RAPID COMMUNICATIONSPHYSICAL REVIEW A 79, 031602共R兲 共2009兲

Direct evaporative cooling of 41K into a Bose-Einstein condensate
T. Kishimoto,1 J. Kobayashi,2 K. Noda,3 K. Aikawa,3 M. Ueda,4,5 and S. Inouye2,5,*
1

University of Electro-Communications, 1-5-1 Chofugaoka, Chofu 182-8585, Japan
Institute of Engineering Innovation, University of Tokyo, Bunkyo-ku, Tokyo 113-8656, Japan3
Department of Applied Physics, University of Tokyo, Bunkyo-ku, Tokyo 113-8656, Japan
4
Department of Physics, University of Tokyo, Hongo, Bunkyo-ku, Tokyo 113-0033, Japan
5ERATO Macroscopic Quantum Control Project, JST, Bunkyo-ku, Tokyo 113-8656, Japan
共Received 18 December 2008; published 30 March 2009兲

2We have investigated the collisional properties of 41K atoms at ultracold temperatures. To demonstrate thepossibility of using 41K as a coolant, a Bose-Einstein condensate of 41K atoms in the stretched state 共F= 2 , mF = 2兲 was created by direct evaporative cooling in a magnetic trap. An upper bound of the three-bodyloss coefficient for atoms in the condensate was determined to be 4共2兲 ⫻ 10−29 cm−6 s−1. A Feshbach resonancein the F = 1 , mF = −1, state was observed at 51.35共10兲 G, which is in good agreement with theoreticalprediction.
DOI: 10.1103/PhysRevA.79.031602

PACS number共s兲: 03.75.Hh, 34.50.⫺s

Quantum degenerate gases are attracting a great deal ofinterest recently as an ideal testbed for studying condensedmatter systems 关1兴. One of the biggest advantages of using
cold atoms is the unprecedented flexibility. One cannot only
choose the strength and symmetry of the confining potential,
but also tune the strength of interatomic interactions. The
availability of a rich variety of atomic species also brings
considerable advantages. It enables researchers to choose thestatistics and the mass ratio of atoms in a quantum mixture ofgases. To date, a variety of quantum degenerate Bose-Bose,
Bose-Fermi, and Fermi-Fermi mixtures has been realized
and studied intensively.
However, there exist certain drawbacks in choosing an
exotic combination of atomic species. For example, a large
difference in mass can be problematic for systematic studies
of a quantum degenerate mixture. The difference in thegravitational sag can result in an inhomogeneous spatial
overlap between the two clouds. Common solutions to thisproblem are to increase the vertical trapping frequencies,
make the trapping potential sensitive to atomic species 关2兴,or use atomic species that are close in mass. The last solution
favors “an isotopic degenerate gas mixture” since the massdifference is minimized. This scheme has been realized for
He, Li, and Yb, but not for K.
Here we report our study on the collisional properties of41
K. Our primary motivation was to establish 41K as a coolant, enabling the production of an isotopic Bose-Fermi mixture of 41K - 40K. Starting from a pure 41K sample, we produced a pure Bose-Einstein condensate with more than 3⫻ 105 atoms. The evaporation trajectory quite remarkably resembled that of 87Rb. We measured the efficiency of evaporative cooling of both the pure 41K sample and the pure 87Rbsample in the same environment and found that they differedby only 15%.
Potassium has another stable bosonic isotope 共 39K兲, which
is more abundant 共93.3%兲 compared with 41K 共6.7%兲. We
chose 41K because the triplet scattering length of 39K is negative, and a Feshbach resonance was needed for producing alarge condensate 关3兴. To date, most of the collisional properties of 41K have been inferred from measurements performedon other isotopes rather than by directly exploring 41K. The
current best estimate for the triplet scattering length of 41K is
a41 = 60.54共6兲a0, where a0 is the Bohr radius 关4兴. This value
was obtained by combining the results from two-photon
spectroscopy of 39K2 关4,5兴 and Feshbach spectroscopy of 39K
关6兴 and 40K 关7兴. 41K has been Bose condensed using Rb as acoolant 关8兴.
For investigating the collisional properties of 41K experimentally, we employed the standard method of producing aquantum degenerate gas in a trap, namely, laser cooling followed by evaporative cooling in a magnetic trap. The laser
cooling of 41K required extra attention, because the hyperfine
splittings of 41K were small. In particular, the hyperfine splitting in the 4 2 P3/2 state was only about 14 MHz, which wason the same order as the natural linewidth of the D2 line 共6.2
MHz兲 共Fig. 1兲. Thus, it is practically impossible to form aclosed transition since off-resonant excitation to the otherexcited states is not at all negligible. In fact, in order toincrease the capture range of the magneto-optical trap
共MOT兲, we had to detune the “cooling beam” to the red of
the whole excited state hyperfine manifold 关9兴. By preparing
almost the same amount of laser power for both “cooling”
and “repumping” transitions, we overcame these problems
and succeeded in capturing a large number of 41K atoms in
the MOT 关10兴.
Details of our experimental setup can be found elsewhere关11兴. We employed a double-MOT system. The first MOT
was loaded from the background gas, which was released
from a homemade dispenser 关12兴. The dispenser contained
98.7% 41K enriched KCl. The glass cell was maintained at
50 ° C in order to increase the loading rate of the first MOT.
A beam of atoms was pushed from the first MOT to thesecond MOT using a resonant push beam. The frequency ofthe push beam was 6 MHz red detuned from 4S1/2 F = 1 to4P3/2 F⬘ = 2 transition. We loaded 1.4⫻ 109 41K atoms in thesecond MOT in 10 s. As the typical temperature of atoms in
the 41K MOT was about 5 mK, we introduced additional
stages of spatial compression 共40 ms兲 and Doppler cooling
共12 ms兲 关13兴. The typical number, density, and temperature*inouye@sogo.t.u-tokyo.ac.jp
1050-2947/2009/79共3兲/031602共4兲

