, typically at 30 positions, with a scanning slit and a surface­ionisation type metastable atom detector with electron multiplier.

For this work, a detector has been installed which records also the position of every incident metastable atom. In this way, the beam profile can in principle be measured more than 30 times faster.

The detector is based on a 2.5 mm diameter triple MCP, which stands for MicroChan­nelPlate. The MCP's consist of small channels, coated on the inside with a material that easily releases electrons. The triple MCP consists of three of these plates in series. An accelerating voltage for the electrans is applied across the plates, as indicated in fig. 3.20.

When the first plateis hit by a metastable atom, its energy is used tofree the fint electrons. These travel into the channels, in every callision with the walls freeing more electrons, thus causing an avalanche. At the end a bunch of typically 107 electrans strikes the anode, which is a cushion-shaped resistor of 39 by 39 mm. For the moment only the position in the x­direction is needed, so the corners of the anode, where electrades are attached, are electrically connected two by two.

Both ends are grounded, so with the electrans impinging at the incidence position on the resistor, the current pulse di vides itself in two pulses to both electrodes, according to

(3.8)

with Q1 and Q2 the total charge of the pulses. x1 and x2 are defined in fig. 3.20. On both electrodes, pulse detecting electranies is attached. The pulses enter initially

through the capacitors, afterwards the charge is bleeded off through the resistor. This is the slowest part of the pulse processing, limiting the countrate of the system to about 20 kHz.

The charge pulses are first transformed into voltage pulses by charge sensitive preampli­fiers. A second amplifier is used to produce pulses between 0 and 5 V. A pulse stretcher holds the maximum of the pulses for several microseconds, to allow fora small time difference between the two pulses. Finally, the pulses each enter an ADC. The two ADC's are simulta­neously triggered by a delayed trigger pulse, produced by the sum of the two amplified pulses. The trigger delay must be long enough to allow both the pulse stretchers and the ADC input buffer amplifiers to reach a steady value.

42

chopper trigger -----.

Figure 3.20: The position sensitive metastable atom detector with detection electronics. a = preamplifier, b = amplifier, c = pulse stretcher. In a detail, a front view of the anode is shown.

43

Problems with nonlinearity of the pulse stretchers necessitated using only pulses having

an amplitude between 1 and 4 V.

3.3.6 collecting data

The ADC's belong to a specially made interface that stores every event as two ADC values and a time label, which indicates the time from the chopper trigger pulse. With these data, the incidence position can he calculated as x1 = v1~v2 x ef 1, with Xef 1 the effective width of the detector surface and V1 and V2 the height of the two pulses measured by the ADC's. A twodimensional array is filled with the number of counts as a function of position and time. Only the array elements which contain more counts than a background level are stored. This

forms the raw data of one measurement. A complete beam profile consists of two measurements for every position of the velocity

defining slit; one with the laser on, and one with laser off.

44

Chapter 4

results

4.1 nulling the magnetic field in the interaction region

A magnetic field causes Larmor precession, which quantummechanically means mixing up of atomie sublevels, and Zeeman shifts of the atomie sublevels. These effects will infiuence the interaction with the laser, so the magnet ie field in the interaction region must he a well defined parameter. Therefore, three sets of Helmholtz coils are placed around the interaction region to control the magnetic field in the three principal directions.

In the farmer experiments, the magnetic field was nulled making use of the Hanle effect. The methad is described in [H0093]. This methad could not he used in this case, because the J =2 to J =2 transition frequency is outside the tuning range of the diode laser system.

Therefore the magnetic field was measured using a 1 mGauss accurate Hall probe, which gives the magnitude of the flux through the probe. Due to the limited precision in positioning the probe, the magnetic field exactly at the interaction region is known with this methad to a few mGauss accurate. One mGauss corresponds to about one promille of a precession in 1 JlS, a typical value for the interaction time.

4.2 testing the detector

For the first measurement of an atomie beam profile, the slit for the atoms is put at its central position. The calculated relative beam positionis, for the moment, normalized to 4095 instead of the detector anode width, which has as yet to he determined. It is denoted as 'channels' in the figures.

First, the main amplifiers must he adjusted to compensate for the difference in amplifi­cation by the two stretchers. This is done by recording the beam position befare and after exchanging the electranies between the anode electrades and the ADC's, and adjusting the amplifiers until the beam position stays the same, which means that the signals from both anode electrades are equally amplified.

The profile thus found, shown in fig. 4.1, is taken in 1 minute measuring time, which appears to he enough to obtain a well resolved peak. The averaged rms width of a series of measured peaks is 6.79(6) channels.

To scan the surface of the detector, the collimating slit was scanned in steps of 1 mm. Using the relation /).xdet = LtLz /).xslit, with L1 = 2219 mm for the distance between the

45

Cf)

c ::;)

0 (_)

100

50

. ....

