q j

DTICFinal Report ELECTE

on contract no. NOOO 1490 F0002 JUL3 0 1992D

rn Rand SCRenewal Research Proposal

1.0 Submitted to the Office of Naval ResearchJuly 1992

LASER COOLING AND TRAPPING OF NEUTRAL ATOMS

To be carried out in theLaser Cooled and Trapped Atoms Group

Atomic Physics Division(D Physics Laboratorym National Institute of Standards and Technology

Gaithersburg, MD 20899

IU Present Contract Period1 October 1989 through 30 September 1992

Period of Proposal1 October 1992 through 30 September 1995

.William D. Phillips Wolfgang WiesePrincipal Investigator Division ChiefLaser Cooled and Trapped Atomic Physics Division

Atoms Group

Katharine GebbieDirectorPhysics Laboratory

The information in this report is approved for general distribution.

74

PREFACE

This report is divided into two main sections: A report on progressmade under the present proposal, covering roughly the period offiscal years 1989 through 1992, and a three year proposal forresearch during fiscal years 1993 through 1995. We are requestinga FY 93 budget of 200 k$, with modest increases for inflation in thesubsequent years. Both the work reported here and the proposalinvolve the participation of three research groups. The first, wherethe majority of the work supported under this contract has beenperformed, is the laser cooled and trapped atoms group at NIST,headed by the principle investigator, William Phillips. The second isthe experimental atomic and molecular collisions group at theUniversity of Maryland's department of chemistry, headed by Prof.John Weiner. The third is the theoretical molecular collisions groupof Paul Julienne at NIST . All three of these groups work closelytogether on certain parts of the work described in this report. Thegroups are administered separately, with the NIST laser coolinggroup taking the responsibility of directing the ONR funds to theother groups as indicated in the budget.

Table of Contents

Background 1Summary of research results 2

Detailed reports on reserch areas

Laser cooling mechanisms 6New traps for neutral atoms 16Fluorescent Spectrum of laser coolod atoms 20Atom Optics 26Atomic Fountain Clocks 28Vacuum Ultra Violet generation 32Collisions of laser cooled atoms 34Supplementary collisions program, Theory 37Supplementary collisions program, Experiment 41

References 43

Plan of research during the proposed contract period 46

Budget 57

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Report on Research Accomplished under ONRContract for the period 1 October 1989 to present

(July 1992).

BACKGROUND

In 1988, before the beginning of the current contract period, ourgroup discovered that sodium atoms could be laser cooled wellbelow the lower limit (the "Doppler limit") predicted by the thengenerally accepted theory. Two main consequences of that discoverywere a revamping of the theory of laser cooling and a renewedinterest in the applications of laser cooling because of the far lowertemperatures. Both of these effects are continuing in full forcetoday, and this report is in large part a record of our group'scontinuing involvement in the new developments in laser coolingduring the past three years. The work of the NIST laser coolinggroup falls functionally into the categories of: investigating lasercooling mechanisms; studies of collisions between laser cooledatoms; development of new trapping techniques for neutral atoms;study of the fluorescent spectrum of laser cooled atoms;manipulation of atoms and atom optics; development of coherentsources of vacuum ultraviolet light for laser cooling and highresolution spectroscopy; application of laser cooling and trappingtechnology to atomic frequency standards. The results of researchin this area are summarized below and explained in detail in thefollowing sections. The supplementary program in experimental andtheoretical collision studies is also summarized below and thendiscussed in detail in separate sections.

SUMMARY OF RESEARCH RESULTS

Laser cooling mechanisms: The early theories advanced toexplain laser cooling below the Doppler limit predicted certainfunctional dependences of the temperature on laser parameters ofintensity and detuning. In collaborative work with colleagues inParis we confirmed these dependences, and confirmedexperimentally the newly emerging understanding that there was athreshold value for the laser parameters that allowed the new lasercooling mechanisms to work. Additional work at NIST was directedto quantitative comparisons with explicit three-dimensionalcalculations, investigating both the absolute temperature and thedependence of the temperature on the atomic structure. Theseresults indicate that in spite of correct prediction of functionaldependence, the theories are not correctly predicting the actualnumbers obtained in experiments. We have also done new theoreticalcalculations of the cooling and forces on atoms in a magnetic field,a problem relevant to the magneto-optic trapping of atoms. Suchtrapping is the most popular form of atom trap at present, but itsoperation is not at all understood in detail

New traps for neutral atoms: In collaboration with Prof. I.Silvera at Harvard we have constructed a microwave trap for cesiumatoms. The principle of this trap is that the energy of interactionbetween the atoms and a microwave field near resonant with thehyperfine transition varies in space, in a microwave cavity, so as tocreate a potential well. The experiment is close to beingoperational, and if successful will be pursued for application totrapping spin polarized hydrogen for Bose condensation. Anothernew trap is the Far Off Resonance Trap (FORT) which is simply alaser dipole-force trap operated so far off resonance that it neitherheats nor seriously perturbs the energy levels of the atom. This ideahas been made practical in part because of the extremely lowtemperatures achievable with sub-Doppler laser cooling. We haveshown that such a trap can be operated cw, without the usualswitching of the trap to avoid cooling inhibition.

Fluorescence Spectrum of laser cooled atoms: Just previousto the present contract period we had begun to investigate the

2

measurement of the spectrum of fluorescent light from atoms as amethod for measuring the temperature of the atoms in situ. Thatwas successful, but we also found that the atoms showed evidenceof being trapped in the sub-wavelength sized optical potential wellscreated by the interference of the laser beams used in the cooling(optical molasses). During this contract period we have improved onthe techniques for obtaining the spectrum, devising some newinstruments for the purpose, and have extended the measurements toatoms trapped in one dimension. In this case the spectrumsimplifies and shows clear evidence of the oscillatory nature of themotion of atoms trapped in the 1-D potentials as well as thequantized nature of that motion.

Atom Optics: This field refers to manipulating atoms or atombeams in ways analogous to the manipulation of light and lightbeams by ordinary optical elements such as lenses and mirrors. Wehave been developing curved mirrors for atoms. Alreadydemonstrated as flat mirrors, these work by reflecting atoms fromthe dipole-force potential in an evanescent wave resulting fromtotal internal reflection of light inside a dielectric. The evanescentwave extends into the vacuum, and reflects sufficiently slow atomsbefore they contact the surface. We have demonstrated this on acurved surface for the first time and have seen two bounces of theatoms.

Atomic Fountain Clocks: One of the most fortunate results ofthe laser cooling of atoms below the Doppler cooling limit is thatthe use of neutral atom atomic fountains for atomic clocks becomesmuch more realistic than previously. The atomic fountain clock isan old idea, dating back to Zacharias in the mid 1950's. Atoms arelaunched vertically through a microwave cavity, falling back throughagain under the influence of gravity. The two passages in the cavityconstitute a Ramsey separated oscillatory field interaction, as in aconventional atomic clock, but with a much longer interaction time.The ultracold atoms now possible allow the interaction time to beon the order of a second without so much transverse spreading thatmost of the falling atoms do not return through the cavity. Incollaboration with our colleagues in Paris we have demonstrated theresonance for such a clock and shown that its potential performance,even for a preliminary experiment, equals the best present daycesium clocks. We have analyzed a new prospective opticalfrequency standard that will use the same fountain technology.

3

Vacuum Ultraviolet generation: We have developed thetechniques for generating coherent VUV at the Ly-a wavelength forcooling and manipulating hydrogen or anti-hydrogen. The sametechniques can also be used for high resolution spectroscopy of He,to test QED in a two-electron system. We have demonstratedextremely high efficiency tor the generation and have partlydeveloped the high resolution frequency sources.

Collisions of laser cooled atoms: During the previous contractperiod we had studied associative ionization of laser cooled andoptically trapped sodium atoms, confirming qualitatively atheoretical prediction of Julienne that the rate of this processshould depend dramatically on laser intensity. Since then both thetheory and the experiment have been refined, with quantitativemeasurements of the ratio of reaction rates at high and low laserintensity, and measurements of the spectrum of ionization as afunction trap laser detuning. These data are compared to newtheoretical calculations and provide some evidence for previouslyunobserved molecular levels.

Suoplementarv collisions Drogram. Theory: (This program isled by Paul Julienne of the NIST Molecular Physics division.)Collisions occurring between atoms cooled to laser coolingtemperatures have properties very different from collisions atordinary temperatures. For example, at more usual collisionenergies, radiative lifetimes are generally long compared tocollision times, so little spontaneous emission occurs during acollision. For cold collisions, this situation is reversed, requiringdifferent theoretical methods to treat the collision process. Anunderstanding of the collisions is not only intrinsically interestingbut also essential for understanding loss mechanisms for lossesfrom traps, shifts in atomic clocks, and the evolution of quantumcollective behavior in dense systems.

Supplementarv collisions Drogram. Experiment: (Thisprogram is led by John Weiner, Dept of Chemistry, University ofMaryland.) Studies of ultra cold collisions in traps can probe thelowest energy interactions of atoms but are less adapted tomeasuring the energy dependence of collisions and collisionproperties that depend on the collision axis relative to the atomicpolarization. Atomic beam experiments allow such measurements.

4

We have performed atomic beam collision experiments usingadvanced velocity selection techniques to obtain collision energiesbetween 1000 K and 18 mK.

Detailed reports on each of the research areas follow.

5

LASER COOLING MECHANISMS

As originally conceived in 1975 [1,2] and expounded in detail in1979, laser cooling results from the velocity dependence of theradiation force on near resonant atoms. The velocity dependencearises from the Doppler shift of the apparent resonant frequency,and so this laser cooling is generally called Doppler cooling. Whenthe laser is tuned below the atomic resonance, increased absorptionby atoms moving opposite to the laser propagation leads to adamping force. This is accompanied by a heating effect due to therandom nature of absorption and emission. The balance betweendamping or cooling and heating leads to a temperature which can beno lower than kBT = hr/2, where r is the linewidth of the resonance.This temperature is known as the Doppler cooling limit, and is 240jK for sodium cooled on its resonance line. In 1988 [4] we measuredlaser cooling temperatures in optical molasses [5,6], an arrangementof counterpropagating laser beams, and found temperatures muchlower than the Doppler limit. Eventually we measured sodiumtemperatures as low as 25 IK, about an order of magnitude belowthe Doppler limit.

The sub-Doppler cooling was explained as arising from themultilevel nature of the atoms, optical pumping among the atomiclevels, and light shifts of the levels [7,8]. One of the major thrustsof our work during this contract period has been the testing of thetheory of sub-Doppler cooling and of more sophisticated theoriesthat followed. A simplified discussion of the theory is given in ref.[9].

Some of our early experiments testing the theory of sub-Doppler cooling were accomplished by the time of the previousreport in 1989, and the complete record of these tests is in ref. [6].One important prediction was that the temperature of the atomsshould depend linearly on 1/8, the intensity divided by the detuningof the laser (in the limit of low intensity and large detuning). Ourmeasurements indeed showed that the temperature depended linearlyon the intensity, but as seen in Fig. 1 below, the dependence ondetuning was not in particularly good agreement with the prediction.

6

I I I I I I I I

500 =

400-

Z 300 - •0

a" -*200-

E0100-

0- I I I I I I0 10 20 30 40

Detuning (MHz)

Fig. 1: Temperature of Na atoms laser cooled in a 3-D opticalmolasses as a function of laser detuning, from ref [6].

The likely explanation for the behavior departing from 1/8 in Fig. 1,and particularly the increase in temperature at large 8 is that in Nathe detuning could not be made very large before the laser started tocome close to resonance with another hyperfine level. Simplystated, one couldn't get into the large detuning limit without makingthe problem far more complicated by the addition of another energylevel. This problem may be solved by using cesium, where theanalogous additional level is much further away. The experimentswith cesium are described below.

Another important observation described in ref. [6] is theexistence of a threshold for the intensity at which the new coolingmechanism would work. We established experimentally that if thelaser intensity were below a critical value the temperatureincreased dramatically. This was expected on the basis of thetheory presented in [7], but the understanding of this phenomenon(now known as ddcrochage or disintegration of the molasses) wasstill imperfect at the time of those experiments. The 1-D theorypredicted that the new cooling mechanism provided a large dampingforce only for velocities smaller than some critical velocity

7

dependent on intensity and detuning. Beyond that velocity, thedamping is less effective, and at larger velocity only Doppler coolingoperates. The point of view, expressed in [6] was that once thecritical velocity (dependent on intensity) became smaller than thewidth of the velocity distribution, the cooling would break down.

