Table Of ContentAll-optical production of a degenerate mixture of 6Li and 40K
and creation of heteronuclear molecules
F.M.Spiegelhalder,1 A.Trenkwalder,1 D.Naik,1 G.Kerner,1 E.Wille,1,2,∗ G.Hendl,1 F.Schreck,1 andR.Grimm1,2
1Institut für Quantenoptik und Quanteninformation,
Österreichische Akademie der Wissenschaften, 6020 Innsbruck, Austria
2Institut für Experimentalphysik und Zentrum für Quantenphysik, Universität Innsbruck, 6020 Innsbruck, Austria
(Dated: 28th January 2010)
We present the essential experimental steps of our all-optical approach to prepare a double-
degenerate Fermi-Fermi mixture of 6Li and 40K atoms, which then serves as a starting point for
molecule formation. We first describe the optimized trap loading procedures, the internal-state
preparationofthesample,andthecombinedevaporativeandsympatheticcoolingprocess. Wethen
discussthepreparationofthesamplenearaninterspeciesFeshbachresonance,andwedemonstrate
the formation of heteronuclear molecules by a magnetic field ramp across the resonance.
0 PACSnumbers: 34.50.-s,67.85.Lm,05.30.Fk
1
0
2 I. INTRODUCTION
n
a
J Thegroundbreakingachievementsinexperimentswith
ultracold Fermi gases [1, 2] have opened up unpreced-
8
2 ented possibilities to study new regimes of strongly in-
teracting quantum matter. Ultracold gases represent
] well-controllable model systems for the exploration of
s
a many-bodyregimesinawaynotpossibleinconventional
g condensed-mattersystems[3]. Anewfrontierinthefield
- is currently being explored in experiments on ultracold
t
n Fermi-Fermi mixtures of 6Li and 40K atoms [4–8]. Be-
a cause of the mass imbalance and the possibility to ap-
u plyspecies-specificopticalpotentials,suchsystemsprom- Figure 1: Electronic ground state energies of 6Li and 40K
q versus magnetic field.
ise manifold intriguing applications both in many-body
.
at physics [9–18] and few-body physics [19–21].
m
To prepare degenerate Fermi gases, all-optical ap-
- proaches have proven to be simple and robust and they
related to interactions and molecule formation near in-
d
facilitate highly efficient evaporative cooling. Therefore
n terspecies Feshbach resonances. In Sec. II, we discuss
they are routinely applied in many present experiments;
o our dual-species cooling and trapping setup and the spe-
c see Ref. [1] for a review of earlier work and Refs. [22–25] cial loading procedures used for the optical traps. In
[ for more recent examples. Spin mixtures of 6Li atoms
Sec.III,wepresentanimportantpreparationstepwhere
near a broad Feshbach resonance are particularly well
1 spin relaxation in the mixture brings the K atoms into
suited for this cooling approach because of their excep-
v their lowest internal state. In Sec. IV, we describe the
3 tional collision properties, which offer extremely large combined evaporative and sympathetic cooling process.
5 cross sections for elastic collisions in combination with In Sec. V, we show how the mixture can be prepared
2 very weak inelastic decay. This favorable situation mo-
near interspecies Feshbach resonances. In Sec. VI, we fi-
5 tivates the general idea of using the strongly interacting
nallydemonstratethecreationofultracoldheteronuclear
1. 6Li gas as a cooling agent for sympathetic cooling of an- Fermi-FermimoleculesbyFeshbachassociationmethods.
0 other species. Following this idea in Ref. [7], we recently
0 demonstrated the sympathetic cooling of 40K atoms by
1 an evaporatively cooled, optically trapped spin mixture
v: of 6Li, reaching the double-degenerate regime. II. DUAL-SPECIES COOLING AND TRAPPING
i SETUP AND PROCEDURES
X InthisArticle,wefirstpresentmoredetailsonourall-
opticalapproachofpreparingadouble-degenerateFermi-
r
a Fermimixtureof6Liand40K.Wethenshownewresults Here, we outline the basic concept of our dual-species
setup (Sec. IIA), and we present the special proced-
ures applied to prepare the optically trapped mixture.
In Sec. IIB we describe how we operate a dual-species
∗Currentaddress: EuropeanSpaceAgency,Noordwijk,TheNeth- magneto-opticaltrap(MOT).InSec.IICwepresentthe
erlands optical dipole traps (ODT) used in the experiments. In
2
Sec.IIDwediscussthespecialloadingprocedureforthe
ODT.Thewholeschemeisoptimizedforalargenumber
of 6Li atoms, as this species is used as the cooling agent
for sympathetic cooling of 40K into degeneracy [7].
Figure 1 shows the atomic ground state energy struc-
ture of 6Li and 40K. We label the energy levels Li|i(cid:105) and
K|j(cid:105), counting the states with rising energy. The hyper-
fine splitting of 6Li is 228.2MHz. For 40K, the hyper-
fine structure is inverted and the splitting amounts to
1285.8MHz [26]. For the low-lying states with i≤3 and
j ≤ 10, the projection quantum numbers are given by
m =−i+3/2 and m =j−11/2.
Li K
Figure 2: Scheme of the atomic energy levels and transitions
usedtocoolandtrapLiandK.Alsoshownarethetransitions
A. Experimental setup
used for hyperfine (hf) and Zeeman pumping of K.