I

.. .

I

.. . • ..;_;..:,:,; :.,~"r.roMI

0~~~~~--~~~u 1900 1950 2000

position ( channels)

Figure 4.1: profile of the atomie beam taken with the position sensitive detector

souree slit and collimating slit and L2 = 2562 mm for the distance between the collimating slit and the MCP surface, this should correspond to a displacement of 2.155 mm at .the detector.

The result of this is shown in fig. 4.2. To the left (in the direction of the laser beam), the peak gradually grows smaller until it is no longer detected. This diminishing detection efficiency is caused by the cutoff of signals below 1 V and above 4 V. The further from the center the atom strikes the detector, the more unequal are the amplitudes of the two pulses that carry the position information, and the smaller the chance that both of the pulses are within the 1-4 V range. To the other side, the beam disappears suddenly. It looks like

-, the atomie beam is cut off by some obstruction between the souree and the detector, e.g. a misaligned differential pumping aperture.

This scan offers a calibration of the detector. In fig. 4.3, the incidence position of the atomie beam is plotted against the slit position. The fitted slope of the curve corresponds to 241'~ per mm displacement of the collimating slit. This results in a sensitivity of the detector of 112 channels per mm for the position on the detector. This means that the total effective width of the resistive anode, corresponding to 4095 channels, is 36.8 mm, of whieh however only 14 mm can be used. The rms width of the measured beam profile can now be evaluated, resulting in 61 J.Lm. The calculated rms width of the atomie profile itself is 36 J.Lm. The rms resolution of the detector is then 49 J.Lm, a satisfactory value. Moreover, the width of the atomie beam profile has been calculated assuming perfect alignment of the slits, and may thus be too low. The resolution of the detecting system, as well as the usabie range, can probably be increased by better electronics.

Ideally, the resolution of the detector should be such that it can resolve the deflection due to the scattering of one photon. One photon recoil gives a velocity change of 12.5 mm/s, causing a deflection of 40 J.Lm. The present resolution is not high enough to resolve such a small deflection. However, it is not far from this goal.

The maximum number of scattered photons, in the case of s=oo, is given by the interaction time (1.2 J.LS), divided by two times the lifetime of the excited state ( 2*28 ns). This gives

46

(/)

c :::J 0 u

150r--------------------.

100

50 ! •

' . aL-~~~~~~~ 500 1 000 1500 2000 2500 3000 3500

position (channels)

Figure 4.2: atomie beam profiles for different positions of the slit for the atoms. The slit has been scanned with steps of 1 mm

3000 .-

00

~ ;:::: 2500 ;:::: Cll ~ u '--"' 2000

;:::: .9 ...., ......

1500 00 0 0.. ~

Cll 1000 Q)

0..

500~~~~--~--~--~

40 42 44 46 48 50

collimating slit position ( mm)

Figure 4.3: The peak positions of fig. 4.2 plotted against the slit position. The slope is 241 channels / mm

47

(/)

ë ::l 0 u

150~--------------------~

100

50

..JA.~ wt\rJ~ ~.fJ.L l!W j,

0 1800 1850 1 900 1 950 2000 2050 21 00

position ( channels)

Figure 4.4: Atomie beam profiles for different slit positions, this time 100 /liD apart

a number of 21 photons. With an intensity parameter of 1, half of this number is scattered. This should give a peak displacement of about 400 /liD, whieh should be easily discernable with the present system.

To simulate this deflection, the slit was scanned in steps of 100 /liD. The result is shown in fig 4.4. In this range, the detection efficiency is constant. Again, the peak position has been plotted against the slit position, giving 259 channels per mm displacement of slit position, or 120 channels per mm of detector position. The discrepancy with the value of 112 channels per mm, obtained from the large~range scan, is significant. It may he due to non~linearities in the translating mechanism. This will have to be investigated further.

4.3 atomie beam profiles with the laser on

The laser intensity was chosen 30 11W/mm2 (s ~ 2) for the first measurements with a running laser beam. This should give a deflection of more than 44 channels of the resonant metastable fraction. In fig. 4.6, the measured beam profiles with laser on are shown, compared toa profile with laser off. The beam position is different of the central position in figs. 4.2 and 4.4, due to a different tuning of the electronics. In this case, the asymmetrie background is more pronounced. This has so far not been explained.

The expected effect of the laser beam on the atoms consists of a shift and broadening argon atoms in the 3 P2 metastable state, while the non~resonant 3 Po metastables are unaffected. Statistieally, the ratio between 3 P2 and 3 P0 metatstables produced in the discharge should be 5:1, so that the non~deflected peak should contain 17 % of the integrated signal. UV photons of the discharge are not included in the data, as they are discriminated against by time~of~flight analysis.