While the experiments confirmed the idea of a thresholdintensity at which the cooling ceased, more quantitativemeasurements, and a closer look at the theory presented a differentpicture.

In collaboration with colleagues at Ecole Normale Sup~rieurein Paris, we studied the behavior of laser cooled cesium in opticalmolasses [10]. As expected, we confirmed the dependence of thetemperature on I/8 for this case where a large detuning could becleanly obtained. Fig. 2 shows that for a wide range of parametersthe temperature depends only on /S, and for most of the range, thedependence is linear. Only at small detuning or large intensity,where the theory is expected to break down, is there a deviationfrom linearity.

UO U

0 0 1.0

lo-

21

0 0.5 1.0

tow iftenSity~o 2 irz2 aii

Fig. 2: Temperature of Cs atoms laser cooled in 3-D opticalmolasses (from ref.f10]). In (a) temperature is plotted as a functionof intensity; in (b) it is plotted as a function of 1/6.

The availability of a large parameter space allowed us to studyhow the threshold intensity varied with detuning. The result was

8

that, except for the smallest detunings, \The threshold occurred at aconstant value of I/S. This finding was at odds with the originalimage of dcrochage, but consistent with the new viewpoint, basedon the understanding that as the atomic velocity exceeds the criticalvelocity, leading to reduced damping, it also leads to reducedheating, with the result that the extent of the velocity distributioncan greatly exceed the critical velocity while the cooling continuesto work well. Thus, the threshold intensity can be much lower thanpreviously supposed, and the temperature also lower. In fact, thelowest temperature is found to be roughly independent of the choiceof intensity or detuning, since the threshold occurs at constant 1/8,the single parameter determining temperature.

For cesium, this lowest temperature was found to be only 2.5 _0.6 giK [10], a value which was at the time the lowest temperatureever measured in 3-D for any substance. The velocity correspondingto this temperature for Cs is about 1 cm/s, or about three times therecoil velocity, the velocity change experience by an atom onemitting or absorbing a single photon. Interestingly, the lowesttemperature measured for sodium in our laboratory [6] alsocorresponded to about three recoil velocities. All this wasconsistent with the theoretical understanding that the lowesttemperature should depend on the recoil velocity.

For the Cs temperature measurements the uncertainty was verymuch reduced from the typical ±10 gK in our early Na measurements.As in the early measurements, the temperature was determined fromthe time-of-flight distribution of atoms released from opticalmolasses. The main reason for the improvement was that for theheavier Cs atoms the time-of-flight distribution is simpler than forthe lighter Na, and the spatial distribution of atoms was "sliced" soas to reduce geometric uncertainties before the atoms werereleased for the TOF measurement.

The agreement between these experiments and the theory,satisfying as it was, was still only qualitative. The dependence onthe parameters was as predicted, but the theory was for only onedimension, and for a simpler set of energy levels than possessed bythe atoms used in our 3-D experiments. I fact, the numerical resultsfor the 3-D measurements in Cs gave temperatures close to threetimes higher than the predictions for the same laser parameters and

9

a simpler level structure. It is tempting to ascribe the factor ofthree to the fact that three times as much total light intensity fallson the atoms in the 3-D experiment. Nevertheless, no directcomparison with theory or a clear expectation nf such a scaling lawexisted. In order to make more quantitative comparisons, we havedone both three dimensional calculations and one dimensionalexperiments. The one dimensional experiments are described in thesection on fluorescence spectra.

In collaboration with a colleague at the University of Aarhus inDenmark, we have calculated the temperature of atoms of variousdegrees of level degeneracy in a three dimensional situation. Themethod of calculation (11] lacks the sophistication of the mostadvanced 1-D theories available in that it is semiclassical andmakes the approximation of low velocity. Nevertheless, these sameapproximations are known to be good ones in the 1 -D case, and it is,in any event, the only available 3-D calculation.

The experiments to compare with this theory have been done inour laboratory at NIST, using the apparatus which was underconstruction at the beginning of this contract period. The atomchosen for these measurements is rubidium. Rb has two abundantisotopes, in contrast to Na and Cs, which have only one. The entiresub-Doppler cooling mechanism depends on the existence of amanifold of normally degenerate ground states. The differentnuclear angular momenta of the two isotopes 85 Rb and 8 7 Rb lead todifferent degeneracy, and therefore, presumably, different coolingcharacteristics. The results of the temperature measurements fortwo isotopes of Rb are shown in Fig. 3 below.

According to the theory, the ratio of the slopes of the linesshowing temperature vs. light shift should be 0.69, where 85 Rb, withthe higher angular momentum, has the lower temperature. In fact,we find that the ratio of the slopes is about 0.90 ± 0.05, where 85R bhas the lower temperature. Thus, the simple theory gives a verywrong result for the ratio of slopes, a number that is quiteinsensitive to systematic errors because everything else about theatoms and the measurement is virtually identical except the angularmomentum and a small mass difference. It is particularly surprisingthat the temperatures should be so close to being equal. Also, theabsolute slope is similar to the absolute slope measured for both Csand Na, although an accurate comparison is difficult because of theuncertainties about calibration that are absent from the isotope

10

500 8 5 10

0

30

'-20 0o0g

10

0 I0 0.1 0.2 0.3 0.4 0.5

a' / rlAi

Fig. 3: Temperature of Rb atoms in 3-D molasses as a function oflaser intensity and detuning, for two isotopes [ref. 12].

comparison. Nevertheless, there appears to be a tendency foruniversality in the temperature of laser cooled atoms that isunexpected. This matter is still under investigation and apublication on the isotope comparisons is being prepared.

In an attempt to improve our understanding of magneto optictrapping, we have made a detailed theoretical study of laser coolingin a a+ - a- configuration, that is, counterpropagating laser beamswith opposite circular polarizations. It is this configuration in 3-D,along with a quadrupolar magnetic field, that forms the magnetooptic trap. This work was done in collaboration with Jean Dalibardwho was a visitor with our group for eight months.

In contrast to previous treatments of this problem, we do notmake the assumption that ground and excited states have the sameg-factor [7], nor do we adiabatically eliminate the excited state(13]. We do, however use a semiclassical treatment. Using thesimpler assumptions, it had been found that the addition of amagnetic field was completely equivalent to a change in velocity ofthe atom. That is, the force on an atom depended only on the sum ofthe Doppler shift and the Zeeman shift. Using the more correctassumptions we find this not to be the case. In particular, becausethe Doppler cooling is sensitive to the excited state g-factor and thesub-Doppler cooling is sensitive to the ground state g-factor, the

11

situation is not so simple and we find that, for example, atsufficiently high fields (several gauss for typical laser parameters)the sub-Doppler cooling is effectively eliminated. The force vs.velocity for several magnetic fields is shown in Fig. 4. below. Whenthe field is sufficient that the high slope portion of the curve doesnot intersect zero velocity, sub-Doppler cooling is ineffective. Weare planning experiments to test these 1-D calculations. We havealso studied theoretically the prospect of magnetically launchingatoms. That is, application of a small enough magnetic field simplyinduces a drift velocity to the cold atoms. This can be used in anatomic fountain (see below) to launch the atoms up in the fountain.The problem with the g-factors limits how much of a launch ispossible, but we predict that it could be of some utility. The detailsof all these calculations are described in a forthcoming publication[14].

0.4 ,

0.2 - g.* gs

-0.2 -

-0.4.4 2 4

p (Mr/k)

Fig. 4: Force vs. velocity in the a +- a- configuration withlongitudinal fields from zero to 1.2 mT. Sub-Doppler cooling isineffective by 0.8 mT.

A final aspect of fundamental studies of laser coolingmechanisms involves the spatial diffusion of atoms undergoing lasercooling. This spatially diffusive motion was one of the keycharacteristics predicted for optical molasses even before sub-Doppler cooling was discovered [5]. It is manifested by the fact thatatoms in an optical molasses are confined for a significant timeeven though there is no restoring force. This viscous confinement

12

results from the long time for the atoms to diffuse out of themolasses. Experimentally, diffusion times on the order of onesecond are observed for a one centimeter diameter molasses. Thisis consistent with estimates made in the absence of sub-Dopplercooling [6] and is considerably shorter than a naive calculation basedon sub-Doppler cooling. In fact, it has been known, but notpublished, from work in our own group and the group at EcoleNormale Sup6rieure in Paris, that the behavior of the diffusion timewas not consistent with truly diffusive motion. In particular, thetime to diffuse out of a certain size molasses did not depend as thesqua re of the diameter of the molasses, but as something closer tolinear in the diameter.

We decided to study both the theory and experiment moreclosely. With Jean Dalibard, we calculated spatial diffusionconstants using the semiclassical form of the sub-Doppler lasercooling force combined with the Doppler cooling force. Forexperimental measurements, done with Rb atoms, we did not simplymeasure the escape of atoms from an optical molasses by observingthe decay of the molasses after it is loaded. This traditional methodsuffers from the fact that any other mechanism for losing atoms,such as scattering by background gases, contributes to the loss.

Instead, we started with a magneto optic trap, made by usingthe appropriately circularly polarized laser beams and theappropriate magnetic field, to capture atoms at fairly high densityin a small (mm-sized) volume. Then the magnetic field was turnedoff, and the polarization of the light, the intensity and detuningwere switched to the desired values. The light polarization waselectronically switched using a fast liquid crystal polarizationswitch. All of this switching takes place in a few milliseconds, sothe atoms hardly diffuse at all. After that, we recorded the spatialevolution of the atom cloud using a video camera and a videorecorder. The recorded video images were digitized and analyzed.By examining the growth of the atom cloud in the molasses, we havea direct measure of the diffusion.

The initial trials showed that there was a substantial driftalong with the diffusion. In fact, the drift was so fast compared tothe diffusion that it was dominating the escape of the atoms fromthe molasses. One reason for such a drift is that thecounterpropagating beams of the molasses are achieved throughretroreflection. Losses on windows and mirrors create an intensity

13

imbalance leading to drift. To correct this we used sixindependently adjustable beams, and found that the drift could beeffectively eliminated. Also, with higher quality coatings we foundthat the drift with retroreflected beams could be reduced to amanageable level.

With the drift under control, we were able to plot the squareof the spatial extent of the atom cloud as a function of time. Fordiffusive motion, this should yield a straight line. In fact, we foundthat for a variety of methods of analysis, all the methods gave alinear evolution and agreed well for the slope, at least for timesshorter than about two seconds. Typical data is shown in fig. 5. Forlonger times the signal becomes small and is difficult to analyze. Inany case, the motion is seen to be diffusive, with diffusionconstants as small as 10-3 cm 2/s. The dependence of the diffusioncoefficient on detuning and intensity is found to be qualitativelysimilar to that predicted by the 1-D theory, but not of the correctmagnitude. This may be understandable considering the difference indimensionality and the fact that the 1-D calculation was done for adifferent transition scheme than Rb. Nevertheless, the qualitativefeature of the theory, that the diffusion minimizes for a finitedetuning, is reproduced in the data. The dependence on detuning isshown in fig. 6. The data for the diffusion measurements is stillbeing analyzed and we expect to be able to submit it for publicationin the Fall of 1992.

0.0035:" o 0

0.003 ..-.. -. ........ ..

0 .0 0 2 5 ...................... - ................................................ .. ................ ....................

Cm 2 0 .0 0 2 .............. - ......................... . ................................................

0 .0 0 1 5 .. ................ . . ..... .. ..... ..................................................................

0 .0 0 1 ........... i .-.. ".... ........................ .......................... ....... ................. .....................

0.00050 0.5 1 1.5 2 2.5

time (sec)

Fig. 5: Spatial extent of the Rb atom cloud as a function of time asit expands into an optical molasses. The different symbols are fordifferent analysis methods.