For the cooling and trapping of Li and K we apply
standardlasercoolingand trappingtechniques[27] com-
bining a Zeeman-slowed atomic beam and a dual-species afew109 LiatomsareaccumulatedintheMOT.Atthis
MOTforinitialcollectionofatomsinthevacuumcham- pointweincreasethemagneticfieldgradientto38G/cm,
ber. A detailed description of the experimental setup where the K MOT works optimally. In 5s, about 107 K
and the laser systems can be found in Ref. [28]. A dual- atoms are added to the trap. The K MOT is operated
speciesoven,whichisconnectedtothemainchambervia with a laser detuning of −34MHz.
a differential pumping section, delivers a well-collimated During the K loading phase we operate the Li MOT
atomic beam. We operate the oven with isotopically en- with a relatively large detuning of −31MHz in order to
riched samples containing 80% of 6Li and 7% of 40K. compensate for the effect of the higher magnetic field
The Zeeman slower can cool both species individually gradient on volume and density. This avoids increased
with the respective settings of the magnetic field gradi- losses by inelastic interspecies collisions, enabling the ef-
ents. The central element of our vacuum chamber is a ficient sequential loading of both species.
glass cell that allows for very good optical access. We In order to reduce shot-to-shot fluctuations of the
achieve excellent vacuum conditions with a pressure on number of atoms in the trap, we control the Li and K
the order of 10−11mbar. MOTloadingbymonitoringtheirfluorescenceindepend-
For both species we use diode laser systems with one ently. When the fluorescence of the Li MOT reaches
grating stabilized master oscillator in combination with its threshold value, Li loading is stopped and loading of
tapered amplifiers. The Li (K) laser system provides the K MOT is initiated. Once the K MOT fluorescence
11mW (12mW) per MOT beam and 80mW (100mW) reachesitsthreshold,theKloadingisturnedoff. Atthis
fortheZeemanslowerbeam. Figure2showsaschematic pointtheODTisrampedonin100ms,andthemagnetic
drawing of the atomic energy levels and optical trans- fields of the Zeeman slower are ramped to zero in 10ms.
itions used for cooling and trapping of Li and K. The
Li MOT laser beams contain two frequency parts tuned
to the cooling (F = 3/2 → F(cid:48) = 5/2) and repumping C. Optical dipole trapping schemes
(F = 1/2 → F(cid:48) = 3/2) transitions and having equal
power. For K the cooling (F = 9/2 → F(cid:48) = 11/2) to
For further storage and cooling of the atomic cloud,
repumper (F =7/2→F(cid:48) =9/2) ratio is three to two.
we use a trapping scheme that employs the optical di-
pole force of an intense infrared laser beam [29] and the
magneticforceinthecurvatureofthemagneticfield[30].
B. MOT loading The latter becomes important when the optical trap is
operated with low laser power. A schematic drawing of
The initial collection and cooling of 6Li and 40K is this hybrid trapping scheme is shown in Fig. 3.
achievedbyconventionallaser-coolingandtrappingtech- The principal ODT is formed by a single beam
niques. As loading of both species requires different set- (beam1)deliveredbya200-Wfiberlaserthatemitslight
tings of the Zeeman slower magnetic field, we use a se- at a central wavelength of 1070nm (IPG YLR-200SM-
quential MOT-loading scheme. The basic idea is to first LP). The beam is focused down to a waist of 38µm at
load Li and then add K in the presence of the Li MOT. the center of the MOT. During loading, the trap is op-
The Li MOT is operated with a field gradient of erated with an optical power of 96W, which results in a
26G/cm along the symmetry axis of the field coils and depthof2.6mKforLi. ForKthetrapdepthislargerby
a laser detuning of −27MHz, for both, cooling and re- a factor of 2.1 and thus amounts to about 5.5mK.
pumping transition. After a loading time of about 15s, Two sets of magnetic field coils are used in our setup
3
Figure 4: Illustration of the loading, transfer and measure-
ment timing sequence. CMOT stands for compressed MOT.
Figure 3: Schematic view of the optical trapping beam
(beam 1) and the coils for the bias field and magnetic
field curvature (shaded areas). Optionally, a second beam
(beam 2) can be used for additional axial confinement. Potassium has ten Zeeman sublevels in the lowest hy-
perfine ground state; see Fig. 1. In order to produce a
spin-polarizedsampleofKinitslowestinternalstate,we
applyanopticalpumpingschemethatnotonlytransfers
tocontrolthebiasandcurvaturefieldindependently;the the atoms to the lower hyperfine state, but also pumps
coilssetupisdescribedinmoredetailinAppendixA.For the atoms to the lowest m state.
