6Li and Cs atoms in microgravity · 2018. 6. 12. · Two-stage crossed beam cooling with 6Li and...

Two-stage crossed beam cooling with 6Liand 133Cs atoms in microgravity

Tian Luan,1 Hepeng Yao,1 Lu Wang,2 Chen Li,1 Shifeng Yang,1

Xuzong Chen,1,3 and Zhaoyuan Ma2,4

1School of Electronics Engineering and Computer Science, Peking University, Beijing 100871,China

2Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences, Shanghai201800, China

[email protected]

[email protected]

Abstract: Applying the direct simulation Monte Carlo (DSMC) methoddeveloped for ultracold Bose-Fermi mixture gases research, we study thesympathetic cooling process of 6Li and 133Cs atoms in a crossed opticaldipole trap. The obstacles to producing 6Li Fermi degenerate gas via directsympathetic cooling with 133Cs are also analyzed, by which we find that theside-effect of the gravity is one of the main obstacles. Based on the dynamicnature of 6Li and 133Cs atoms, we suggest a two-stage cooling process withtwo pairs of crossed beams in microgravity environment. According to oursimulations, the temperature of 6Li atoms can be cooled to T = 29.5 pK andT/TF = 0.59 with several thousand atoms, which propose a novel way to getultracold fermion atoms with quantum degeneracy near pico-Kelvin.

© 2015 Optical Society of America

OCIS codes: (020.0020) Atomic and molecular physics; (020.2070) Effects of collisions;(020.7010) Laser trapping.

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#232812 - $15.00 USD Received 19 Jan 2015; revised 22 Mar 2015; accepted 6 Apr 2015; published 22 Apr 2015 © 2015 OSA 4 May 2015 | Vol. 23, No. 9 | DOI:10.1364/OE.23.011378 | OPTICS EXPRESS 11378

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1. Introduction

Since the first sympathetic cooling has been demonstrated, this technique has been successfullyextended to the ultracold atoms field, which serves as a unique tool that opens up many pos-sibilities for researches such as ultracold molecules, Efimov trimers, many-body physics andthe exploration of BEC-BCS crossover [1–3]. In particular, one can get the different staticsby mixing bosonic and fermionic atomic species. When combining the mixture with opticallattices, the mixture provides new opportunities for exploring the quantum phases such as su-persolids, insulator with fermionic domains and boson mediated superfluids [4–6].

Among the different possible heteronuclear mixtures, the Li-Cs mixtures can be consideredas an excellent candidate. Firstly, the large mass ratio of mCs/mLi=22 leads to an advantageousuniversal scaling factor of 4.88 for Efimov resonances, compared with 22.7 for a homonuclearsystem, which is a smaller scaling constant that facilitates the text of the scaling law in Efimovphysics [7, 8]. Secondly, the Cs atoms can be cooled down to nano-Kelvin and the Fermi tran-sition temperature of Li atoms can be 1μK. Through effective sympathetic cooling process, theLi atoms can be prepared at a temperature of T/TF=0.01 theoretically. Finally, the ground-stateLi-Cs molecules have the largest dipole moment of 1.8×10−29 C·m among the combinationsof two stable alkaline-metal atoms [9, 10].

Although there are certain advantages of ultracold Li-Cs mixtures, little is known about theinteraction properties of Li and Cs until now. Recently, Chin’s and Weidemüller’s group bothsucceeded in producing an ultracold mixture of fermionic 6Li and bosonic 133Cs atoms andobserving interspecies Feshbach resonances [9, 11]. However, they both take the tragedy thatcooling 6Li atoms and 133Cs atoms separately, then transferring and mixing them together toobserve Feshbach spectroscopy. It’s a good arrangement for the observation of 6Li-133Cs Fesh-bach resonances, but due to the inevitably heating effects in the long distance transferring, the6Li atoms can not achieve a much lower temperature [12, 13].

During the evaporation cooling process, the gravitational sag is one of the main obstacles tothe mixture of 6Li and 133Cs. In one species situation, magnetic levitation may be a unique tech-nique to counteract the effect of the gravitational force, which can improve the efficiency of the


evaporation cooling [13, 14]. However, one can not compensate the gravitational force of twodifferent species at one time, which means that even with magnetic levitation, the gravitationalsag still exists as the sympathetic cooling goes on [15]. The microgravity environment can con-sequently be regarded as an indispensable condition to improve the efficiency of sympatheticcooling with 6Li atoms and 133Cs atoms [16].