031602-1©2009 The American Physical Society

RAPID COMMUNICATIONSPHYSICAL REVIEW A 79, 031602共R兲 共2009兲KISHIMOTO et al.
F

=32P3/214MHzFDLin

=2F



=1F



=0RbK

e

2=,/27F

6=66.

.

72nMmHz

F

2254M

H=2z

S
1/2F=1FIG. 1. The energy level diagram of 41K atoms. Hyperfine splitting of the 4 2 P3/2 state is comparable to the natural linewidth of theD2 line 共6.2 MHz兲.

of the cloud following the cooling were 1.0⫻ 109, 5.1⫻ 1010 cm−3, and 100 ␮K, respectively. The obtainedphase-space density was about 1.0⫻ 10−6, which was sufficient to start evaporative cooling.
The efficiency of evaporative cooling is difficult to predict, since it is quite sensitive to small inelastic loss processes. In general, the efficiency depends sensitively on theratio between “good” 共elastic兲 and “bad” 共inelastic兲 collisions, which is typically more than a factor of a few hundred
for alkali metal atoms. Evaporative cooling of alkali metal
atoms in the stretched state is often quite efficient, since one
can expect a very tight confinement from the trap, and there
should be no scattering resonances. A prominent exception
has been 133Cs, whose evaporative cooling in the stretchedstate is hindered by the strong dipolar relaxation process induced by the second-order spin-orbit interaction 关14兴.
For loading 41K atoms into a magnetic trap, we optically
pumped the atoms into the stretched state 共兩F , mF典 = 兩2 , 2典兲.
The weak-field seeking state in the lower hyperfine manifold
共兩1 , −1典兲 was not ideal for magnetic trapping, since the maximum trap depth for the 兩1 , −1典 state was limited to around
0.8 mK due to the Paschen-Back effect. Our magnetic trapwas in the Ioffe-Pritchard configuration. In order to minimize
heating during the transfer to the magnetic trap, we loaded
atoms in a loose magnetic trap with a high bias field, andthen atoms were adiabatically compressed by increasing theradial confinement and lowering the bias field. The trapping
frequency after compression was ␯r = 325 Hz 共␯z = 15.0 Hz兲
in the radial 共axial兲 direction. The typical initial condition
following adiabatic compression was N = 8.2⫻ 108 and T= 680 ␮K, which gives the phase-space density of 4.5⫻ 10−7.
Figure 2 shows a typical evaporation trajectory for 41K
atoms in the 兩F , mF典 = 兩2 , 2典 state. We first tried to evaporatively cool 41K atoms by driving the rf transition between
Zeeman sublevels. However, we found that it was necessary
to actively remove atoms in the 兩2 , 1典 and 兩2 , 0典 states. We
believed that this purification was necessary because a large
second-order Zeeman shift increased the accumulation of atoms in the 兩2 , 1典 and 兩2 , 0典 states and also increased the en-FIG. 2. The typical evaporative cooling trajectory for 41K共squares兲 and 87Rb 共circles兲 atoms. The efficiency of evaporative
cooling ␥ ⬅ −d共ln D兲 / d共ln N兲 was 2.7 for 41K and 3.1 for 87Rb.
Here, D is the phase-space density of the gas.