F
small bias fields the magnetic confinement is very small
For optical pumping the quadrupole field is switched
in the axial direction; here additional axial confinement
off for 2ms and only a small guiding field is kept on.
can be obtained from another infrared beam (beam 2) Parallel to the field we shine in a σ−-polarized laser
delivered by a 5-W fiber laser with a central wavelength
beam for 10µs, which optically pumps the K atoms into
of1065nm(IPGYLP-5-LP).Thesinglebeamisfocused
state |1(cid:105). The optical pumping beam contains two fre-
to a waist of 97µm and intersects beam 1 at an angle of
quency components, one for Zeeman pumping tuned to
53◦. the(F =9/2→F(cid:48) =9/2)transitionandanotheronefor
hyperfine pumping tuned to the (F = 7/2 → F(cid:48) = 9/2)
transitionasshowninFig.2. Eachfrequencycomponent
D. Dipole trap loading has about 50 times the saturation intensity. During the
optical pumping stage, the cloud of Li atoms remains
Loading cold atoms of a single species from a MOT trapped in an optical molasses and can be recaptured
into a dipole trap is a standard procedure in many ex- without significant losses.
periments. Sub-Doppler cooling and MOT compression The high-power trapping laser induces a large light-
are common methods to enhance transfer into the op- shift on the optical cooling and pumping transitions.
ticaltrap. Theoptimizedloadingoftwospecies,however, Potassium has two optical transitions between the ex-
needsspecialprocedures. Herewedescribethesequential cited42P stateandthe52S and32D stateswith
3/2 1/2 5/2
loadingschemethatgivesusexcellentstartingconditions wavelengths of 1252nm and 1177nm, respectively. At
fortheevaporationofLiandKinacommonopticaltrap. high intensities of the ODT these two transitions shift
A schematic illustration of the loading and transfer se- the 42P level by several 100MHz. Therefore optical
3/2
quence is shown in Fig. 4. We found that an optimum pumping cannot be performed in the trap and we have
is achieved by first transferring K into the optical trap to switch it off for a short time. After the 10µs off-time
while keeping Li stored in the large-volume, low-density of the ODT needed for the optical pumping, essentially
MOT and then performing the Li transfer. all K atoms are recaptured into the ODT.
AfterswitchingontheODT,inafirststeptheKMOT At this point we have a sample of a few 104 polar-
is compressed by ramping up the magnetic field gradient ized 40K atoms in the ODT, surrounded by a magneto-
within 50ms to 96G/cm and bringing the frequencies of optically trapped cloud of 6Li atoms. We finally apply a
the K lasers closer to resonance to a detuning of a few compressed MOT stage for Li in order to efficiently load
MHzwithanintensityloweredto70%. Atthesametime this species into the dipole trap. For this, the quadru-
the detuning of the Li MOT is increased to −47MHz to pole field is ramped back up to 64G/cm and the MOT
avoid compression of the Li MOT. At this point the K lasers are operated at a very small detuning of −3MHz
MOT light is extinguished and the K atoms are confined fromresonancewhilethepowerisloweredto180µWper
in the dipole trap while Li is stored practically undis- beam for a duration of 15ms. Hyperfine pumping of Li
turbedinaMOTatareducedmagneticfieldgradientof tothelowerstateisperformedbyswitchingtherepump-
64G/cm. WiththeKMOTbeamsoff, untrappedatoms ing laser off during the last 50µs of the pulse. With this
are allowed to escape for 50ms. sequence we obtain a few 105 Li atoms in the lowest two
4
Figure 5: Magnetic field dependence of spin relaxation. The Figure6: Interpretationofthe207Gspinrelaxationfeaturein
numbers of atoms in different spin states are measured by terms of Feshbach resonances. The dots show the calculated
state-selective absorption imaging after a storage time of positionsofFeshbachresonancesbetweenLi|2(cid:105)andK|2≤j ≤
500ms in the dipole trap. The filled (open) squares give the 10(cid:105) [33]. Also plotted is the Lorentzian fit to the Li|2(cid:105) loss
Li|2(cid:105) (|1(cid:105)) atom number, the filled circles are K|1(cid:105). The two feature from Fig. 5 for comparison.
pronounced features that are visible at 40G and 207G are
fittedbyLorentzianstodeterminetheirpositionsandwidths.
|1(cid:105) (open squares) and |2(cid:105) (filled squares) as well as K in
state |1(cid:105) (filled circles). Two distinct peaks in the K|1(cid:105)
spinstatesintheODTatatemperatureofabout300µK.
atom number are visible at 40G and 207G and coincide
with dips in the Li|2(cid:105) atom number. These features are
fitted with Lorentzians to determine their positions and
III. SPIN RELAXATION
widths.
The release energy E at 40G (207G) corresponds to
r
A Li|i(cid:105)K|j(cid:105) mixture can undergo rapid decay via 2.1mK (5.8mK). For an inelastic collision between two
spin relaxation if exoergic two-body collisions can take atoms with different masses, the resulting kinetic energy
place that preserve the total projection quantum num- contributionsareinverselyproportionaltothemass. For
ber mtot =mLi+mK =−i+j−4. In such a process, the 6Li-40K combination, 87% of the released energy is
transferred to the lighter Li atoms (mass M ) and only
Li
Li|i(cid:105)+K|j(cid:105)→Li|i−1(cid:105)+K|j−1(cid:105)+E ,
r 13% to the heavier K (mass M ). A necessary condi-
K
tion for the trap depth U under which a K atom stays
K
the energy E is released. Whenever one of the species
r confined is
is in the absolute ground state, and the other one is in a
low-lying state (i = 1 and j ≤ 10 or j = 1 and i ≤ 3), M
U > Li E , (1)
spin relaxation is strongly suppressed [31]. K M +M r
K Li
Since optical Zeeman pumping does not lead to a per-
fect transfer of all K atoms into the lowest spin state, and analogously for U . The mass factor along with the
Li
we exploit spin relaxation to fully spin polarize K into abouttwotimeslargertrapdepthforKexplainswhywe
state |1(cid:105). We investigated the conditions under which observe loss of Li atoms during the spin relaxation while
spin relaxation can be used for this purpose. In these K stays trapped. Furthermore, a K atom in a Zeeman
measurements we apply only hyperfine pumping, but no level higher than |2(cid:105) will need multiple collisions with
Zeeman pumping. We start with an almost equal mix- Li|2(cid:105) in order to fully polarize. That explains why much
ture of Li in its lowest two hyperfine states, |1(cid:105) and |2(cid:105), moreLi|2(cid:105)islostthanK|1(cid:105)isgainedduringthisprocess.