Moreover, in the microgravity environment, owe to the stable fully mixing and interactingof the 6Li atoms and 133Cs mixture, further cooling process can be applied on the two sp-ceies. In 2003, A. E. Leanhardt et.al employed an adiabatically decompression and subsequentevaporation cooling process of partially condensed atomic vapors in a very shallow gravito-magnetic trap to obtain a temperature of hundreds of pico-Kelvin [17]. In 2013, the situationin microgravity was studied by Lu Wang et.al, and they proposed a two-stage path for 133Cs topico-Kelvin temperatures in microgravity with a multi-beam dipole trap [16]. But until now, allthe two-stage cooling process are proposed for the evaporation cooling of single bosonic atom,which leads to the good result of pico-Kelvin. Thus, we think that a similar two-stage processmight also be efficient for the 6Li-133Cs mixture’s sympathetic cooling, which could lead tolower temperature with acceptable quantum degeneracy in the microgravity environment.

In this paper, we first analyze the obstacles to cooling 6Li atoms via direct sympathetic cool-ing with 133Cs atoms. The obstacles to producing 6Li Fermi degenerate gas via direct sympa-thetic cooling with 133Cs are also analyzed, by which we find that the side-effect of the gravityis one of the main obstacles. Then based on the dynamic nature of 6Li atoms and 133Cs atoms,we suggest a two-stage cooling process with two pairs of crossed beams in microgravity envi-ronment. According to our simulations, the temperature of 6Li atoms can be cooled to T = 29.5pK and T/TF = 0.59 with several thousand atoms. In the end, factors that may affect the finaltemperature of 6Li atoms are also analyzed.

2. The simulation

We employ the DSMC method described in [18]. In our simulation, the atoms are prepared inthe lowest hyperfine ground state (|F = 3,mF = 3〉 for 133Cs, |F = 1/2,mF = 1/2〉 for 6Li).And the atoms are treated as semiclassical particles, solely for the purpose of modeling theircollision processes in the framework of well-established classical collision dynamics, so thatthe hard-sphere model and energy and momentum reservation laws can be utilized. However,the quantum nature of particles is also taken into consideration. The elastic collisions betweenparticles are mostly induced by s-wave elastic scattering. As the frequencies of an atom collid-ing with others depend on the s-wave scattering cross section σ , which is a key factor for thesimulations [14]. Since 133Cs atoms are bosonic particles, we set σ as

σ =8πa2Cs

1+ k2Csa2Cs

, (1)

where aCs is the s-wave scattering length and kCs is the de Broglie wave vector of the 133Csatoms. As kCs depends on the temperature, the scattering cross section is related to the tempera-ture as

σ =8πa2Cs

1+ 2πmCskBTh̄2

a2Cs. (2)

At ultralow temperature (T→0), σ reduces to σ =8π a2Cs, which is the case of weakly in-teracting identical bosons. For weakly interacting identical fermions, the s-wave scattering isforbidden, thus we neglect the elastic collisions between the 6Li atoms themselves.

The three-body recombination is the dominant inelastic collision and the loss due to thebackground scattering is also considered [16].


The crossed dipole trap is created by two orthogonally focused laser beams with equal waistsin the horizontal plane. The dipole potential can be expressed as,

U(x,y,z) =−U1e−2(x2+z2)/w2 −U2e−2(y2+z2)/w2 , (3)with the individual trap depths, U1 and U2 :

U1(2) =3πc2

2ω30(

Γω0 −ω1 +

Γω0 +ω1

)P1(2)πw2

, (4)

in which, P1(2) are the powers of the two beams, w is the waist of the beams, c is the speed oflight in space, Γ is the scattering rate, ω0 and ω1 are the resonance frequency of atoms and thefrequency of laser beams.

The dipole potential near the center can be well approximated as a symmetric harmonicoscillator,

U �−Ucenter(1−2x2 + y2 +2z2

w2). (5)

In our simulation, we consider that the atoms with higher kinetic energies move to the bound-ary of the trap and then escape [19].