ergy release from 兩2 , 1典 + 兩2 , 1典 → 兩2 , 2典 + 兩2 , 0典 collisions
关15,16兴. To obtain a pure 兩2 , 2典 sample, we first selectively
removed atoms in the 兩2 , 1典 and 兩2 , 0典 states by driving rf
transitions to the lower hyperfine manifold when the bias
field was high. Then, we evaporatively cooled the cloud bydriving the 兩2 , 2典 → 兩1 , 1典 transition, which was 254 MHz atzero magnetic field.
The efficiency of evaporative cooling is defined as␥ ⬅ −d共ln D兲 / d共ln N兲, where D is the phase-space density ofthe gas 关17兴. We observed an efficiency of ␥K = 2.7 in oursystem. This was comparable with or even better than someof the typical ␥ values for other alkali metal gases. For example, alkali metal gas ␥ values shown in “Overview ofEvaporative Cooling Experiments” in Ref. 关17兴 range from
1.5 to 2, with the prominent exception of 87Rb, which shows␥ = 3.0. In fact, by completing the rf sweep for evaporation, it
was possible to pass the phase transition for the Bose condensation of 41K and obtain a pure condensate 共Fig. 3兲. A
typical number of atoms in the pure condensate was3 ⫻ 105.
For a more direct comparison, we prepared a gas of 87Rbatoms in the 兩F , mF典 = 兩2 , 2典 state and performed rf-induced
evaporative cooling in the same magnetic trap 关18兴. The typical evaporative cooling trajectory is shown by the filled
circles in Fig. 2. The initial condition was NRb = 9.3⫻ 108 and
TRb = 1.2 mK. The number of atoms in the pure 87Rb condensate was 7 ⫻ 105. The obtained efficiency was ␥Rb = 3.1,
which was only ⬃15% higher than 41K 共Table I兲. This difference in efficiency can be partly attributed to the differencein the elastic cross section. The cross section for 87Rb is afactor of about 2.8 larger than that for 41K.
The three-body loss coefficient is important, since it practically limits the highest density one can achieve with a conTABLE I. A comparison between typical conditions before andafter the evaporative cooling of 41K and 87Rb.
Species

Initial PSD

NBEC

␥41

4.5⫻ 10−7
2.5⫻ 10−83 ⫻ 105
7 ⫻ 105

2.7
3.1

KRb

87031602-2

RAPID COMMUNICATIONSPHYSICAL REVIEW A 79, 031602共R兲 共2009兲

DIRECT EVAPORATIVE COOLING OF 41K INTO A…

Integrated OD(arb. units)(a)(b)(c)

FIG. 3. A Bose-Einstein condensate of 41K
atoms obtained by direct evaporation in a magnetic trap. Absorption images of 41K atoms after
40 ms expansion showed 共a兲 a thermal distribution at T = 750 nK, 共b兲 a bimodal distribution at
T = 580 nK, and 共c兲 an almost pure condensate of3 ⫻ 105 atoms. The evaporative cooling was performed by driving an rf transition between hyperfine levels of 41K atoms. No coolant was used in
the experiment.