14

0.003- 1 I ! I

0.0025 -

00.002 -

x CX

0.0015 0o0

0.001 - $X

0.0005- I I I I I

0 10 20 30 40 50 60 70Detunning (Mhz)

Fig. 6: Measured spatial diffusion constant in Rb as a function oflaser detuning.

Diffusion coefficients as small as 10-3 cm2 /s imply thatatoms live for about 100 s in a spherical molasses with boundariesat 1 cm radius [6]. In fact, such long times are never seen, althoughwe did see a mean lifetime longer than 12 s in a 9 mm radiusmolasses. The actual lifetime in our experiments is limited bycollisions with background gases, and we suspect that in many caseswhere molasses lifetimes were measured the lifetimes weredominated by drift, as was the case for us before great care wastaken to balance the beams. Furthermore, any non-uniformity of thelaser beams could create local imbalance that would look very muchlike diffusion. We sometimes observed that after long times, withwell balanced beams, the atoms would drift in different directionsin different parts of the molasses. All of this indicates that thegeneral failure to see long molasses lifetimes is not because thediffusion constant is too large, but because there are other factors,which may mimic diffusion, that limit the lifetime.

15

NEW TRAPS FOR NEUTRAL ATOMS

One of the applications for trapping of neutral atoms is to thesearch for Bose condensation of a cold atomic gas. Bosecondensation is a condensation in momentum space, producing, in theidealized case, a macroscopic fraction of the population in thelowest energy state of the trap when the temperature and density ofthe gas are such that the deBroglie wavelength is on the order of theinterparticle spacing. While something akin to Bose condensationevidently occurs in liquid He at the superfluid transition, thatsystem is a dense liquid with many strong interactions between theatoms. The goal discussed here is to see the phenomenon in a weaklyinteracting gas.

The search for BEC has centered on spin polarized atomichydrogen because it does not form molecules, nor condense even atabsolute zero. One problem has been that it sticks to the walls of acontainer at very low temperature, allowing spin flips and moleculeformation. Magnetic trapping eliminates the walls, but a staticmagnetic trap can only hold the magnetic sublevels whose energyincreases with increasing field. This means that in any finite field,the opposite direction of the spin has lower energy and collisionscan lead to a spin flip by an exothermic reaction. Such flipped spinsare expelled from the trap. A dynamic, or oscillating magnetic fieldcan trap either direction of the spin, but the oscillating field,typically oscillating at an audio frequency, must be fairly large. Ithas generally been thought that the eddy currents likely to beinduced by such an oscillating field would be incompatible with thecryogenic environment of a spin polarized hydrogen sample.

Recently, Silvera and colleagues (15] proposed a different sortof trap, based on the same principle used in laser dipole traps, butusing radio frequency fields. Briefly, the trap works because thespatially varying rf field in a microwave cavity leads to a spatiallyvarying potential energy of interaction between the field and theatom having a spin resonance near the rf frequency. The interactionHamiltonian mixes the two spin states, producing two new (dressed)eigenstates having opposite energy shifts. In the absence ofrelaxation either dressed state can be occupied, although only one istrapped, depending on whether the tuning of the rf is above or belowresonance. An appropriate choice of detuning can make the trap holdatoms which are predominantly of one spin state or the other, andthus the trap can be made to hold the most stable of the spin states.

16

Such a trap has not yet been demonstrated, but should make itpossible to trap a larger density than has been possible with staticmagnetic traps, where the density is limited by the spin flippingcollisions.

We have, in collaboration with Silvera's group at Harvard,constructed a microwave cavity having the required inhomogeneityand resonant frequency to trap cesium atoms using the hyperfinetransition at 9.2 GHz. This is to be used as a test of principle beforeconstructing a trap for hydrogen. To the microwave trapping fieldwe have added a gradient magnetic field to compensate for thegravitational potential. Cesium is so heavy that the microwavepotential is not sufficient to hold an atom up against gravity. Withhydrogen, there should be no such problem. The gradient will bearranged in such a way that by itself it does not constitute a trap,but merely cancels the effect of gravity.

The experiment will work as follows: Cesium atoms will becooled and trapped in a magneto optic trap using laser beams passingthrough optical access holes in the microwave cavity. Once themagneto-optic trap is turned off, the atoms should be held by themicrowave field. As the magnetic field of the magneto-optic trap isturned off, the anti-gravity field will be turned on. Success of thetrapping process will be assessed by recapturing the atoms in amagneto-optic trap and observing the fluorescence.

The status of the experiment is that the cavity is undergoingfinal tests and the apparatus used for the studies of laser cooling inRb has been converted to Cs. Trapping and cooling of Cs atoms totemperatures as low as 2.5 giK has been confirmed. The depth of themicrowave trap is a several tens of microkelvins, depending on theamount of microwave power delivered to the cavity. We expect to betrying the trapping experiment shortly.

Another new prospect for trapping atoms is the Far OffResonance Trap (FORT). This is a variation of the laser dipole trapalready in use in our laboratory for collision studies (see below). Asalready noted, the operation of this kind of trap is similar to the rftrap described above. The laser polarizes the atoms and the inducedoscillating dipole moment interacts with the spatially varying laserfield to create a trapping potential. Because of relaxation fromspontaneous emission the most populated dressed level is always

17

the one which is predominantly ground state. This leads to trappingat a maximum of the laser field for detuning below resonance.

The dipole trap has so far [16,17] been used only in analternated mode. That is, the trap is switched on and off, withperiods of trapping alternated with periods of laser cooling inoptical molasses. There are two reasons for this. First the trappingfield causes heating that needs to be counteracted by repeatedcooling. Second, the trap induces a strong light shift (the trappingpotential) that makes the cooling inoperative by introducing asubstantial inhomogeneous change in the effective detuning. Thus,the cooling is only effective when the trap is off.

The idea of the FORT is that the trapping laser is tuned so farfrom resonance that the light shift is small enough not to interferewith cooling. Ultimately the trap is far enough off resonance that itproduces little heating, so that cooling is hardly needed [18]. Thething that makes such a possibility realistic is the new coolingmechanisms producing sub-Doppler cooling. First, the improvedcooling produces such low temperatures that the trap does not haveto be very deep. Second, good cooling with the sub-Dopplermechanism is accomplished with large detuning from resonance.This means that the small light shift of the trapping potential doesnot much disturb the cooling.

Using sub-Doppler cooled sodium atoms we have succeeded indemonstrating the operation of a FORT under conditions that do notrequire alternated operation. The trap is a single laser beam, tightlyfocussed so as to produce an strong maximum of intensity at thefocus. By tuning the trap about 5 nm red of resonance, the trap waseffective in holding the atoms without having to turn it off to allowcooling by the molasses which was always present [19]. Theseresults represent only a preliminary demonstration. We expect touse even larger detunings so that atoms may be held for severalseconds without any cooling from molasses.

In connection with these experiments we have observedanother interesting phenomenon. When the trapping laser is not verystrongly focussed, we observe trapping of atoms at a number ofpoints along the axis of the trapping laser. These points do not movealong this axis as the focus is moved, but do move with the trappinglaser as it moves transverse to the axis of the beam. Instead themultiple points appear to be tied to a structure fixed in the cooling

18

molasses. Apparently there is a dipole force caused by aninterference in the molasses that is sufficient to pin atoms atvarious points along the axis of the "trapping" laser. We have not yetidentified the exact mechanism for this additional pinning force, butit is related to interference between the multiple laser beamsforming the 3-D molasses, but with a spatial periodicity muchgreater than an optical wavelength. We suppose that it has to dowith misalignments between the laser beams, but we have not fullyinvestigated the phenomenon. Ultimately, for a strongly focussedtrapping laser, we do not expect the molasses trapping effect to bedominant. Furthermore, it should be minimized when the trap istuned far enough off resonance that less cooling is needed. For thesereasons, we do not expect the molasses pinning effect to causedifficulties, but we do expect to understand the origin of the effect.

19

FLUORESCENCE SPECTRUM OF LASER COOLED ATOMS

At the end of the previous contract period we reported that wehad just made the first observations of the spectrum of thefluorescence of Na atoms being cooling in a 3-D optical molasses.The techniques used involves mixing the fluorescent light and lightderived from the molasses laser on a photodiode. The beat signalcontains all the spectral information about the fluorescence withoutthe fluctuations of the laser. An example of the type of spectrumseen after we had made sufficient improvements in the S/N is shownin fig. 7.

*C

I !

I I

S -. ) 0.5 1Relative Frequency (MHz)

Fig. 7: Spectrum of fluorescence of laser cooled Na atoms.

The spectrum shows a broad pedestal that reflects the Dopplerwidth of the cold atoms. In this case the temperature deduced fromthe Doppler width was fairly high, about 80 gK, since a high laserintensity was used to get a good signal. This temperature agreedwith a measurement using the time-of-flight method. The narrowfeature on top of the pedestal represents atoms trapping in the sub-wavelength sized potential wells formed by the interference of thelaser beams making up the molasses. The narrowing is due to theDicke effect, whereby Doppler broadening is suppressed when anatom is confined to a region much smaller than a wavelength. Wealso studied the behavior of the broad and narrow peaks as afunction of laser intensity and detuning and compared thesemeasurements with some simplified models. These results aredescribed in ref. [20].

The spectrum of Fig. 7 was obtained using a conventional rfspectrum analyzer to analyze the beat signal from the photodiode.

20

While this works quite well, it has the disadvantage of being asingle channel technique in which only a single frequency element ofthe spectrum is obtained at a time, while the information aboutother frequency elements is wasted. In order to make more efficientuse of the small signal, we developed a parallel processing spectrumanalyzer. The principle of this analyzer is that the rf signal to beanalyzed is used to drive an acousto-optic modulator (AOM). Withinappropriate limits the AOM deflects light (from an alignment laser,for example) by an angle proportional to the frequency applied andwith an intensity proportional to the power applied. In this way, thedistribution of deflected light represents the rf spectrum. Theinstrument made in this way exceeded the resolution capabilities ofany commercial device and three of our group members received anRD100 award from Research and Development magazine for itsdesign.

The new instrument allowed us to obtain more spectra morequickly, and to see features not easily seen with the conventionalspectrum analyzer. For example, we were able to see an evenbroader pedestal which is the central component of the so-calledMollow triplet. This feature has a width on the order of the naturalline width (10 MHz in Na) and is difficult to see compared to themuch narrower central part of the spectrum just because it is sowide and has low spectral density. The spectrum in Fig. 7 is oftencalled the *elastic" part of the fluorescence spectrum and inprevious measurements of fluorescence has not been fully resolved.By contrast, our measurements resolve the substructure of thiscomponent and see the wider components only with difficulty.Therefore, these measurements are complementary to themeasurements made of the Mollow triplet at much lower resolution.More details of these later measurements are found in ref. [21].

One of the puzzles about a spectrum such as Fig. 7 is thatwhile the atoms are trapped, there is no evidence in the spectrum ofthe oscillation of atoms in the potential wells. If the atoms wereoscillating, that should, in a classical picture, lead to phasemodulation sidebands, or in a quantum picture, sidebands at theoscillation frequency due to transitions between bound levels of thepotential well. We never saw such sidebands, and we attributed thatto the fact that they were broadened by relaxation mechanisms thatdid not broaden the central sharp feature. Very briefly, we expectedthe sidebands to be broadened by the rate at which photons wereabsorbed (lifetime of the ground state) but the central feature to be

21

broadened only by the inverse of the residence time in a potentialwell. Calculations [22, 23] showed that for an atom like Rb or Cs itshould be easier to see the sidebands. The laser could be detuned farenough from resonance that the atoms would oscillate many times inthe potential well before absorbing and spontaneously emitting aphoton, a situation that should lead to resolved sidebands. The factthat the laser would be substantially detuned meant that it wasimportant to use a parallel processing spectrum analyzer to get goodS/N. Unfortunately, the AOM based spectrum analyzer had at best 30kHz resolution, which was insufficient for a spectrum as narrow asexpected from Rb. The problem with Rb, compared to Na, is that thetemperature would be lower, because the recoil energy is smaller(see the section on cooling mechanisms above). Furthermore, theheavier mass would lead to a smaller velocity for the sametemperature, and the longer wavelength would give a smallerDoppler shift for the same velocity.