trapped together with a population of K in all Zeeman Weinterpretourdatabycomparingthepositionofthe
substates j (cid:54)10. two spin relaxation features with the location of known
We investigate the magnetic field dependence of the interspecies Feshbach resonances, since we expect en-
spin relaxation by holding the sample for 500ms at a hanced inelastic loss close to a Feshbach resonance [34].
variable magnetic field. The trap is operated under the As Fig. 6 shows, there is a series of s-wave Feshbach
same conditions as during trap loading, i.e. with a trap resonances between Li|2(cid:105) and K|2 ≤ j ≤ 10(cid:105) near the
depthof2.6mKforLiand5.5mKforK.Theatomnum- 207G feature. The distribution of Feshbach resonances
bersaremeasuredusingspin-selectiveabsorptionimages, coincides with the width of the observed spin relaxation
whicharealwaystakenatabiasfieldof1190G[32]. Fig- feature. Note that the experiment is performed at relat-
ure 5 shows the resulting atom numbers of Li in states ively high temperature causing considerable broadening
5
of the Feshbach resonances. Therefore individual reson-
ances cannot be resolved.
For the feature of enhanced spin relaxation at 40G,
there are no interspecies s- or p-wave Feshbach reson-
ances and thus we cannot explain it by means of scatter-
ing resonances. However, at low magnetic fields B the
release energy E increases ∝ B, which leads to a cor-
r
responding increase in the density of continuum states
in the decay channel. We speculate that the correspond-
ing threshold behavior may explain the increase at lower
fields. Then, alreadyat afew ten Gaussthe nuclear spin
of Li decouples from the electron spin, which may lead
to a reduction of loss.
In a second set of experiments we investigate the time
scale on which spin relaxation occurs at the two relevant
magnetic fields 40G and 207G. For both fields we find
Figure7: LiandKatomnumbersafterevaporationperformed
thatthetimescalefortheprocessis150msandasteady
atvariablemagneticfield. Opensquaresshowthenumberof
state is essentially reached after 500ms.
Li atoms per state, filled circles show the K atom number.
Spinrelaxationisaveryefficientprocessthatallowsus
to fully polarize our K sample without loss of K atoms.
Since initially much more Li atoms are present in the
trap,theLilossisaminorproblem. Theresultingimbal- Before starting the evaporation process, we carefully
ance of the two Li spin states can be removed by driving balance the population of the two spin states Li|1(cid:105) and
radio-frequency (rf) transitions between the two states. Li|2(cid:105). This is particularly important in cases when the
spin relaxation stage has caused considerable losses in
|2(cid:105). The spin balance is accomplished by driving the rf
IV. EVAPORATION AND SYMPATHETIC transition|1(cid:105)↔|2(cid:105)usingaseriesof20rampsover10kHz
COOLING withadurationof50mseach[36]. Thisprocedureisper-
formedat1190G,wheretheLispinmixtureisoutsideof
A spin-mixture of Li|1(cid:105) and Li|2(cid:105) near the broad 834- the strongly interacting regime and interaction-induced
G Feshbach resonance facilitates highly efficient evapor- rf line shifts are relatively small. Note that the evapora-
ative cooling, as it is well known in the field of strongly tion process is much more sensitive to a spin imbalance
interactingFermigases[1,35]. Theefficiencyofthecool- on the BCS side of the resonance than on the BEC side
ing process is due to the very favorable combination of a of the resonance. The reason is that in the latter case
largeelasticscatteringcrosssectionwithverylowlosses. the molecule formation can lead to a self-balancing of
In Ref. [7] we have already demonstrated the possibil- the spin population during evaporation [37].
ity of using the 6Li spin-mixture as an efficient cooling Evaporation of the mixture is performed in the prin-
agent to sympathetically cool another species. In this cipal ODT, beam 1. The evaporation ramp consists of
way we have demonstrated the attainment of a double- twostages,technicallyimplementedindifferentways. In
degenerateFermi-Fermimixtureof6Liand40K.Herewe the first stage, we use a digital input of the laser control
present additional information on the experimental pro- unittoreducetheODTpowertoabout15W.Thisramp
cedures, and the combined evaporative and sympathetic is linear and takes 1.5s. In a second stage, an acousto-
cooling process. optical modulator (AOM) is used to decrease the power
Let us first summarize our main findings of Ref. [7] on in a nearly exponential ramp. The evaporation ramp is
thecollisionalstabilityofthethree-componentFermigas typicallystoppedafter6swhenthelaserpoweris60mW.