3. The sympathetic cooling process

In order to study the sympathetic cooling process, we numerically simulate the 6Li-133Cs sym-pathetic cooling process of Mudrich in 2002 [20]. They simultaneously trap typically 4 ×1046Li atoms with 105 133Cs atoms in a quasi-electrostatic trap (QUEST) which is produced bya focused 10.4 μm CO2 beam. The radial and axial oscillation frequencies of trapped Cs(Li)atoms are ωx,y/2π=0.85 kHz (2.4 kHz) and ωz/2π=18 Hz (50 Hz). The effective s-wave scat-tering lengths are |aLi−Cs|= 180a0, |aCs−Cs|= 140a0 (a0 is the Bohr radius). We set the initialsimulation parameters according to the chart in [20] and get the evolution curve of the 6Li-133Csatoms’ number and temperature. As a comparison, the origin experimental results by Mudrichet.al are also illustrated. From the comparison in Fig. 1, we can see that the simulations areconsistent with the experiment.

Based on the discussions above, we take several series of simulations to find out the relationbetween the atom numbers and the final degeneracy T/TF of 6Li atoms, and the relation betweenthe initial temperature of 133Cs atoms and final degeneracy of 6Li atoms. Here,

TF =h̄ϖkB

(6N)13 , (6)

in which h̄ is the reduced Planck constant, kB is the Boltzmann constant, ϖ = (ωxωyωz)13 is the

mean trapping frequencies and N is the atom number of 6Li atoms.In our simulations, the dipole trap is still formed by crossing two focused beams in the

horizontal plane at the wavelength of 1064 nm, waist of 60 μm. The initial atom numbers andtemperature of 6Li are 2× 105 and 20 μK, which is accessible according to [9,11]. We take thesimulations under different initial conditions of 133Cs atoms. The initial atom number rangesfrom 1× 105 to 1× 108 and the initial temperature ranges from 1 μK to 90 μK. The beampower is nonlinearly ramped down as,

P(t) = P0 × (1+ t/τ)−β , (7)where P0 is the initial beam power, τ and β are parameters associated with the ramping curve.We set P0=10 W, and the minimum beam power can be 3 mW. We take different τ (0.001 to


Fig. 1. The simulated evolution of the Li-Cs atoms’ number and temperature (blue curvesfor the Cs atoms, red curves for the Li atoms). As a comparison, the experimental results byMudrich et.al are also illustrated as black squares and dots, courtesy of professor Grimmand professor Weidemüller.

100) to find the maximum degeneracy T/TF in each group of simulations. The results in Fig.2(a) shows the relationship between the final degeneracy of 6Li atoms and the initial number of133Cs atoms. And Fig. 2(b) shows the relationship between the final degeneracy of 6Li atomsand the initial temperature of 133Cs atoms. From the figure we can see that the compatible atomnumber of 133Cs lies approximately between 5× 105 and 1× 106, and that the lower the initialtemperature of 133Cs atoms is, the better degeneracy of 6Li atoms can be. However, when theinitial temperature of 133Cs atoms is below 2 μK, the condition is hard to keep because of theinevitable heating effects in the long distance transfering.

In order to find out the obstacles to producing degenerate fermionic 6Li gases, we simulatethe cooling process and depict the diagram of the evaluation of atom number and temperatureof the 6Li atoms during the cooling process. The process is illustrated in Fig. 3(a), in whichthe initial conditions are TCs= 3 μK, NCs = 1×106, TLi= 20 μK, NLi=2×105 with the rampingparameters set to τ = 25 and β = -44.5, which is the best set according to the group simulationsin Fig. 2.

From Fig. 3(a), we can see that the degeneracy T/TF reaches the lowest value 1.09 at 3 sand then shifts upward. In fact, the dipole force of the red-detuned laser serves to lift the atomsagainst the gravity of the earth, so that the equilibrium position of 6Li atoms(ΔzLi = −g/ω2Li)shifts downward as the beam power ramps down. At 3 s, ΔzLi = 83.8 μm is greater than thebeam waist(60 μm). So the 6Li atoms begin to fall down and leak out from the dipole trap.Because of the fast loss of the atom, the degeneracy T/TF shifts upward.