In order to overcome these difficulties, we designed stillanother type of spectrum analyzer, this time a real time, averagingfast Fourier transform analyzer. This analyzer used a digital signalprocessing board dedicated to the data acquisition and transforming,producing a device with both large bandwidth and high duty factor.Various combinations of parameters could be used, but a typicalchoice was a resolution of 4 kHz, a frequency span of 500 kHz, and a25% duty factor.

In order to simplify the interpretation of the spectral data, wemade the experiment one-dimensional as follows: Rubidium atomswere trapped and cooled in a magneto-optic trap, then further cooledin 3-D optical molasses, the 3-D molasses was switched off, and a1-D molasses, consisting of counterpropagating beams withorthogonal linear polarization was switched on. After this 1-Dmolasses had equilibrated the atoms, we observed the fluorescence,beat it on a photodiode with the reference laser and Fourier analyzedit with our FFT analyzer. The fluorescence was observed at a verysmall angle from the 1-D axis in order to minimize the effects ofuncooled transverse motion on the spectrum.

A typical spectrum is shown in Fig. 8. The spectrum isinterpreted as follows: The polarization configuration used createsperiodic potential wells for atoms in a given magnetic sublevel.These potential wells have a number of bound states. The centralfeature results from transitions beginning on a given bound

22

0.6

: 0.4

C 0.2)x 20

o0

-200 -100 0 100 200frequency (kHz)

Fig. 8: Spectrum of fluorescence from Rb atoms laser cooled in a I-D optical molasses with orthogonal linear polarizations in thecounterpropagating beams. (From ref. [24].)

vibrational level with the absorption of a photon and the subsequentemission of a fluorescent photon upon return to the same boundlevel. Because the state of the atom does not change, the frequencyshift of the fluorescent photon, compared to the absorbed laserphoton, is zero. The sidebands result from transitions that end onhigher or lower vibrational levels than the original level, and so arehigher or lower in frequency by the vibrational level spacing.

The asymmetry in the sideband height results from the non-uniform distribution of population among the various bound levels ofthe wells. Since the lowest levels are most populated, transitionsfrom lower to higher vibrational levels are most common, so thelower frequency sideband is strongest. The degree of asymmetrygives us a measure of the temperature, assuming a Boltzmanndistribution among the levels. If we plot the temperature obtainedin this way as a function of light shift (as is done in Fig. 2 for 3-Dcooling) we find a straight line, just as in the 3-D experiments. Thetemperature is about a factor of 3 smaller than the 3-Dtemperatures measured for Rb, as described in the section on coolingmechanisms. At present we do not have calculations of thetemperature for Rb in 1-D with orthogonal linear polarizations, but

23

such calculations are doable and will be compared with theexperiments.

The spectra give information about the vibration frequency ofatoms in the potential wells. This vibrational frequency should varyas the square root of the light shift, because the stiffness (springconstant) of the potential well restoring force varies as the depth ofthe potential, which is the light shift, and the oscillation frequencygoes as the square root of the stiffness. Fig. 9 shows the

250* -4r

200 o -8rfit.

t 150

0 100 -

50

0I I

0 0.5 1 1.5(. /rlAI) 1 1

Fig. 9: Sideband spacing (vibrational frequency) as a function of thesquare root of the light shift. (From ref. [24J.)

measured sideband spacing as a function of A1/2, where A = !22/AF,where Q is the Rabi frequency, A the detuning and r the linewidth. Ais proportional to the light shift, and as expected, the oscillationfrequency varies linearly as the root of A. The observed slope agreeswith the calculated oscillation frequency, including the effect ofanharmonicity, to better than 10%. The difference is only marginallysignificant, but might be due to neglect of the effect of damping andsaturation in the calculation.

The smallness of the sidebands in Fig. 8 provide a measure ofthe confinement of the atoms in the potential wells. Classically,the sidebands are small because they result from phase modulation

24

with small modulation index. Quantum mechanically, they are smallbecause transitions in which the vibrational quantum numberchanges are suppressed more strongly for low-lying vibrationallevels. We find that the rms spread of the atomic positiondistribution is only 1/15 of an optical wavelength for most valuesof the laser parameters. For the lowest temperatures (smallestlight shifts), this implies that 60% of the population is in the groundvibrational state.

The highly quantum mechanical nature of this system suggeststhat it should be possible to manipulate the bound atoms so as toproduce coherent states of oscillation or even to produce squeezedstates of oscillatory motion.

25

ATOM OPTICS

Atom optics is the manipulation of atoms or atomic beams inways analogous to the way light is manipulated by optical elementssuch as lenses and mirrors. A few such analogs have beendemonstrated. One dimensional lenses using radiation pressureforces have been used to focus and image atomic beams. Flatmirrors using evanescent light waves have been used to reflectatoms or atomic beams. Our work in this area has been to make acurved mirror for atoms, with a view to its use for focussing orstoring atoms.

An evanescent wave atomic mirror [25] is based on the actionof the dipole force. Light, totally internally reflected from adielectric-vacuum interface, extends into the vacuum withexponentially decreasing intensity. The resulting gradient ofintensity produces the force that can reflect atoms of sufficientlysmall velocity. Such a plane mirror has been demonstrated forglancing reflection of a thermal atomic beam [26] and normalreflection of cold atoms dropped from a trap [27].

In the absence of spontaneous emission, the reflection ofatoms from the evanescent wave is elastic and specular, just as inthe reflection of light from a mirror. The requirement for reflectionis that the kinetic energy of the atom normal to the mirror surfacebe smaller than the dipole potential at the surface. In this way, theatom never makes contact with the substrate surface, an occurrencewhich would normally lead to inelastic processes. If the surface ofthe mirror is curved, it can be used to focus or confine the atoms. Inparticular, atoms dropped from above a curved mirror surface can betrapped by the dipole potential on the mirror and the gravitationalfield. This sort of "gravito-optical trap" has been studied in detail,including the quantum mechanical modes atoms can occupy in thetrap. Because of the wave nature of the atoms, the trap or "gravitycavity" behaves in a way analogous to a Fabry-Perot etalon,supporting certain distinct quantum modes. Even for very coldatoms, however, the typical mode is of very high order, with manymodes of the cavity being occupied.

One difficulty in making a curved evanescent wave mirror isthat light must reflect from a curved interior surface, resulting in areflected beam with large divergence. This presents the practicaldifficulty of disposing of the reflected beam without allowing a

26

significant amount of lignt to illuminate the region above the mirrorwhere the atom will bounce. By using a monolithic designincorporating a prism and a concave lens, we have minimized thestray light problem.

Another difficulty is in avoiding spontaneous emission duringthe time the atoms are bouncing. This is achieved by tuning thelaser far from resonance, which causes the rate of spontaneousemission to decrease more rapidly than the dipole force. Since thegradient in the evanescent wave is very strong, the wave having acharacteristic decay length on the order of X/2x, the time forbouncing is short and the probability of spontaneous emission is low.We calculate that an atom should bounce about 10 times from aheight on the order of a centimeter using an evanescent waveproduced by a few hundred milliwatts of laser power. Since thetime spent bouncing is short, on the order of a microsecond, and thetime between bounces is long, on the order of 100 milliseconds, theintensity of the light above the mirror must be five orders ofmagnitude smaller than the intensity on the mirror to have a similarrate of inducing spontaneous emission. Hence the great concern forreducing stray light from the laser.

Very recently we have reported the successful bouncingsodium atoms from a curved mirror with a radius on the order of 2cm [28]. We have observed two bounces. This is insufficient to seethe trapping effect of the curvature, but we expect to extend thenumber of bounces so as to see this effect.

27

ATOMIC FOUNTAIN CLOCK

The idea of an atomic fountain was first proposed by Zachariasin the 1950's. He envisaged sending an atomic beam of cesium atomsup through a microwave cavity tuned to the hyperfine frequency, andallowing them to fall again through the same cavity, executing aRamsey separated oscillatory fields resonance. The long interactiontime would give a narrow resonance feature, while the doublepassage through the cavity would cancel certain systematic errors.Realization of a fountain had to wait for the development of lasercooling, and in fact, it was not until sub-Doppler cooling wasdemonstrated that the first fountain was made [29]. The difficultyencountered by Zacharias was that in a thermal atomic beam thereare essentially no atoms going slowly enough that, after beingdirected upward, they would fall back within a reasonable distance.Laser cooling certainly provided such atoms, but the problemremained that even at the lowest temperatures achievable withDoppler cooling, the transverse thermal velocities of the atoms wasso great that after any reasonable fountain round trip time, theatoms would have spread out so much that very few would make itback through the microwave cavity.

As an example, consider Na atoms cooled to the Doppler coolinglimit. The rms velocity along a given axis would be 30 cm/s a theDoppler temperature of 240 1tK. If the fountain were a meter high,the round trip time would be about a second, and the atoms wouldspread out to cover an area greater than 3000 cm 2 by the time theyreturned to the starting point. By contrast, cesium atoms, lasercooled by the sub-Doppler cooling mechanism to 2.5 giK, have an rmsvelocity of about 1 cm/s, and so would spread to an area threeorders of magnitude smaller. Under such conditions a substantialfraction of all the launched atoms could return through a hole in amicrowave cavity.

The first demonstrated fountain [29] used Na atoms launchedinto a section of waveguide where the microwaves were pulsedtwice to produce the Ramsey resonance. This produced a narrow linebecause of the long parabolic trajectory in the large waveguide, butit did not realize the idea of Zacharias to pass twice through acavity, a process that tends to cancel systematic errors due tovariations in the microwave field across the cavity. In addition, themethod of launching the atoms was to push them vertically using a

28

single laser beam. The disadvantage of this method is that theatoms heat In both the vertical and transverse directions due to therandom nature of photon absorption and emission.

Our experiment, performed in Paris, used a different launchmechanism, a modification of the moving molasses proposed in ref.[6]. In this moving molasses the frequency of the two laser beams inthe vertical arms is shifted compared to that of the horizontal arms.The descending beam is shifted down and the ascending beam isshifted up. An atom moving up with the appropriate velocity seesthese beams Doppler shifted to the same frequency as the horizontalbeams. This is the configuration the atoms perceives as being astatic molasses and it cools to a low temperature in this movingframe. The result is atoms moving with a uniform vertical velocityat as low a temperature as can be obtained in stationary molasses.

The experiment, described in ref. [30], involved first collectingCs atoms in an optical molasses, then sweeping the frequency of theappropriate beams so as to accelerate the atoms into a movingmolasses, then equilibrating at a low temperature in the movingmolasses before turning off the molasses beams allowing the atomsto be launched. The atoms were optically pumped into a givenhyperfine state, and the change of state was detected by selectiveoptical excitation after the Ramsey resonance. The experimental setup is shown in fig. 10.

~,rTTEagC*vity

9.2GHzinput

Mollse vL molasses

MEF siglnal

probe beam V+ t

Fig. 10: Apparatus for the Cs fountain Ramsey resonance experiment.

29

The resonance signal, which shows the usual Ramseyinterference pattern is given in Fig. 11. Each point corresponds toseveral launches and detections at a given frequency driving themicrowave cavity. A significant source of noise is the variation inthe number of atoms launched at any given time. This effect isminimized by a normalization technique where after the secondpassage through the atoms making the hyperfine transition aredetected for part of the detection period and the total number ofatoms launched is detected during another part. The signalcorresponding to the atoms making the transition is normalized tothe total number of atoms to reduce the noise.

Another source of noise is the instability in the frequencysource used to generate the microwave signal. If this latter sourceof noise is eliminated (which would be the case for a high qualitycrystal oscillator being used as the reference for generating themicrowaves) then the short term, noise limited performance of aclock operated using this device would be 3 x 10-12 in one second.This is as good as the performance of any laboratory standardcesium clock currently in operation.

-50 0 50frequency detuning (Hz)

Fig. 11: Resonance signal from the Cs atomic fountain.