ofLiinthelowesttwospinstatestogetherwithKinthe Atthispointthetrapfrequenciesintheradialdirections
lowestspinstate. Interspeciescollisionallossisnegligible are 394Hz for Li and 219Hz for K. In the axial direc-
on the BCS side of the broad Li resonance (B > 900G) tion the trap frequency is dominated by the magnetic
and quite weak even exactly on resonance (834G). Sub- confinement and is 27Hz for Li and 11Hz for K.
stantial loss, however, occurs on the BEC side of the The experimental data in Fig. 7 show the number of
resonance in a range between about 650 and 800G. The atomsremainingafterthecompleteevaporationrampfor
latter is a result of inelastic collisions between K atoms amagneticfieldvariedacrossthefulltuningrangeoffered
with weakly bound Li dimers. Consequently, the com- by the Li Feshbach resonance. The data correspond to
binedevaporationandsympatheticcoolingprocessneeds the observations of Ref. [7], showing pronounced loss on
tobeperformedontheBCSsideoftheLiresonance. For the BEC side of the Li Feshbach resonance and large
our experiments we choose a field of 1190G. Here the Li stabilityonitsBCSside. Inthehigh-fieldregionbetween
scattering length is −2900 a and the interspecies scat- 950G and 1250G, where the Li scattering length varies
0
tering length is about +60 a . between −5300 a and −2800 a , the magnetic field has
0 0 0
6
Figure 8: Evolution of the atom numbers during the second
Figure 9: Temperature evolution during the last part of the
stage of evaporation. The Li atom number per state is plot-
evaporation. Open squares (filled circles) indicate the Li (K)
tedusingsquareswhilecirclesrepresenttheKatomnumber.
temperature. Alsoplottedarecurvesthatrepresenttheevol-
Filled (open) symbols represent data from measurements us-
ution of the Fermi temperature for Li (dotted line) and K
ing fluorescence (absorption) imaging.
(dashed line).
no significant influence.
adjust the amount of K with which evaporation starts
In order to analyze the cooling process, we stop the
such that at the end of evaporation we have about ten
evaporation ramp at a variable endpoint and measure
times more atoms of Li in each spin state than atoms
the number of Li and K atoms. The measurements are
in K|1(cid:105). In this situation K can be used as a probe for
performed by recapture into the MOT and subsequent
the Li mixture. One example of this idea has already
detectionofthefluorescenceintensityor,atlowerpower,
been presented in Ref. [7]. The measurement of the K
by absorption imaging after release from the ODT into
temperaturewasusedinordertogetafirmupperbound
free space. Figure 8 shows that the Li atom number
for the temperature of the Li bath even in the strongly
steadily decreases while the K cooling proceeds essen-
interactingregime. Thismethodwasrecentlyadoptedto
tially without losses. Note that the trap depth for K is
using 7Li as a probe in Ref. [38].
a factor of 2.1 larger than for Li. This changes at about
100mW, as the gravitational sag of K reduces the trap
depth and we begin to see significant loss of K when fur-
ther lowering the power of the ODT. V. PREPARATION NEAR INTERSPECIES
FESHBACH RESONANCES
Figure 9 shows the temperature evolution of Li and K
in the last part of the evaporation ramp. We extract the
Li temperature by fitting a Thomas-Fermi profile to ab- The 6Li-40K mixture offers several s-wave Feshbach
sorption images of the atomic cloud after time-of-flight. resonances in the range between 150G and 200G [5, 8].
The K temperature is determined using a simple Gauss- All of them tend to be quite narrow, which is a com-
ianfit, asthesamplehereremainsinthenon-degenerate mon situation in cases of moderate values of the back-
regime. Throughout the whole evaporation the temper- ground scattering length [34]. The broadest resonances
ature of K lags behind the temperature of Li. were found for the channels Li|1(cid:105)K|7...10(cid:105) with widths
Attheendofanextendedevaporationramp,atatrap between1Gand2G[33]. Theenergeticallylowestchan-
power of 40mW, the radial trap frequencies for Li (K) nel Li|1(cid:105)K|1(cid:105), which is of particular interest because of
amounts to 320Hz (160Hz). In the axial direction the theenergeticsuppressionofanytwo-bodydecay,features
trap frequency is dominated by the magnetic confine- two resonances with calculated widths around 100mG.
ment and is 27Hz for Li and 11Hz for K. The Fermi In this work, we focus on the resonance near 168G. We
temperatures are calculated to be TLi = 390nK for Li showhowadegeneratetwo-componentLi-Kmixturecan
F
and TK = 135nK for K. Following the scheme we have be prepared near this resonance after sympathetic cool-
F
presented in Ref. [7], we continue cooling of the mixture ing at high magnetic field and present measurements on
by holding it in this shallow trap for 5s. This way we inelastic and elastic properties of the mixture.