2.0
1.00.0densate. By studying the decay of the condensate, we determined the upper bound for the three-body loss coefficient for41
K atoms in the 兩F , mF典 = 兩2 , 2典 state. We took a decay curvefor the number of atoms in a condensate and fitted the dataassuming exponential decay accelerated by the three-bodyloss processes. The obtained three-body loss coefficient was4共2兲 ⫻ 10−29 cm−6 s−1. We must point out here that this value
is merely an upper bound for the three-body loss, since wecannot rule out any contributions from the two-body loss
processes. This coefficient was slightly larger than thatof 23Na 共1.6⫻ 10−29 cm−6 s−1兲 关19兴 or 87Rb 共1.8
⫻ 10−29 cm−6 s−1兲 关20兴 in the upper hyperfine state.
We also performed “Feshbach spectroscopy” for 41K atoms in the F = 1 state. By determining the position of Fesh×

FIG. 4. A Feshbach resonance of 41K in the 兩F , mF典 = 兩1 , −1典
state. The number of trapped atoms after 500 ms hold time 共circles兲
showed a pronounced dip at a Feshbach resonance because of anenhanced three-body loss. The typical number density at the centerof the cloud was about 1 ⫻ 1013 cm−3. In a separate experiment, theloading rate of a crossed-beam dipole trap from a single-beam dipole trap was measured as a function of the bias magnetic field共squares兲. In order to determine the position and width of the resonance, the loss data were fitted with a Lorentzian curve centered at
the resonance 共solid line兲, and the loading rate data were fitted
assuming that the loading rate is proportional to the elastic crosssection 关21兴. The extracted center and the width of the resonancewere 51.35共10兲 G and −0.3共1兲 G, respectively, which are in good
agreement with theoretical predictions of Ref. 关6兴 共51.4 and−0.3 G, respectively兲.

bach resonances, it was possible to check the validity ofassumptions used for calculations of interatomic potential. AFeshbach resonance of 300 mG wide has been predicted for41
K atoms in the 兩F , mF典 = 兩1 , −1典 state at 51.4 G 关6兴. That
was the only s-wave Feshbach resonance predicted for 41K
atoms in the F = 1 manifold below 100 G. Here, resonances
wider than 1 mG only were considered.
For identifying the position and width of the Feshbachresonance, we performed two measurements using a crossedbeam optical dipole trap 共␭ = 820 nm兲. In the first experiment, we measured the trap loss rate as a function of the biasmagnetic field. A pronounced loss feature was observed foratoms in the 兩1 , −1典 state near 51.4 G. In the second experiment, we measured the loading rate of the crossed-beam optical dipole trap. For this, atoms were first confined in asingle-beam optical dipole trap and the second beam wasthen switched on suddenly. Atoms were accumulated to thecrossed region and the rate was determined as a function of
the bias magnetic field 共Fig. 4兲. The data were analyzed byassuming a symmetric loss feature around the resonance andproportionality between the loading rate and the elastic crosssection. The observed center and width of the Feshbach resonance were 51.35共10兲 G and −0.3共1兲 G, respectively, which
are in good agreement with theory 共51.4 and −0.3 G, respectively兲 关6兴.
In conclusion, we studied the collisional properties of 41Katoms. A Bose-Einstein condensate of 41K atoms in the兩F , mF典 = 兩2 , 2典 state was created by direct evaporation in amagnetic trap. The efficiency of evaporative cooling was ␥= 2.7, which was only ⬃15% lower than 87Rb under thesame condition. By measuring the lifetime of a condensate,
the upper bound of the three-body loss coefficient was determined to be 4共2兲 ⫻ 10−29 cm−6 s−1. A Feshbach resonance inthe 兩F , mF典 = 兩1 , −1典 state was observed at 51.35共10兲 G, whichis in good agreement with the theory. The observed highefficiency of evaporative cooling makes 41K a good candidate for a coolant. We can also expect good thermalization
between 40K and 41K, since the interspecies scattering length
is relatively large and positive 共a40–41 = 97a0兲 关4兴. This opens
up the possibility of performing Bose-Fermi mixture experiments using a mixture of 41K and 40K, which should display
negligible difference in sag due to gravity. Furthermore, 41K
can be a good substitute for 87Rb. This is especially true
when one wants to cool atomic species that have a poor
elastic cross section with 87Rb 关22兴.
K.A. acknowledges support from the Japan Society for
the Promotion of Science.

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