The relative effect of many random and systematic errors inatomic clocks can be reduced by using a higher clock frequency. Wehave examined [311 a transition in metastable Xe as a possibility forsuch a clock transition. Metastable xenon (Xe*) can be laser cooledin much the same way as ground state Cs. That is, there is an

30

allowed transition whose excited state decays back to the originalmetastable state, with the metastable state being long-lived enoughthat it can be treated effectively as a ground state. In addition,there is a narrow, two-photon transition from the lower metastablestate to a different excited metastable state that can serve as theclock transition. The transition scheme is shown in Fig. 12. The

, '

n I, 1, I (

I' I J

Fig. 12: Cooling and clock transitions in Xe*.* Some additionaltransitions useful for detection are also shown.

clock transition is at 2.19 g~m for each of the two photons, awavelength that can be obtained with high stability by nondegenerate parametric down conversion from a monolithic YAG laser.We are communicating with the group of Bob Byer at Stanford on theproduction of such radiation suitable for driving the clocktransition.

The apparatus for producing and cooling Xe° is beingconstructed and is nearly completed. Most of the vacuum apparatus,the source and the pumps are in place, and the magnet for Zeeman-tuned deceleration of the atomic beam is being designed. We hopethis beam will soon be operational.

31

VACUUM ULTRAVIOLET GENERATION

Laser cooling of atomic hydrogen on the resonance transitionrequires the generation of narrowband radiation at the Ly-xwavelength of 121.6 Im. One interest in laser cooling of hydrogenis as an alternative to cooling with a dilution refrigerator in acontainer whose walls are coated with liquid He. Such cold hydrogencould be used to load a magnetic or other trap for studies of quantumcollective behavior or as a sample for high resolution spectroscopy,such as the measurement of the ls-2s interval. Another interestingapplication of such short wavelength light is the high resolution, 2-photon spectroscopy of the ls-2s transition in He at 120.3 im. Anabsolute determination of the energy difference between the 1 s2ground state and the ls2s first excited state, together with existingprecision measurements of higher excited states allows ameasurement of the ground state Lamb shift. The last measurementof this Lamb shift was in 1957 with conventional gratingspectrometer techniques. Although the ground state Lamb shift is byfar the largest quantum electrodynamic shift in He, it is also theleast well known. A new laser-based measurement will test thecalculation of electron correlation effects in 2-electron quantumelectrodynamics.

We are carrying out experiments on VUV generation incollaboration with T. Lucatorto of NIST and T. Mcllrath of NIST andthe University of Maryland. Our scheme for production of VUV lightis based on resonantly-enhanced sum-difference four-wave mixingin a gas, such as Kr or Xe. The general scheme uses two UV photons(around 215 nm) minus one IR photon (850-1000 nm), with theresulting 4th wave being a VUV photon (120-122 nm). The two UVphotons are nearly resonant (10-100 cm-1) with an excited state inthe mixing gas. Phase matching is achieved by using a gas mixturecomposed of two gases with opposite dispersions around thefrequency of interest.

Using a broadband ( 5-10 GHz) pulsed dye laser we haveinvestigated VUV production with such schemes. We generate the UVphotons by quadrupling the pulsed dye laser (30 mJ) operating withIR dyes. We have generated approximately 10 nJ of VUV light, bothat 121 nm (Ly-ut) and at 120 nm (He 2-photon), using slightly

32

different laser wavelengths and different excited states for theenhancement. We investigated phase-matching in the gas, and findagreement with calculations. This system is based on a 10 Hz Nd:Yagpump laser, and produces a pulsed output a few ns long. Although thepower levels are adequate for both hydrogen and helium, the pulseddye laser is not capable of producing a small enough bandwidthnecessary for either the laser cooling experiments or the highresolution spectroscopy.

More recently we have built a pulsed Titanium:sapphire laser.It is an unstable resonator configuration with a graded reflectivityoutput coupler to produce a good spatial mode. We havedemonstrated injection seeding with a single longitudinal modediode laser. With this seed laser we will have a transform-limitedsource of IR for the nonlinear generation.

We are proceeding with the rest of the frequency mixing chainto produce narrowband Ly-a and narrowband light for the He two-photon transition. We will re-investigate thb VUV generation withthe narrow-band source, and evaluate linewidth and frequencychirps. Frequency chirps are a well known source of broadening andshifts in pulsed systems, occurring as the optical properties of thematerials used for generation and mixing change during the rapid,intense pulses. We have started construction of an apparatus for theDoppler-free two-photon He measurement using photo-ionizationdetection of the He excitation. The wavelength metrology will bedone in collaboration with C. Sansonetti of NIST, who has previouslymade the best measurements of many of the higher lying levels inHelium.

33

COLLISIONS OF LASER COOLED ATOMS

We have studied the associative ionization collisions of lasercooled atoms. In such a collision, at least as normally viewed athigher temperatures, two optically excited Na atoms combine toform Na2 + e-. The ionization cannot proceed without moleculeformation because the two excited atoms lack sufficient energy toeject a single electron. This reaction is appealing because the ionsare easy to detect and no other process produces ions, so onemeasures a very specific reaction. Previously [17], we havemeasured the collision rate for laser cooled atoms, below 1 mK, andjust before the beginning of this contract period we had observed aninteresting form of laser control of the reaction.

Our colleague Paul Julienne had predicted that the rate ofassociative ionization would be dramatically reduced when the laserintensity was low (or moderate) compared to when the intensity washigh. This, in spite of thp fict that the fraction of atoms in theexcited state was not muci different for the two conditions. Ourexperimental procedure turned out to be ideal for testing thisprediction because we needed to switch between the high intensity,detuned trap laser and the low intensity, near resonant cooling laserfield. The results obtained shortly before this contract period beganconfirmed the prediction qualitatively, but did not produce a goodmeasurement of the ratio of the high intensity to low intensity rate.The initial prediction was that the high-intensity and low-intensityionization rates should be in the ratio of about 104 . Theexperiments, however, gave a ratio consistent with no ionizationduring the low intensity phase, but with a large uncertainty. Duringthis contract period we have refined those initial measurements andreported [32] more definitive measurements of the ratio.

In contrast to the initial predictions, we measured ratios,depending on parameters of the molasses and trap lasers, in therange of 20 to 200, with most data falling in the range of 40 to 100.An example of the kind of data obtained is shown in Fig. 12.Simultaneous measurements of the fluorescence and the ionproduction rate as the trap was being switched on and off providedthe required information.

34

10

6

4

2

0S

E, -(d)

0 W W

0 5 10 Is 20 25 0 2 4 6 1 10 12TM (PS) ime ( )

Fig. 12 (From ref.[29]): Fluorescence and ionization rates vs. time .

Perhaps even more significant than the fact that the ratio wasmuch lower than predicted was the fact that the ionization rateremained high even when the trap was detuned several GHz fromresonance. This was surprising in light of the original theorybecause the original idea was that associative ionization resultedfrom two excited atoms starting at large separation and colliding toform a molecule. At large detuning the population of the fielddressed molecular level which is asymptotically a doubly excitedpair of atoms becomes extremely small. This implied that theexcited-excited picture of the collision was not correct.

In fact, the theory was also undergoing a significant change(see below in the supplementary program section for more details)and the new view was that the quasi-molecule was being excited instepwise fashion as the collision progressed, passing throughmolecular levels. That this was happening was strongly suggestedby the spectrum of ion production as a function of trap detuningshown in Fig. 13. The existence of clear resonant structure in theionization spectrum implied the existence of intermediateresonances on the path to ionization, and the new theory confirmedthe general nature of the ionization spectrum.

35

4

13

0-

.4 -3 -2 -1 0

Fig. 13. The spectrum of ionization rate vs. detuning of the traplaser frequency from resonance. (From ref. [32]).

One additional remarkable observation points to still moreexperiments. We have seen than when the trap laser accidentallyoperates in two modes so that about 10% of the trap light is detunedby an additional 10 GHz to the red, the ionization rate increases byabout an order of magnitude. This is presumably due to exciting avery strong intermediate resonance and implies that there is a richresonant structure to be probed by superimposing a separatelytunable laser on the trap laser. Unfortunately, we cannot tune thetrap laser so far as 10 GHz off resonance without losing the trappingeffectiveness. The separate laser should allow us to explore theregion where we expect to see additional strong resonances.

36

SUPPLEMENTAL COLLISIONS PROGRAM: THEORY

The new experimental techniques for optical manipulation ofatomic velocity offer the prospects of studying atomic collisions incompletely new regimes of collision physics. It is critical toexplore these new areas of opportunity, not only because of theirfundamental interest but also because collisions can adverselyaffect potential applications of cooled and trapped atoms, e.g.,ejecting atoms from traps or inducing pressure shifts in clocks. Wehave therefore taken the leadership in developing a very productivetheoretical program to investigate ultracold atomic collisions. Thisprogram has relied heavily on numerous national and internationalcollaborations.

Ultracold collisions are completely different depending onwhether they occur in the presence or absence of cooling lasers.Collisions in the absence of light can be described by the wellestablished wave function methods of scattering theory. Thesecollisions can often occur in the Wigner law limit for laser cooledspecies, where only s-waves contribute to the cross sections. If theinteratomic potentials and spin-dependent interactions are known,the cross sections can readily be calculated by standard techniques.Although actual cross sections are extremely sensitive to smalldetails of the potentials and interactions, we have shown how thegeneralized form of the multichannel quantum defect theory can beused to get qualitative insights into the onset of such Wigner lawbehavior and to estimate the order of magnitude of inelasticreaction rates in the T - 0 limit. We have examined ground statehyperfine changing collisions and ionizing collisions of metastablerare gas atoms. These results are summarized in a review articlefor Advances in Atomic. Molecular. and Optical Physics [33].

Completely new methods are required to describe excited statecollisions, which occur when a cooling or trapping laser is on. Thisis because the collision "duration" can be many natural lifetimes,due to the extremely long range nature of the excited state resonantdipole interaction and the very slow relative velocities of theatoms. The atoms almost act as if they were quasistaticallydistributed and optically pumped by the laser and then drawn into acollision by the accelerating influence of attractive excited statepotentials. A fully quantum mechanical description of this processthat accounts for coupling of the relative motion to the spontaneous

37

emission degrees of freedom still is to be developed, although weare making progress on such a formulation. We have alternativelydeveloped semiclassical models which permit the calculation ofeffective rate coefficients for excited state collision processes.We have implemented several approximate schemes and have appliedthem to several excited state collisional processes.

One process we have thoroughly examined is the fine structurechanging and radiative heating processes that eject cooled atomsfrom a magneto-optical trap (MOT). Our first attempt used asemiclassical quasistatic model to examine the detailed molecularmechanisms for trap loss collisions in alkali species [34].Predictions were made for Li, Na, K, Rb, and Cs traps, and goodagreement was found with measurements on a Cs MOT. We foundthat retardation corrections to the molecular lifetimes were crucialfor calculating the rates of Na and K trap loss. We have extended thesemiclassical methods once more by developing a new optical Blochequation (OBE) treatment of atomic collisions [35]. The OBE methodtreats the case of saturation of the cooling transition. Although theOBE method is semiclassical in the sense that it uses semiclassicallocalization within the framework of the WKB approximation forgenerating the OBE's, the method actually gives answers that arecompletely independent of the choice of a reference trajectory forintegrating the equations. The primary approximation in the methodrelates to how energy conservation criteria are applied to choosingthe excited state WKB wave function in the case of dissipation byspontaneous emission. Questions relating to this issue can not beanswered within the framework of our semiclassical OBE theory. Wehave therefore used an alternative quantum approach based on adifferent WKB treatment of the weak field limit to justify the waywe apply energy conservation criteria in the semiclassical OBEformulation [36]. We have carried out new calculations of the finestructure changing probabilities in Cs and Rb [37], and applied theOBE method to predict new trap loss rates. The calculated rates arein reasonable agreement with measurements on Na, Rb, and Cs MOTs,but there are still important differences in detail that need to beunderstood before we can have real confidence in the ability oftheory to be quantitative.