achieveafinalKtemperatureof50nKcorrespondingtoa When ramping down the magnetic field from its evap-
degeneracyofTK/TK ≈0.6whileLiisdeeplydegenerate oration setting (1190G) to the interspecies resonances,
F
with TLi/TLi <0.2. one has to cross the region of the broad 834-G Li|1(cid:105)|2(cid:105)
F
Since Li is the coolant of our evaporation scheme, we Feshbach resonance. If this spin channel is populated,
7
Figure 10: Preparation scheme of a two-component mixture
near interspecies Feshbach resonances. The horizontal lines
indicate four different Li-K spin channels being of partic-
ular relevance for our experiments. The numbers give the
magnetic field values in Gauss. Filled (open) circles repres- Figure 11: Loss measurement and evaporative cooling near
ent s-wave (p-wave) interspecies resonances. The Li|1(cid:105) and an interspecies Feshbach resonance. Plotted is the K atom
Li|2(cid:105) intraspecies p-wave resonances (not shown) are located numbernormalizedtothebackgroundvalueofthelossmeas-
at 160G and 215G respectively [39, 40] and nearly coincide urement away from resonance. The open squares show a set
with interspecies resonances. For the s-wave resonances, the oflossmeasurementsholdingthesampleatvariablemagnetic
relativewidthsareindicatedbythesizeofthesymbols. State field for 5s. The solid line is a Gaussian fit to the data. The
transfer, indicated by vertical dashed lines, is achieved by rf filledcirclesshowacorrespondingsetofmeasurementswhere
transitions. After the evaporation at 1190G, the Li|2(cid:105) pop- evaporation was performed by lowering the optical power to
ulation is removed by a resonant laser pulse, as indicated by one third of its initial value within 3s.
the x.
to ∼200G, thus converting the sample into a Li|2(cid:105)K|1(cid:105)
the formation of 6Li dimers inevitably leads to strong mixture. Thiscanbedonewithveryhighefficiencyusing
losses from the atomic sample. To avoid this problem, rftransfermethods. Thentherampiscontinueddownto
we remove one of the Li spin components by the light a value close to 155G and three subsequent rf transfers
pressure of a resonant laser pulse [41] before starting the are applied to convert the population from Li|2(cid:105)K|1(cid:105) to
ramp. Note that already the momentum kick from one Li|1(cid:105)K|3(cid:105). This procedure avoids all detrimental reson-
photon is sufficient to push a Li atom out of the shal- ances. Analogous schemes can be applied to reach any
lowtrapafterevaporation. Thepulseisappliedfor10µs other desired resonance.
with a few times the saturation intensity. We find that In a set of experiments performed at the 168-G in-
at 1190G the interaction between the two spin compon- terspecies Feshbach resonance in the Li|1(cid:105)K|1(cid:105) channel,
entsisweakenoughtoavoidanysignificanteffectonthe we investigate aspects of inelastic and elastic collisions.
population in the remaining spin state. In this way, we Initially, we prepare about 2 × 105 Li atoms together
reduce the three-component Fermi-Fermi gas to a two- with about 1.4×104 K atoms at a temperature of about
component mixture. 300nK. The power of the trapping beam (beam 1) is
Toapproachaspecificinterspeciesresonance,itisalso 170mW,correspondingtoaradial(axial)trapfrequency
importanttoavoidtheeffectofotherinter-andintraspe- of 660Hz (14Hz) for Li. For K the trap frequencies are
cies resonances. We find that our ramps are fast enough 375Hz and 6Hz respectively. The peak densities of the
(rampspeedupto20G/ms)tocrossallthep-wavereson- clouds are nLi ≈2×1012cm−3 and nK ≈4×1011cm−3
0 0
anceswithoutanyproblem. However,wefindsubstantial and the degeneracies are TLi/TLi ≈ 0.3 and TK/TK ≈
F F
losses on the interspecies s-wave resonances, even on the 1.5. Note that these conditions are deliberately pre-
weaker ones. This already points to efficient molecule pared with an incomplete evaporation ramp, stopped
association [34] as we will discuss in Sec. VI. at 170mW instead of the usual final power of 60mW
Figure 10 illustrates the procedures applied to reach (Sec. IV).
specific interspecies Feshbach resonances. While it is In the first series of measurements, we ramp the mag-
straightforward to reach the 168-G resonance in the neticfieldtoavariablevalueandstudythelossofatoms
Li|1(cid:105)K|1(cid:105) channel by a fast ramp after removal of the after a hold time of 5s. For detection, the remaining
state Li|2(cid:105), other resonances require more elaborate atomsarerecapturedintothetwo-speciesMOTandtheir
methods. Asanexample,wediscussthe155-Gresonance fluorescence is recorded. The K atom number, normal-
intheLi|1(cid:105)K|3(cid:105)channel,whichisofinterestasoneofthe ized to the background value away from resonance, is
broadest resonances (width between 0.5 and 1G) in the plotted in Fig. 11 (open squares). We observe a loss
low-lyingspinchannels. Hereapossiblewayistotransfer feature centered at 168.22G. Ramping across the Fesh-
theLiatomsfrom|1(cid:105)to|2(cid:105)afterrampingdownthefield bach resonance does not lead to loss, indicating that the
8
ing one second and the sample is left to thermalize for
anothersecond. ThenLi|2(cid:105)isremovedbyashortpulseof
resonant light. At this point the sample has a temperat-
ureof∼200nKandcontainsabout1.3×104 Katomsand
8×104 Li atoms. With the trap oscillation frequencies
of axially 90Hz (50Hz), and radially 390Hz (210Hz) for
Li(K),wecalculateFermitemperaturesofabout900nK
for Li and 270nK for K, corresponding to TLi/TLi ≈0.2
F
and TK/TK ≈ 0.7. The K cloud has less than half the
F
size of the Li cloud. For both components the density in
the center of the trap is about 2×1012cm−3.