The other factor that may affect the cooling efficiency is the gravitational sag between the


(a) (b)

0 15 30 45 60 75 90

0.75

1.50

2.25

3.00

3.75

4.50

NCs

=1X106

NCs

=2X105

NCs

=1X105

T/T

F

TCs( K)10

510

610

710

80.6

1.2

1.8

2.4

3.0

3.6

T/T

F

TCs

=10 K

TCs

=5 K

TCs

=2 K

NCs

Fig. 2. (a) Relationship between the final degeneracy of 6Li atoms and the initial number of133Cs atoms. The black blocks, red dots and the blue triangles show that the initial tempera-ture of 133Cs atoms is respectively 10 μK, 5 μK, and 2 μK. (b) Relationship between thefinal degeneracy of 6Li atoms and the initial temperature of 133Cs atoms. The black blocks,red dots and the blue triangles show that the initial number of 133Cs atoms is respectively1×106, 2×105, and 1×105.

(a) (b)

103

104

105

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.51.01.52.02.53.03.54.04.5

T/TF TLi

time(s)

T/T

F

0.0

5.0x10-6

1.0x10-5

1.5x10-5

2.0x10-5

TLi

NLi

103

104

105

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.50.51.01.52.02.53.03.54.04.5

T/TF TLi

time(s)

T/T

F

0.0

5.0x10-6

1.0x10-5

1.5x10-5

2.0x10-5

TLi

NLi

Fig. 3. Evolution of the total atom number NLi (black curve above), degeneracy T/TF (redcurve) and the temperature of 6Li atoms (blue curve). (a) The sympathetic cooling pro-cess of 6Li atoms with gravity(g=9.81 m/s). The lowest degeneracy T/TF is 1.09. (b) Thesympathetic cooling process of 6Li atoms in microgravity(10−3g). The lowest degeneracyT/TF is 0.52.


two atomic species. In the direction of the gravitational force, the total gravitational sag canbe expressed as Δz = ΔzCs −ΔzLi = g · (1/ω2Cs −1/ω2Li). The characteristic resonant lengths ofthe two species in the direction of the gravitational force are ζCs =

√2kBTCs/mCsω2Cs, ζLi =√

2kBTLi/mLiω2Li. The gravitational sag and the characteristic resonant lengths in the coolingprocess are shown in Table 1.

Table 1. Gravitational sag and characteristic resonant lengths in the cooling process.

t Δz ζCs ζLi0.5s 1.60 μm 9.80 μm 33.1 μm0.75s 2.52 μm 11.1 μm 34.7 μm1s 3.83 μm 12.3 μm 36.1 μm

1.25s 5.87 μm 13.7 μm 37.1 μm1.5s 8.95 μm 15.2 μm 37.5 μm1.75s 13.6 μm 16.9 μm 37.0 μm2s 20.7 μm 18.7 μm 36.9 μm

2.25s 31.0 μm 20.7 μm 38.3 μm2.5s 46.5 μm 22.9 μm 39.3 μm

From Table 1 we can see that the gravitational sag increases as the cooling process goes on.After 1.75 s, the gravitational sag can be compared with the characteristic resonant lengths.When the two atom clouds separate too far apart, the inter-species collisions are not effective.This is one of the main obstacles to the sympathetic cooling. Thus, a microgravity environmentcould be a better condition for the cooling process.

Under the same initial conditions, we also simulate this sympathetic cooling process in themicrogravity environment(10−3g). The process is illustrated in Fig. 3(b). Without the side-effect of the gravity, the sympathetic cooling process lasts 5.5 s. The final degeneracy T/TFis 0.52, the final temperature is 7.36 nK and the final atom number is 2985. In order to studyhow the gravity acceleration affects the final temperature and degeneracy of 6Li atoms, we runseveral simulations under the same initial conditions and summarize the results in Table 2.

Table 2. Gravity acceleration, final temperature and degeneracy of 6Li atoms.

Gravity Acceleration Temperature(K) Atom Number Degeneracyg 1.05×10−7 2999 1.39

10−1g 1.44×10−8 2994 0.5610−2g 7.58×10−9 2997 0.5210−3g 7.36×10−9 2985 0.5210−4g 7.36×10−9 2989 0.5210−5g 7.36×10−9 2985 0.52

From Table 2, we can see that for the first stage cooling, the final temperature can be differentif the microgravity level is bigger than 10−3g. However, the final temperature stays almost thesame when the micro-gravity level is smaller than 10−3g.