The process of associative ionization in a Na trap is a processwhich we have previously studied theoretically and experimentally[38, 39]. New experiments (see the section on collisions of lasercooled atoms, above) verified the prediction that the effective rate

38

coefficient for this process should be much smaller in the molassesphase of the NIST hybrid trap than during the trapping phase [39]. Wehave now carried out detailed calculations that attempt to providedetailed molecular mechanisms and predictions concerning thisreaction [40, 41]. We now view the process as one ofphotoassociative ionization in which the doubly excited state whichionizes is produced at long range by a two step molecular processwhich operates in a fundamentally different way during the trappingand molasses phases of the hybrid trap. In the trapping phase, thelaser detuning and Rabi frequency are many times the naturailinewidth of the atomic transition. Molecular bound state resonancestructure, strongly perturbed by the intense laser field, modulatesthe photoassociative ionization signal [40]. This process can befully described by a conservative Hamiltonian, unaffected by excitedstate decay. In the molasses phase, the detuning and Rabi frequencyare on the order of the natural linewidth. Since the molecule canonly be excited when the atoms are very far apart, the excited statehas a high probability of decaying by spontaneous emission beforethe atoms move close enough together to form a molecular ion. Wehave used the semiclassical OBE treatment of this process and findthe right order of magnitude for the effective rate coefficient if therole of hyperfine structure in the excited state is taken into account[41].

The theoretical studies to date have laid the foundation forunderstanding the basic physics which occur in ultracold atomiccollisions. ihere are still many aspects of this problem that havenot yet been correctly treated and many fundamental questions thatremain unanswered. There is still a strong need for experimentalverification (or falsification) of theoretical predictions, as well asa need to develop the experimental phenomenology of ultracoldcollisions, including the connection between ultracold and normaltemperatures. Theory predicts that excited state collisions aresubject to manipulation by varying the detuning and intensity of oneor more external fields. One aspect of this is the "catalysis laser"concept of Sesko et al. [42]. We have calculations in progress thatshow how a weak blue detuned laser should be able to turn off or onthe photoassociative ionization signal. We also have calculation inprogress showing that the effective rate coefficient of Penningionization of trapped He metastable atoms can be varied by twoorders of magnitude by turning the light on or off, a resultconsistent with recent measurements by the Paris group. Thepredicted role of retardation corrections in determining trap loss

39

rates in Na and K MOTs has not yet been verified experimentally.Recent experiments point to the likely role of excited statehyperfine structure in trap loss collisions, an effect not yetaccounted for in the theories. Recent calculations by Verhaar andcolleagues suggest that collisional processes may be favorable forachieving Bose-Einstein condensation of laser cooled Cs. Thesecalculations do not take into account the likely role of second-orderspin-orbit contributions to the ground state effective spin-spininteraction in the Cs2 molecule. We estimate that such terms in theHamiltonian may cause orders of magnitude changes in certaincollision rates.

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SUPPLEMENTAL COLLISIONS PROGRAM: EXPERIMENT

The program in cold collisions at the University of Marylandhas centered on the development of techniques for studying cold andultra cold collisions in atomic beams where the energy dependenceand polarization dependence of collisions are more accessible thanin the cell-type experiments conducted in atom traps. Theseexperiments complement the laser trap collision experiments whichachieve lower temperatures, but without the wide range of possiblecollision energies.

In the past year we have developed a robust travelling waveoptical buildup cavity from which we extract up to 500 gW watts of285 nm light through a temperature -tuned frequency-doubling ADAcrystal. The UV beam selects a velocity group from the Na(3s 2S1/ 2)--+ Na(5p 2P) transition with a sodium atomic beam. We havemeasured and reported the first results from these experiments--associative ionization rate constants at 18 mK collision energy --asa function of polarization and optical field intensity. The ability toindependently vary polarization, intensity, and frequency of thecollision -inducing light field distinguished atomic beamexperiments from optical trap experiments.

The dynamics of associative ionization (AI) between excitedNa atoms,

Na(3p 2P3/2) + Na(3p 2P3/2) --+ Na2+ + e-

continues to be a convenient test case for theory and experiment ofinelastic processes in radiation fields. We began a series of atomicbeam experiments (43] measuring the probability of Al as a functionof velocity and polarization, under "conventional" collisionconditions, as a prelude to entering the ultracold regime. We soonrealized that velocity group selection would be a fruitful techniquefor examining new collision physics when the collision timebecomes long compared to the characteristic time of radiativedissipation. By exploiting the low relative velocity of collisionwithin and between narrow velocity groups we were able tomeasure the excitation function and polarization dependence of Alfrom 1000 K to about 65 mK [44,45]., which is just at the thresholdof the ultracold regime. The relative velocity of collisions within avelocity group is limited by the width of the group itself. The

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absence of power broadening the radiative lifetime of the excitedstate determines this width. Collision energies in the ultracoldregime dictate the selection of a velocity group narrower than thatobtainable from the Na (3s -* 3p) transition. The Na (3s -+ 5p)transition appeared to be a likely candidate because frequencydoubling 570 nm light, available from a ring dye laser, generated theresonant frequency at 285 nm. The natural width of the Na (3s -+ 5p)transition, less than 1 MHz, is over one order of magnitude narrowerthan the Na (3s -- 3p) transition, and effectively lowers collisionenergy to a few millikelvin. Frequency doubling cw lasers, however,is nontrivial and required constructing an optical buildup cavity andthe regulation of an ADA crystal to a stability of 10 mK. Wecommitted last year's resources of time and money to developing areliable, sufficiently intense source of UV light and to acquiring thenecessary acousto-optic modulators so as to begin to carry ourultra-narrow velocity group experiments. This effort has recentlyyielded the first results on the polarization and intensitydependence of Al at 18 mK and was reported at the Cold Collisionsworkshop in April [46]. We will submit a Phys. Rev. Lett. on theseresults before the end of July.

Concurrent with the Al experiments we have also beenpursuing the theory of fine-structure changing collisions in theheavy alkalis, RB and Cs:

Rb(5s 2S1/2) + Rb (5p 2P3/ 2) -- Rb(5s 2S1/2) + Rb(5p 2p1 /2)

Olivier Dulieu from the Laboratoire des Collision Atomiques etMoleculaires in Orsay, France has been working with Weiner andJulienne, using his fully quantal close-coupling codes to investigatethe sensitivity of theoretical results to small changes in the formof molecular potentials, the strength and form of the spin-orbitmatrix elements, and the possibility of a quantal mass isotopeeffect. These studies have been inspired by the importance of finestructure changing collisions to optical trap loss rates, recentmeasurements of which have been reported [46] with significantdepartures from the predictions of Julienne and Vigue. We havereason to believe that a surprising isotope effect in the observed Rbtrap loss rate may be due to the mass difference between 85Rb and87Rb, but reliable results await more precise potential parametersbefore publication.

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REFERENCES

[1] T. Hansch and A. Schawlow, Opt. Commtn. 13. 68 (1975).[2] D. Wineland and H. Dehmelt, Bull. Am. Phys. Soc. 20, 637 (1975).[3] D. Wineland and W. Itano, Phys. Rev. A 20, 1521 (1979).[4] P. Lett, R. Watts, C. Westbrook, W. Phillips, P. Gould, and H.Metcalf, Phys. Rev. Lett. 61, 169 (1988).[5] S. Chu et al., Phys. Rev. Left. 55, 48 (1985).[6] P. Lett, W. Phillips, S. Rolston, C. Tanner, R. Watts, and C.Westbrook, J. Opt. Soc. Am. B6, 2084 (1989).[7] J. Dalibard and C. Cohen-Tannoudji, J. Opt. Soc. Am. B 6, 2023(1989).[8] P. Ungar et al, J. Opt. Soc. Am. B6, 2058 (1989).(9] C. Cohen-Tannoudji and W. Phillips, Physics Today, October, p. 33(1990).[10]. C. Salomon, J. Dalibard, A. Clairon, W. Phillips and S. Guellati,Europhys. Left. 12, 683 (1990).[11]. K. Molmer, Phys. Rev. A 44, 5820 (1991).[12] C. Gerz, T. Hodapp, P. Jessen, W. Phillips and C. Westbrook, inpreparation.[13] G. Nienhuis, P. van der Straten, and S-Q. Shang, Phys. Rev. A. 44,462 (1991).[14] M. Walhout, J. Dalibard, S. Rolston and W. Phillips, to bepublished in J. Opt. Soc. Am. B.[15] C. Agosta, I. Silvera, H. Stoof, and B. Verhaar,Phys. Rev. Left. 62,2361 (1989)[16] S. Chu, et al., Phys. Rev Left. 57, 314 (1986).[17] P. Gould, P. Left, P. Julienne, W. Phillips, H. Thorsheim, and J.Weiner, Phys Rev. Lett., 60, 788 (1988).[18]. S. Chu et al., Opt. Lett. 11, 73 (1986).[19] K. Helmerson, presented at the Interdisciplinary LaserConference, Monterey , CA, September, 1991.[20] C. Westbrook, R. Watts, C. Tanner, S. Rolston, W. Phillips, and P.Left, Phys. Rev. Left.., 65, 33 (1990).[21] C. Westbrook, P. Jessen, C. Tanner, P. Lett, S. Rolston, R. Watts,and W. Phillips, in Atomic Physics 12, J. Zorn and R. Lewis, Eds.,(American Institute of Physics, New York, 1991) p. 89.[22] Y. Castin, J. Dalibard, and C. Cohen-Tanoudji, in Light InducedKinetic Effects on Atoms, Ions and Molecules, L. Moi et al., Eds., (ETSEditrice, Pisa, 1991) p. 5.[23]. Y. Castin, Ph. D. Thesis, Ecole Normale Superieure, Paris, 1992.

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[24] P. Jessen, C. Gerz, P. Lett, W. Phillips, S. Rolston, R. Spreeuw,and C. Westbrook, to appear in Phys. Rev. Lett.[25] R. Cook and R. Hill, Opt. Commun. 43, 258 (1982)[261 V. I. Balykin et al., Phys. Rev. Left., 60, 2137 (1988).[27] M. Kasevich, D. Weiss, and S. Chu, Phys. Rev. Left. 15, 607(1990).[28] K. Helmerson et al. presented at the Workshop on Optics andInterferometry with Atoms, Insel Reichenau, Germany, June 1992,unpublished.[29] M. Kasevich et al., Phys. Rev. Left. 63, 612 (1989)[30] A. Clairon, C. Salomon, S. Guellati, and W. Phillips, Europhys.Lett. 16, 165 (1991).[31] S. Rolston and W. Phillips, Proc. IEEE, 79, 943 (1991).[32] P. Left, P. Jessen, W. Phillips, S. Rolston, C. Westbrook, and P.Gould, Phys. Rev. Lett. 67, 2139 (1991).[33] Julienne, P. S., Smith, A. M., and Burnett, K., "Theory ofCollisions between Laser Cooled Atoms," Adv. At. Mol. Opt. Phys. 30,141(1992).[34] Julienne, P. S., and Vigue, J., "Cold Collisions of Ground andExcited Alkali Atoms," Phys. Rev. A 44, 4464(1991).[35] Band, Y. B., and Julienne, P. S., "Optical-Bloch-Equation Methodfor Cold-Atom Collisions: Cs Loss from Optical Traps," Phys. Rev. A46, July(1992).[36] Smith, A. M., Burnett, K., and Julienne, P. S., "SemiclassicalTheory of Collision-Induced Loss from Optical Traps," J. Phys. B,submitted(1 992).[37] Dulieu, 0., Weiner, J., and Julienne, P. S., unpublished, 1992.[38] Julienne, P. S., and Heather, R., "Laser Modification of UltracoldAtomic Collisions: Theory," Phys. Rev. Lett. 67, 2135(1991).[39] Julienne, P. S., "Laser modification of ultracold atomiccollisions in optical traps," Phys. Rev. Letters 61, 698 (1988).[40] Heather, R. W., and Julienne, P. S., "Theory of laser-InducedAssociative Ionization of Ultracold Na," Phys. Rev. A,submitted(1 992).[41] Band, Y. B., and Julienne, P. S., "Associative Ionization of Na inLaser Traps", unpublished, 1992.[42] D. Sesko, T. Walker, C. Monroe, A. Gallagher, and C. Wieman,Phys. Rev. Left. 63, 961 (1989).[43] See for example, M.-X. Wang and J. Weiner, Phys. Rev. A39, 405(1989) and references cited therin.[441 H. Thorsheim, Y. Wang, and J. Weiner, Phys. Rev. A41, 2873(1990).[45] Y. Wang and J. Weiner, Phys. Rev. A42, 675 (190).

