-
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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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
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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
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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
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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].
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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
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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
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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
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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
#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
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(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.
#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
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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
#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
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(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,
#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
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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
#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
11386
-
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.
#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
11387