Underthesedeepcoolingconditions,wedetectthefast
atom loss as a function of the magnetic field. In order
to approach the magnetic field value of interest without
forming molecules, K is transferred into state |2(cid:105) by an
Figure12: ScanoftheLi-KFeshbachresonanceat168Gwith
rf π-pulse prior to the magnetic field ramp. At the final
10msholdtime. The1/e-widthofthelossfeature(indicated
field, K is transferred back to state |1(cid:105) by another π-
bythedottedlines)isdeterminedbyfittingaGaussiantothe
pulse. After a hold time of 10ms, the remaining K atom
experimental data and amounts to 33mG.
number is measured. Figure 12 shows the corresponding
data. We observe maximum loss of atoms centered at
168.217G, with an estimated calibration uncertainty of
10mG.
phase-space density used in these experiments is insuffi-
cientforadiabaticmoleculecreationduringthemagnetic
field ramp.
VI. CREATION OF ULTRACOLD
In the second series of measurements, we investigate
FERMI-FERMI MOLECULES
whether an effect of enhanced elastic collisions can be
observedinevaporativecoolingneartheinterspeciesres-
Here, we describe our basic methodology for molecule
onance. Here we lower the power of beam 1 to 55mW
creation and detection (Sec. VIA), present experimental
within3s,whichresultsinaradial(axial)trapfrequency
results (Sec. VIB) and discuss our findings (Sec. VIC).
of 375Hz (14Hz) for Li and 210Hz (5Hz) for K. As be-
fore,thenumberofremainingatomsisdeterminedbyre-
captureintoaMOTandfluorescencedetection. Thecor-
A. Creation and detection schemes
respondingdata,plottedinFig.11(filledcircles),showa
pronounced asymmetry and thus a different behavior on
thetwosidesoftheFeshbachresonance. Onitshigh-field The creation of the molecules starts with a Li|1(cid:105)K|1(cid:105)
side, corresponding to large negative scattering length, mixture under the same conditions as prepared for
we observe a maximum in the recaptured atom number Fig. 12. The molecules are associated by a magnetic
at 168.26G. This signifies evaporative cooling with an
enhanced elastic scattering cross section as compared to
the background value. At lower fields, however, loss en-
hanced by the resonance dominates and leads to a min-
imuminatomnumberat168.18G.Thelosspropertieson
thetwosidesoftheFeshbachresonancearethusfoundto
be strikingly different with more favorable conditions on
the side of negative scattering length, where no weakly
bound molecular state exists.
Todeterminetheresonancepositionmoreprecisely,we
prepare a sample with higher phase-space density than
used for the previous sets of experiments. Now both
beamsoftheODTareused. Beam2isheldataconstant
power of 250mW, corresponding to a trap depth of 1µK
forLiand2.1µKforK.Itspurposeistoaddconfinement
along the weak direction of beam 1 at the very end of Figure13: Moleculesareassociatedbyamagneticfieldramp,
evaporation. Evaporationat1190Gandtheramptolow indicated by the arrow labeled ∆B, across a Feshbach reson-
magnetic field proceed as described above. For further ance. Transitionstohigheratomicspinstatesaredrivenbyrf
cooling, we create a balanced mixture of Li|1(cid:105) and |2(cid:105) at pulses. Atoms bound in a molecule are not affected because
170.5G,usingasequenceofrfsweeps. Afterwards,beam of the binding energy Eb.
1isrampedfromaLitrapdepthof1.9µKto1.5µKdur-
9
Figure15: LowerboundofmoleculefractionF independence
of the final magnetic field value of the molecule association
magnetic field ramp. Molecules are detected for fields below
168.218G. This field corresponds to the center of the loss
featureshowninFig.12,whichismarkedbytheverticalsolid
linehere. Thedashedverticallinesmarkthe1/e-widthofthe
lossfeatureandthehorizontaldashedlinemarksasystematic
offset.
Theresultingpicturesareshownintheleft-handcolumn
of Fig. 14 [43]. A second pair of images, this time of the
unpaired atoms, which have been transferred to the |2(cid:105)
states, is taken 1ms later and shown in the right-hand
Figure14: AbsorptionimagesofLiKFeshbachmoleculesand column of Fig. 14 [44].
unpaired atoms taken at a magnetic field of 168.19G. The
Absorption imaging of the molecules gives lower
upper row shows images of molecules and atoms taken with
boundaries NK and NLi for the real molecule num-
lightresonanttotheKtransitionwhereasthelowerrowshows mol mol
bers NK and NLi since the absorption cross section
images taken with light resonant to the Li transition. The mol mol
of atoms bound in LiK molecules is somewhat smaller
leftcolumnshowsmoleculesimagedafter0.4mstime-of-flight
(TOF) expansion and the right column unpaired atoms im- than the one of unpaired atoms. Close to the Feshbach
aged 1ms later. resonance the cross section is similar to the one of free
atoms and decreases for increasing binding energy. The
numberofremainingunpairedatomsNK andNLi can
free free
be obtained from the second pair of absorption images.