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[46] Workshop in the Dynamics of Ultracold Collisions, held at theInstitute for Theoretical Atomic and Molecular Physics, Harvard-Smithsonian Observatory, April 25-28, 1992.[471 A. Giusti, F. Masnou, and J. Weiner, Adv. At. Mol. Opt. Phys. 26,209-296 (1989).

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PLAN OF RESEARCH DURING THE PROPOSED CONTRACT PERIOD

There are a number of projects already well underway in eachof the areas that have been described above. Our immediate goalwill be to bring those projects to completion. Most of thoseprojects also have longer range goals, some of which involvesubstantial changes in direction from the research now beingpursued in those areas. Below, we describe for each of the researchareas both our short term and longer teim plans. To be perfectlyhonest, we must note that the long range plans are at best guessesas to the areas of research that will actually be pursued. In lookingat the long range plans in the previous proposal, we note that whilemany of them have been successfully pursued, many highly fruitful,yet unanticipated avenues have been followed. We expect similarthings to happen during the coming proposal period, and we expect asimilarly exciting and productive period of research.

Laser Cooling Mechanisms: The immediate goals are to finish thework on temperature and spatial diffusion measurements in 3-D Rbmolasses and publish these results. The observation of extremelysmall diffusion constants, with apparent diffusion often dominatedby drift, has led us to speculate as to whether the observations of"supermolasses, " a particularly long-lived from of opticalmolasses, by a number of groups, including our own, might beexplained as drift which is frustrated by a vortex force formed bymisaligned molasses beams. The connection between supermolassesand misalignment has been pointed out repeatedly, but without aclear mechanism for explaining how it leads to long confinement.We intend to investigate this theoretically at least. Even moreinteresting is the fact that measurements of a 1-D a + -a-configuration by heterodyne spectroscopy gives information aboutthe temperature in 1-D that can be compared to existing theory, andpreliminary data indicates a significant discrepancy. This is quitesurprising, considering that the 1-D theory should be quite reliable.We intend to make more 1-D measurements, using the time-of-flightmethod as well as fluorescence spectroscopy. If the discrepancy isin fact upheld, this would have a profound effect on our view of thelaser cooling process. It is interesting that so far the only highquality measurements of temperature have been in 3-D, while theonly calculations believed to be truly reliable are in 1-D.

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We will also make tests of the 1-D theory of cooling in amagnetic field which we developed recently. As part of this weexpect to make measurements of the damping force as a function ofvelocity. Much of our conceptual understanding of how laser coolingworks is based on the semiclassical picture of the force as afunction of velocity, yet it has never been directly measured. (ADutch group has made measurments on transverse laser cooling of anatomic beam trying to determine force vs. velocity, but the resultsare, so far, inconclusive.) We will do this by either launching atomsat a fixed velocity and seeing how this velocity is damped, or byimposing a moving molasses on very cold atoms and seeing how theyre-equilibrate to the moving molasses.

New Traps for Neutral Atoms: One immediate goal is to makethe first test of the rf cavity trap for Cs atoms. The idea will be tocapture Cs atoms in a magneto-optic trap (MOT), cool to a fewmicrokelvins in molasses, and release into the microwave trap.Then these atoms will be recaptured using a MOT, so as to measurethe fraction trapped and the trapping lifetime. Later we mayconsider schemes for multiple loading of the trap. This could beaccomplished, for example, by collecting atoms in a MOT in onelocation, and transferring them to the microwave trap, using opticalpumping to put them into a trapping state. This procedure has beenused by Wieman to load an audio frequency ac magnetic trap. If allgoes well with the microwave trap we will design a trap appropriatefor hydrogen to be interfaced with the Harvard spin-polarizedhydrogen experiment.

The work on the Far Off Resonance Trap (FORT) will continue,pushing the detuning farther and the focus of the trap tighter toreach the regime where the cooling is no longer needed to hold theatoms in the trap for times on the order of seconds. We calculatethat this should be possible for detunings of one or two hundrednanometers for Na atoms, and a laser beam focussed to about 10 g±m.Assuming this is successful, we are hoping to load a large number ofatoms into such a trap, using molasses to laser cool the atoms totemperatures near the recoil limit, then turn off the cooling so thatmost of the bad collision processes that destroy trap density arealso turned off. This should allow us to study ground statecollisions such as elastic collisions, which could lead to evaporativecooling and approaches to the regime of quantum collective behavior.The fast loading times and fast cooling possible for such aconfiguration should allow the high densities and low temperatures

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needed. The usual problem is that collisions limit the density, butwe will turn off most collisional loss when we turn off themolasses.

Another area we are anxious to investigate is magneto-optictrapping. We have started some theoretical work, but there aresome intriguing experimental observations to be pursued as well.We (and others) observe that certain misalignments of the trapproduce short lifetimes, and the question arises as to themechanism for escape under these conditions. It is unlikely thatbackground gas collisions are sufficient to explain the observations,so one wonders whether the MOT develops leak paths withmisalignment. This has never been investigated, but is an importantpractical question since MOT's are now being so widely used andconsidered for other kinds of measurements.

Fluorescence spectrum of laser cooled atoms: As mentionedabove, we will be studying the temperature of atoms in the 1-Dconfiguration, with both a+ - + and linear-orthogonal-linearpolarizations. We can calculate the temperatures for these cases,both semiclassically and quantum mechanically, and the comparisonsbetween experiment and theory should be very telling.

There remain slight discrepancies between the observedlocation of the sidebands and the ones calculated from shape of thepotential induced by the light. We intend to do a direct calculationof the spectrum using the newly developed quantum Monte Carlowavefunction techniques. The use of these techniques is called forin this instance because the density matrix calculations wouldrequire the storage of more matrix elements than is possible withthe available computer memory.

The high degree of localization already measured in theexperiments convinces us that we should be able to create coherentstates or squeezed states of the atoms. More familiar as states oflight fields, such states for our atoms would correspond, in the caseof coherent states, to classical-like oscillation of atoms in thepotential wells, with all atoms having the same phase of oscillation,and in the case of squeezed states to a non-classical state wherethe position or momentum uncertainty of the atomic wavepacketwas less than that of the minimum uncertainty wavepacketexemplified by the harmonic oscillator ground state. Making acoherent state should simply involve driving the atoms at the

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resonant frequency of the trap, or displacing the trapping fields soas to start the atoms oscillating. The oscillatory motion could thenbe seen mechanically, by time resolved time-of-flight, or byspectroscopic means, possibly also time resolved. Squeezed statescould be produced by a technique similar to one proposed by Winelandfor trapped ions. The atoms trapped near the bottom of an opticalpotential well, mostly in the lowest eigenstate, would be subjectedto a sudden change in the depth of that well. This would result in awavefunction that is not an eigenstate of the new well, but whoseposition and momentum distribution corresponded to an eigenstateof the old well. For a proper choice of the new well, this willcorrespond to a squeezed state of the new well, a state that willevolve in time, so that one or the other variable will periodically besee to be squeezed. This could then be detected mechanically orspectroscopically. Such a technique, with proper timing, could leadto temperatures even colder than obtained by laser cooling. Similarpossibilities have been discussed, although not in the context ofsqueezing, by Chu and colleagues and by Hulet who has examineadiabatic cooling.

We are also considering the extension of the high resolutionspectroscopic measurements to 3-D. In principle this isstraightforward, and we are anxious to look at the 3-D spectra, butwe expect the sidebands to wash out unless we control the opticalphase of all the laser beams so as to produce regions of purecircular polarization. It is this condition in the 1-D case that leadsto the particularly well resolved sidebands, and it will not happen in3-D unless the optical phase differences are controlled. Oneadvantage of doing this in 3-D is that 3-D momentum squeezingshould be possible, leading to extremely low 3-D temperatures.

Atom Qtics: This area represents a major new thrust for us aswell as being an area of growing interest in the AMO community. ourimmediate goal is to extend the number of bounces from our curvedevanescent wave mirror, to the extent that we see the effects oftrapping due to the curvature of the mirror surface. Long rangegoals include the multiple or continuous loading of the gravitycavity from atoms cooled in molasses above the cavity, dropped ontothe mirror and optically pumped into a less strongly reflected statewhile bouncing on the evanescent wave. This should allow us tobuild up the density in the cavity. One application for such a cavitywould be as an atomic clock. The difficulty with such an applicationis the light shift during the bounce. The effect is much like a wall

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shift in a hydrogen maser. For an optical frequency clock, the lightshift may be acceptable, but for a microwave transition it isprobably too big to allow substantial accuracy improvement overpresent clocks. Another, longer range possibility for the gravitycavity is to load sufficient density of atoms into the cavity that themean mode occupation number approaches unity. This would resultin enhanced loading of atoms into the occupied modes, a kind ofstimulated emission of atoms.

We will also be pursuing the development of other opticalelements, particularly lenses and beamsplitters, as well asapplications for the mirrors. Very little work has been done on laserlenses for atoms, even though they have been demonstrated severalyears ago. We intend to develop two dimensional lenses, includinglenses that take advantage of the dissipative properties of atom-light interactions. The lenses will be used as beam-brighteners forother experiments, and we will explore the imaging properties of thelenses with a view to lithography, writing on substrates, or surfaceprobes.

Beamsplitters, devices that can split an atomic beam into twobeams having coherence relative to each other, are important foratom interferometry. The problem at present is that no splittersexist that can split the atomic beams by large angles, a process thatis easy for light beams. We are exploring adiabatic populationtransfer as one avenue to a better beamsplitter. The idea, discussedby Zoller and Hall, among others, is to create a coherentsuperposition of two energy levels, transfer one of those levels tostill anther level with the transfer of a significant number of photonmomenta. The process is completely coherent, so it will createatoms in a coherent superposition of two paths. Another idea is touse partial reflection from an evanescent wave. The problem is theusually an evanescent wave is made on a substrate, so there can beno transmission of atoms. We are investigating the idea of using anarray of optical fibers with spaces between them to create acorrugated evanescent wave mirror, actually a diffraction grating,and getting both reflected and transmitted beams of atoms. Theproper operation of such a grating requires spatial coherence of theatomic beam on a length scale greater than the grating spacing.

All of these various prospects for atom optics are enhanced byour capabilities in laser cooling. Most of the atom opticsexperiments done so far have been with thermal beams of atoms.

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However, most would work better with cold atom. Therefore, weexpect to make significant new contributions in this field.

Another related topic is the observation of the Hanbury BrownTwiss effect for atoms. In the 1950's Twiss and Hanbury Brownobserved that photon detection from a thermal source was positivelycorrelated for short times. This photon bunching effect is oftenexplained as a manifestation of the Bosonic character of photons,but can also be explained classically. The same effect should occurfor Bosonic atoms if the source is sufficiently dense and cold. Therequirement for see a large effect is the same as the requirementfor Bose Einstein condensation, bui a much smaller effect can stillbe seen, as evidenced by the fact that the Hanbury Brown Twissexperiment was done with starlight. For us the experiment wouldrequire a fast atom counting detector, small enough and far enoughaway from a cold dense source of atoms that the detector areacovers a region of spatial coherence of the source (the size of a"speckle"). We envision multiple detectors and parallel processingof the correlation signals. The experiment is challenging, but itoffers the opportunity to study quantum collective effects withoutachieving Bose Condensation. Also, because the atoms can befermioins, we may be able to see the inverse HBT effect, an anticorrelation at short times.

Atomic Fountain Clocks: This area of research in ourlaboratories at NIST in still in the construction phase. Theprinciples have already been demonstrated in our experiments inParis, and now we are constructing a new apparatus here, to beoperated in collaboration with colleagues in the Time and FrequencyDivision in Boulder. We have finished the atomic Cs beam apparatus,laser cooled and trapped the Cs, and demonstrated temperatures nearthe lowest ever reported for laser cooling of Cs. The mostimmediate thing to do is to demonstrate the launching procedure forthe atoms and to see the Ramsey resonance. After that, we want toattack the major source of noise seen in the Paris experiments: thevariation of the number of atoms from one launch to the next. Webelieve that this is due to fluctuations in the slowing laser, but thisremains to be verified. We will improve the amplitude and frequencystability of the lasers used to load atoms so as to reduce this sourceof noise. Another improvement will be to develop a betternormalization technique for correcting the noise. In the oldexperiments, a single detection region was used both for detectingthe hyperfine transition and for normalizing the signal. We are

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planning a double detection region, each devoted to one of thesetasks. Also, we are exploring ways in which to either control ormeasure more accurately the mix of magnetic sublevels which islaunched, since variations in this mix show up as noise.