4. The two-stage crossed beam cooling process in microgravity

From previous analysis, we can see the advantages of microgravity for sympathetic cooling.However, in order to get sufficiently high degeneracy and low temperature, it is necessary to


(b) (c) (a)

Fig. 4. The proposed setup of the multi-beam optical dipole trap, which is designed forthe two-stage sympathetic cooling. The arrowheads illustrate the process of the two-stagesympathetic cooling. (a) Sympathetic cooling in a tight-confining crossed dipole trap. (b)Overlapping the trap with a wider and weaker one. (c) Adiabatically decompressing thecombined trap.

find an efficient method for cooling. We study the two-stage cooling process for 133Cs atomsin microgravity suggested by Lu Wang, which cools down the atoms’ temperature to pico-Kelvin [16]. We think that this process might also be workable for the sympathetic coolingprocess of boson-fermion mixture. So we take this method to the simulation of our coolingprocess to check if it also works well for the Bose-fermi mixture.

Similar with the two-stage cooling of boson atoms, the whole cooling process is dividedinto two parts. The schematic drawing of the multi-optical dipole trap is illustrated in Fig. 4and the gravity acceleration is set to 10−5g. In the first stage, atoms are loaded into a tight-confining dipole trap created by two crossed laser beam of 1064 nm, each with a waist of 60μm and power of 10 W. The loaded atoms are 1×106 133Cs atoms with a temperature of 3μK and 2×105 6 Li atoms with a temperature of 20 μK, which produce the initial degeneracyT/TF = 4.28. In this tight confining dipole trap, the initial trapping frequency of 6Li(133Cs) isωz/2π=1137.65 Hz(ωz/2π=616.24 Hz). In the first 5.5 s, the beam power is ramped down to 3mW by Eq. (7), with τ=25 and β=-44.5. During this process, the waist of the laser beam is re-mained. The condensate we get from this process is 2985 6Li atoms with a temperature T=7.36nK and a degeneracy T/TF = 0.52. At the same time, there also leaves 1.8×104 133Cs atomswith a temperature of 6.8 nK. At the end of this stage, the trapping frequency of 6Li(133Cs) isωz/2π=13.99 Hz(ωz/2π=6.58 Hz). The first stage is same as the situation describe in Fig. 3(b).

Then, we come to the second stage. It is an adiabatically decompressing process where amuch shallower and wider crossed-beam trap is overlapped to the trap. The result of the sim-ulation is shown in Fig. 5. The waist and power of this new trap is 3 mm and 80 mW each.We ramp down the power of the narrow laser by parameters τ=0.03 and β=0.8683 with Eq.(7). With another 9.5 s, the narrow beam is nearly shut down and there only remains a weakerconfinement, in which the trapping frequency of 6Li(133Cs) is ωz/2π=0.058 Hz(ωz/2π=0.027Hz). Finally, we get 2684 6Li atoms at the temperature of 29.5 pK , degeneracy of T/TF = 0.59,


103

104

105

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 150.00.51.01.52.02.53.03.54.04.5

T/TF TLi

time(s)

T/T F

10-1110-1010-910-810-710-610-5

TLi

NLi

Fig. 5. The time evolution of atom number NLi (black curve above), degeneracy T/TF (redcurve) and the temperature of Li atoms(blue curve). The lowest temperature is 29.5 pKwith the degeneracy of T/TF = 0.59.

and 15295 133Cs atoms with temperature of 26.1 pK. The whole process is under the conditionof microgravity(10−5g), which allows for the persistent flatness of the very shallow trap andavoids the separation of the two different species. In the end, the fermions could reach tens ofpico-Kelvin with degeneracy T/TF around 0.5.