field ramp from 170.5G to 168.19G within 10ms, cross- From K images (top row of Fig. 14) we obtain NK =
mol
ingtheLi|1(cid:105)K|1(cid:105)168-GFeshbachresonance(rampspeed 3×103 and NK =9×103 and from Li images (bottom
free
0.23G/ms). Instantly after the ramp, the sample is re- row of Fig. 14) NLi =4×103 and NLi =8×105. The
mol free
leased from the ODT. smallcloudofKisimmersedinamuchlargerdegenerate
Selectiveimagingofmoleculesandremainingunpaired Li bath. The molecule conversion efficiency is therefore
atoms is possible after transfer of the unpaired atoms to bestcharacterizedbytheKconversionefficiency. Alower
the states Li|2(cid:105) and K|2(cid:105). An rf π-pulse, tuned to the bound for the molecule fraction can be determined from
atomic |1(cid:105)→|2(cid:105) transition, is used for this purpose [42]; K absorption images as F =NK /(NK +NK ). From
mol mol free
seeFig.13. AtomsboundinLiKmoleculesarenottrans- the images shown in Fig. 14 we obtain F =0.25.
ferredtostate|2(cid:105)ifthemolecularbindingenergydetunes
thetransitionfarenoughfromthefreeatomtransitionto
be outside of the Fourier spectrum of the rf pulse. This B. Experimental results
condition requires a detuning of 23kHz for K, which is
reached 9mG below resonance according to the relative We now examine the molecule creation process and
magnetic moment of the molecular state [33]. The rf properties of the molecules in more detail. First, we de-
pulses are applied one after the other during the 0.4ms termine the magnetic field value of the onset of molecule
free expansion of the sample. creation. For this, we perform experiments as the one
State-selective absorption images are taken simultan- justdescribed, butwevarytheendpointofthemagnetic
eously on cycling transitions starting from the Li|1(cid:105) and field ramp, keeping the ramp duration fixed. The fre-
K|1(cid:105) states. This way, molecules are imaged directly. quency of the rf pulse for the separation of free K atoms
10
Figure 16: Decay of LiK molecules at 168.204G. Plotted is
thenumberofmoleculesNK independenceontheholdtime
mol
after the fast magnetic field ramp. The solid line is an expo-
nential fit to the data, yielding a lifetime of 1.7ms.
Figure 17: Comparison of the free expansion of LiK Fesh-
bach molecules (circles: detection of the bound K atoms, tri-
and LiK molecules and the probe beam frequencies are angles: detection of the bound Li atoms) and unpaired Li
√
adapted accordingly. The Li rf pulse was not used in atoms(opensquares)at168.196G.Shownistheradial1/ e-
these experiments. width of Gaussian fits to integrated density profiles.
Figure15showsthelowerboundforthemoleculefrac-
tion F. Imperfect rf pulses lead to a 3% systematic
offset in the data, indicated by the horizontal dashed
line [45]. It is found that the detected molecule frac- conversion efficiency is also determined to be 40%. The
tion depends strongly on the endpoint of the magnetic assumption that no molecules are lost is well justified
field ramp. No molecules are detected down to a final since the time spent in the Feshbach resonance region
field of 168.217G. Only 13mG lower the maximum mo- during the magnetic field ramp to 168.19G (120µs) is
lecule fraction is observed. This magnetic field range short compared to the lifetime of the molecules.
corresponds well to the required detuning from reson- The lifetime of the LiK molecules is determined by
ance for our atom-molecule separation method to work, holding the sample after molecule creation for a varying
as discussed above. For lower fields the molecular signal timeintheODTataconstantmagneticfieldof168.204G
drops again, first steeply down to about 168.19G and and measuring the molecule number afterwards. A fit
then much slower. At about 167.5G (outside the range to the decay of the molecule number gives a lifetime of
of the plotted data) it becomes indiscernible from the 1.7ms; see Fig. 16. This lifetime does not change if the
background noise. The dependence of the detected mo- remaining free Li atoms are removed just after molecule
lecule fraction on the field may have several reasons. It creation by a resonant flash of light, indicating that the
mightbecausedbythechangeinabsorptioncrosssection dominantlossmechanismdoesnotinvolvefreeLiatoms.
of the molecules with the magnetic field. The slow de- WedidnotinvestigatetheeffectofunpairedKatomson
creaseawayfromresonancecomesfromlossofmolecules the molecule lifetime.
as more time is spent between molecule association and A striking manifestation of molecule formation can be
detection. observed by comparing the expansion behavior of clouds
Within the measurement precision of a few mG the of LiK molecules with the one of clouds of unpaired Li
onset of molecule detection coincides with the center of atoms in imaging with Li light. For this comparison,
the loss feature from Fig. 12, marked by the solid ver- we record the expansion of the molecules and the re-
tical line in Fig. 15. This observation is in accordance maining unpaired Li atoms after a molecule association
with the standard picture of molecule formation close to magnetic field ramp to 168.196G; see Fig. 17. We find
a Feshbach resonance [46]. the average expansion velocity of molecules to be slower
ThemaximumKmoleculeconversionefficiencyextrac- by a factor of 3.3, as determined by fits to the expan-
ted from this data is reached at 168.204G and amounts sion. We interpret this difference mainly as a result of
to about 40%. A different method to determine the K the higher mass of the molecules compared to unpaired
molecule conversion efficiency is to examine the number Li atoms. It corresponds well to the expected velocity
(cid:112) (cid:112)
offreeKatomsatamagneticfieldjustabovetheonsetof ratio of v /v = M /M = 46/6 = 2.8 in the
Li LiK LiK Li
molecule production and just below 168.19G. Assuming approximation of thermal clouds of equal temperature.
all missing atoms have formed molecules, the molecule This observation tells us that Li atoms that remain in