Another major source of noise in Paris was the localoscillator. Our colleagues in Boulder have constructed a state-of-the-art frequency multiplier, crystal controlled with the bestavailable crystal. This should eliminate local oscillator problems.

The apparatus for the optical clock is still under construction.Once it is operational, besides observing the first laser cooling ofXe, we intend to perform other experiments with this and othermetastable noble gas atoms. In particular, we want to study Penningionization of these atoms. Penning ionization is one of theprocesses expected to limit density in a MOT, and it is interesting inits own right as a good probe of cold collision dynamics. Inparticular, with Xe* we have a choice of a number of differentisotopes, at least one of which is a fermion. The spin statisticaleffects on cold collisions should be especially interesting. At lowtemperatures atoms will scatter on each other only by s-waveprocesses, so a spin polarized sample of fermions will not scatterat all, since the total wavefunction must by antisymmetric onparticle interchange and the spin function is symmetric.

We will also have the opportunity to use the various isotopesof Xe and other noble gases to look at the variation in laser coolingbehavior with angular momentum, in experiments analogous to thosealready performed on Rb, but with more choices of angularmomentum.

Vacuum Ultraviolet Generation: Having demonstrated theprinciple of VUV generation in the wavelength ranges of interest,our next objective is to realize the same generation scheme with allsources being narrow band. The injection locked pulsed Ti:Sapphirelaser is the first step. Next we will quadruple this and use theoutput in the four wave mixing cell. At that point we will again do acareful study of the efficiency of generation as a function of variousparameters such as phase matching, focus, overlap of beams, etc.Experience with the broader band sources sometimes led to behaviorwhich was not in good accord with expectations. In many cases thiswas ascribed to poor beam quality, spatial, temporal and spectral.All of these will be improved in the next round of experiments.

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As described above in the report of the last contract period,we are preparing an experiment to measure the l s-2s interval in He.The chamber for the excitation and detection of the He is partlyfinished and work is continuing on it. When the narrowband VUVgeneration is completed we should be able to begin thespectroscopic measurements. A crucial issue will be absolutewavelength metrology. This will be done in collaboration with ourspectroscopy colleagues who routinely make measurements accurateto the order of 1 MHz. We will measure the frequency of the cwsources seeding the pulsed lasers and we will evaluate anyfrequency chirping both by looking at the average wavelength of thepulsed output and by looking at the temporal evolution of the pulsefrequency by beating it with a cw reference. We expect that most ofthe chirping problems will occur at the highest power, longwavelength, stages where it should be easiest to evaluate. Accuracyof 100 MHz will already be a significant advance over presentknowledge of the ls-2s interval, and we anticipate no significantproblems at that level. Further into the future, we anticipateimprovements to the 10's of MHz level. Whether we will improvebeyond that will depend on what we learn and whether there issufficient interest at that level for comparisons between theory andexperiment.

The Ly-ca generation narrowband will be suitable for coolinghydrogen atoms trapped for long periods of time. We are alsointerested in developing the capability to producing long pulses orlong pulse trains of VUV for cooling atomic hydrogen beams fromthermal sources (possibly near liquid helium temperatures.) Wehave some schemes for producing such pulse trains from a longpulse, mode locked laser, but such plans are not very immediate.

Collisions of laser cooled atoms: There are a number ofmeasurements having high priority for the immediate future. Wewant to measure the associative ionization of Na in a laser trapwith an additional, strong laser beam tuned several GHz to tens ofGHz from resonance. It is clear that there are strong resonances inthis region, and we have not been able to study them simply bytuning the trapping frequency. Also, we now have a MOT and an iondetector in a vacuum system so that we can measure Na Al in thehigh density but low laser intensity environment of a MOT. This willgive us much better values for the Al rate at low laser intensity,where the laser dipole trap data is relatively poor because Al is so

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suppressed at low intensity. We can also compare the Al rate to thetotal trap loss rate, and compare with theory to see if the ratio ofAl to other loss processes is correctly predicted. In addition, wecan measure the Al and total trap loss as a function of trap detuningor of catalyst laser detuning. While experiments measuring traploss have been done in this way, they have not been done for Na, norfor Al, since Al does not occur in other alkalis. The behavior of Natrap loss with detuning should be different from other alkalis. As anadded advantage, we can perform the same kind of measurements onCs and Rb MOTs using the neighboring apparatus for heavy alkalicooling and trapping. These kinds of comparisons will provide goodtests of the calculations.

Another area of interest is to measure fine structure changingcollisions. So far, Al has been the only specific collision processmeasured at ultralow temperature, and that has been done only inour group. All other collision measurements have been of trap loss,which does not distinguish very well among various possiblemechanisms. Fine-structure-changing collisions are calculated tobe a major contributor to trap loss in some cases, while Al is not.Therefore, these sorts of measurements are particularly interestingto be done in conjunction with traps loss measurements.

Here, our idea is to excite one of the fine structure levelsthrough laser cooling and trapping and measure transfer to the otherby exciting from that level to a still more highly excited state (suchas 5s) and observing decay on a channel not open to atoms notmaking the fine structure change. We estimate that it should berelatively easy to see the signal with a reasonable MOT size anddensity, and we can then compare the fine structure changing rate tothe total trap loss rate and the Al rate for a very detailedcomparison with the theory.

We have already described planned experiments with cooledmetastable atoms. We are also interested, in the long term, inexperiments involving ultra cold beams such as atoms dropped froma MOT onto other atoms, proving both an ultra low energy of collisionand a well defined collision axis.

Supplementary Collision Program--Theory: Our basictheoretical program for ultracold atomic collisions will move inseveral directions. We will continue to push for a correct quantummechanical understanding of ultracold excited state collisions.

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There are three components to this. One, we will develop apropagator for the quantum density matrix using Lanczos propagatormethods. We will compare these results with those of wavefunctionmethods based on new quantum Monte Carlo methods. We also havehopes that, except for extremely low temperatures near the recoillimit, the semiclassical OBE method will prove to be accurateenough for practical calculations of collisions with fine andhyperfine structure. We will use the understanding of coldcollisions that comes out of these studies to do realisticcalculations on trap loss and ionizing collisions, including thetemperature dependence, the effect of hyperfine structure, and therole of polarized light in affecting the collision rates. We hope to beable to compare predictions to good experimental data on sucheffects. We already have in progress the development of a code tocalculate the interatomic potentials of alkali excited states in ahyperfine basis. We have the realistic expectation that a nearlyquantitative understanding of these excited state collisions can beachieved through the cooperation of experimental and theoreticalstudies. We also intend to look more carefully at ground statecollisions of alkali species and metastable rare gases. Theseinclude assessing the role of second-order spin-orbit coupling in theheavier alkali species. Another subject that is important to study isthe pressure shifts that can occur in optical frequency clocktransitions in alkaline earth or rare gas metastable species. Wealso intend to explore the issue as to whether a type ofphotoassociative spectroscopy of ultracold collisions can be used toprepare translationally cold molecules.

Supplementary Collision Program--Exoeriment: Theexperimental program at the University of Maryland has three nearterm objectives: (1) measurement of the associative ionizationexcitation function continuously from 18 mK to 1000 K. Thisexperiment will probe the region where conventional collisionphysics transforms to ultracold collision physics,and theorypredicts specific changes in polarization and intensity behavior atthe transition temperature (65 mK in Na). (2) At 18 mK we willmeasure the associative ionization probability as a function of redand blue detuning from the D2 resonance line. The results will showwhich of two competing theories (if either) is correct. (3) Incollaboration with Vanderlei Bagnato we will measure Na (3p 2p)fine-structure changing collisions in a magneto optic trap.

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We are now well positioned to mearure the frequencydependence of the Al probability around the center of the resonanceexcitation. Ultracold theory predicts off resonant structure arisingfrom optical excitation of ground state atom pairs, but a quantaltheory (Julienne and Vigue) and a semiclassical approach (Gallagherand Pritchard) do not predict the same form of the profile to the redand blue sides of resonance. The experiments we are about to beginshould distinguish between the two theories. Later in the year weplan to extend the experiment to the selection of two ultra-narrowvelocity groups, and measure Al collisions between them. Therelative velocity between the two groups can be continuously variedfrom 18 mK to 1000 K and will be the first complete measurementof Al probability dependence on velocity, polarization, and intensity.The theory of Al dynamics has never fully taken into account theinfluence of the radiation field in ultracold collisions. Theseresults should provide the necessary impetus to push development oftheory into this regime.

In collaboration with V. Bagnato, who will bring an optical trapapparatus to Maryland from the University of Sao Paulo, Brazil, wewill measure fine structure changing collisions in sodium. Fine-structure changing collision and radiative escape are the two maininelastic processes responsible for collisional trap loss. Theorypredicts that the relative contribution between the two is verysensitive to detuning from the atomic resonance line. A directmeasure of Na(3p 2P1 /2) production as a function of detuningtogether with total trap loss will determine the relativecontributions of the two inelastic channels. Concerning the fine-structure-changing mechanism itself, theory predicts that corioliscoupling rather than spin-orbit coupling should be the dominantmechanism in the lighter alkalis. The fine-structure changingprocess therefore will also be measured in the atomic beam velocitygroup experiments where the predicted differences in energy(temperature) dependence of the spin-orbit and coriolis mechanismsshould show a markedly different form. The theoretical work withOlivier Dulieu is presently being extended to sodium and willcomplement the experiments to be undertaken with Bagnato.

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BUDGET: year one

Lasers and Optics ...................................................................................... 64 k$Lasers, laser maintenance (plasma tubereplacements), optical tables, mounts, supportstructures, lenses, mirrors, polarizing optics,gratings, fibers, electro-optics and acousto-optic devices, etc.

Vacuum and mechanical equipment .................................................... 20 k$Pumps, gauges, flanges, chamber and partsfabrication,clean air and water supply equipment, etc.

Electronics Equipment .............................................................................. 30 k$Power supplies, data acquisition, experimentcontrol, data analysis hardware and software,communication, repairs and maintenance, etc.

Graduate student/postdoc support ..................................................... 30 k$Support for graduate students and/or postdocsregistered at the university, andpursuing their research in our laboratory at NIST

Miscellaneous ........................................................................................... 20 kTravel to conferences, publication charges,expensesfor short term visitors, gases, cryogenics liquids,storeroom supplies, other miscellaneous suppliesand expenses.

TOTAL. in laser cooling group ............................................................ 164 k

Supplemental budget supporting experimental workperformed at the University of Maryland on coldcollisions ............................................................................................................ 28 k

Supplemental budget supporting work in the MolecularPhysics Division at NIST on theory of cold collisions ..................... 8 k$

GRAND TOTAL, year one ............................................................................. 200 k

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.. .. ... ... .

BUDGET: year two

Lasers and Optics ............................................................................... 66 k$

Vacuum and mechanical equipment .................................................... 21 k$

Electronics Equipment .............................................................................. 31 k$

Graduate student/postdoc support ..................................................... 33 k$

Miscellaneous ................................................................................................ 21 k$

TOTAL. in laser cooling group .............................................................. 172 k$

Supplemental budget supporting experimental workperformed at the University of Maryland on coldcollisions ........................................................................................................ 29 k$

Supplemental budget supporting work in the MolecularPhysics Division at NIST on theory of cold collisions .................. 9 k$

GRAND TOTAL, year two .......................................................................... 210 k$

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%

BUDGET: year three

Lasers and Optics ............................................................................... 68 k$

Vacuum and mechanical equipment .................................................... 22 k$

Electronics Equipment .............................................................................. 33 k$

Graduate student/postdoc support ..................................................... 35 k$

Miscellaneous ................................................................................................ 22 k$

TOTAL. in laser cooling group .............................................................. 180k$

Supplemental budget supporting experimental workperformed at the University of Maryland on coldcolisions ........................................................................................................ 30 k$

Supplemental budget supporting work in the MolecularPhysics Division at NIST on theory of cold collisions ................. 10 k$

GRAND TOTAL, year three .......................................................................... 220 k$

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