48

§ 1980 ...... . ~ 00 0 0.. 1920

~ Q)

0.. 1860

1800 '-----'-----'------'-------'----' 45.50 45.70 45.90 46.10 46.30 46.50

collimating slit position ( mm)

Figure 4.5: The peak positions of fig. 4.4 plotted against slit position. The slope is 259 channels/mm.

The observed effect is completely different. More than half the signal remains in the unchanged peak, while the other part seems to disappear completely. Although non-statistica! ratios have been observed in argon beams, these observations only resulted in higher ratios than 5:1. Thus, the predominanee of the unaffected peak can not be explained in this way. Presence of non-argon (e.g., nitrogen from an air leak) metastable atoms could offer an explanation. To check this, the conditions of the discharge have been varied, as shown in fig. 4.6, to change the relative abundance of argon and possible other metastable atoms. Increasing the pressure and lowering the discharge current seems to increase the fraction of resonant metastables, although the effect is not very strong. Also, this offers no explanation for the absence of a clear defl.ected peak. Thus a puzzle remains.

4.3.1 scanning the laser angle

If the laser beam crosses the atomie beam perpendicularly, the light force at resonance is maximaL Any deviation from this angle gives the laser a velocity component in the direction of the atoms, due to which the atoms will see the laser Doppier shifted off resonance.

Therefore the last mirror in fig. 3.14 is rotated and shifted by two stepper motors, to aim the laser beam from different angles on the slit. The idea is to align the laser beam by maximising the defl.ection of the atoms. To see if any trace of the expected behaviour could be observed, the averaged defl.ection of the atomie beam profile ( only shifting because, with decreased amplitude, the asymmetrie background becomes more dominant) has been measured as a function of the angle of incidence.

The result is shown in fig. 4. 7. The observed effect is indeed dependent of the laser beam angle. However, until the previous problem has been solved, the laser beam cannot be reliably aligned in this way.

49

rn

= = 0 u

250r-------------------ï

200

laser off 150

100

50

250

250 --

laser on 200 laser on

20 Torr, 18 mA 20 Torr, 14 mA 150

200

~ ( I

I' \

~tl.(f \. ... ~.,»..J,!,-1 4.;t-.. \~".l·' ·-.\.11_

100

A 50

' ., ~y·. ,,.~~•~'~)ti \~.,.~. •..• ' ... Q

150

100

50

laser on

laser on 20 Torr, 10 mA

200 30 Torr, 12 mA

150 200

~

0 )\ \~ \

0 1/·'> ....... ,x \,._,\'"'"'' I•"

"

100

f 50

w.l \ 9

' ,, -~Y'.' \y ~.~.~ ••..•• '"

laser on

5

150

100

laser on 200

30 Torr, 8 mA

20 Torr, 10 mA 200

150

15 0 100

5

0 ~\ 0 j \

~1 \

'"-t\· ""''"' ..... ,..., No,. •rJ>h

50 ~ .(

.,, .\.Jri'I'J~ \., p

~000 2050 2100 2150 2200 2250

10

0 2000 2050 2100 2150 2200 2250

position ( channels)

Figure 4.6: Beam profiles with laser on for some different souree conditions. The profiles are all taken with 30,000 counts, so in spite of the differences in count ra te, they can be compared. The collimating slit is at central position.

50

30

c

:~ 20 + "' 0 ++

""' • +

~ ++

"' +

""' "' OI) 10 "' .... "' > •• + "' + + +

+ + +

00 6 12 18 24 30 mirror angle (mrad)

Figure 4. 7: Measuring the interaction with the laser as a function of the angle with which the laser intersects the atomie beam.

51

'

Chapter 5

conclusions

In this thesis it is shown that the new position sensitive detector with processing electranies works as expected, enabling a measurement of the atomie beam profile in only one minute as compared to 30 minutes with the previous detection system. The resolution of.the total system is not yet one photon recoil, as desired, but this can probably be improved by upgrading the electronics. Especially the pulse stretchers, which cause serious problems by their nonlinearity,

should be replaced. The vacuum equipment of the setup needs to be drastically improved. Especially near the

detector the vacuum conditions are unsatisfactory. The laser system proved to be suitable for the experiment, stayingin loek easily for several

hours with adequate stability and linewidth. The influence of the laser beam on the atomie beam does not agree with the expectations

and is as yet not understood.

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special thanks to ...

Maarten, for being an overflowing souree of inspiration Ton, for being a great help in hard times Herman, for believing in me Rien and Louis, for the magie they use to keep our setups running Stefan and Evert-Jan, for patiently answering my imbecile questions about computers The SCEPTER team, for taking over the Looptijd II poltergeist Jan, for trying to control the chaotic behaviour of my supervisors Tabe, for still speaking to me after all the times I ignored his advices and love to Frank, for making life beautiful.

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