We also make several simulations to test how gravity acceleration affects the final tempera-ture of the atoms in two-stage cooling process. We set different gravity acceleration valuesand get the final temperature of 6Li atoms when the reach the same degeneracy 0.59. The fi-nal temperature (gravity acceleration) of 6Li atoms are 5.72×10−9 K (10−2g), 1.03×10−9 K(10−3g), 8.52×10−11 K (10−4g), 2.95×10−11 K (10−5g). From the simulation results, we cansee that the gravity acceleration must be smaller than 10−5g in order to achieve the temperatureof pico-kelvin regime. To realize this microgravity environment, we can use techniques such asspecies-specific dipole trap, or setting up microgravity platforms such as recoverable satellites(10−5g), drop towers (10−5g) and space station (10−6g) [21, 22].

To insure the validity of two-stage cooling, we also estimate how the power and frequencydithering of laser can affect the final temperature of the mixture. From Eq. (3) and Eq. (4), nearthe center of the crossed dipole trap, the potential can be approximated as,

Udip(r)� 3πc2

2ω30· Γ

ω0 −ω1 ·P

πw2, (8)

here we use the rotating-wave approximation and assume the two beams of the trap are pro-duced by one laser. In the ultracold regime, the temperature is a statistic data according to theaverage kinetic energy K and potential energy Udip of the atoms in three direction.

32· kB ·T = K+Udip. (9)

So we can estimate the influence of power dithering to the final temperature through the


partial differential of P in both sides of Eq. (9).

32· ∂T

∂P· kB = ∂Udip∂P

= −3πc2

2ω30· Γ

ω0 −ω1 ·1

πw2. (10)

Taking the parameters of 6 Li atoms, Γ = 5.8724 MHz, ω0 = 2π×4.47×1014 rad/s, the con-ditions of the laser, ω1=2π×2.82×1014 rad/s, w=60 μm and the constants c=3×108 m/s, kB=1.38×10−23 J/K [23]. We can find out

∂T = 4.6×10−7( KJ/s

) ·∂P

= 4.6 · ( pK10−2mw

) ·∂P. (11)

So we get the final expression of the temperature influenced by the power dithering of thelaser, which means that if we want to keep the atoms’ temperature stable at 10 pK scale, wemust insure the power dithering of laser less than 2×10−2 mW. In the same way, we get theexpression of the temperature influenced by the frequency dithering,

∂T =−0.447×10−2(pK /MHz) ·∂�, (12)here, �= ω0 −ω1. Eq. (12) means that if the frequency of laser dithered 1 MHz, the tempera-ture of atoms in the shallow dipole trap will change -0.447×10−2 pK. Through the discussionabove, taking the current experiment condition into consideration, we can see that the frequencystability of the laser can meet the requirement of 10 pK scale while the power stability needs afurther development. We think that the multilevel feedback circuit might be a good choice.

5. Conclusion

We studied the sympathetic cooling process of 6Li and 133Cs atoms in crossed optical dipoletrap with the direct simulation Monte Carlo(DSMC) method developed for ultracold Bose-Fermi mixture gases research. Applying two-stage cooling technique to sympathetic coolingprocess, we put forward a new cooling process with two pairs of crossed beams for 6Li-133Csmixture, which leads to tens of pico-Kelvin with degeneracy T/TF around 0.5. Even though thetwo-stage process just provides a possible path to ultralow temperature with no more increasingon quantum degeneracy, there are still several advantages for reaching such a ultracold Bose-Fermi system. With a slower atoms’ velocity, we are able to study the physics phenomenathat only occur on very low energy scale such as phase transitions and new forms of matter.It can also be benefical to the precision measurement by enabling ultra-precise atomic sensorswhich contribute to the test of basic physical quantities, general relativity and gravitationalwave detection [16, 17, 24]. This new cooling process can also be useful to create other Bose-Fermi mixtures such as 133Cs-40K, 87Rb-40K and 87Rb-6Li, which may be a new method forexploring the ultracold atoms world.

Acknowledgment

The first two author contributed equally to this work. We thank Professor Cheng Chin andProfessor Xiaoji Zhou for their helpful discussions and suggestions. This work is supportedby the National Fundamental Research Program of China under Grant No.SQ2010CB511493and No.2011CB921501, the National Natural Science Foundation of China under GrantNo.61027016, No.61078026, No.10934010 and No.91336103.


6Li and Cs atoms in microgravity · 2018. 6. 12. · Two-stage crossed beam cooling with 6Li and...

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Transcript of 6Li and Cs atoms in microgravity · 2018. 6. 12. · Two-stage crossed beam cooling with 6Li and...