Degenerate Bose-Bose mixture in a three-dimensional optical lattice

0.46 MB·English

by  J. Catani

Degenerate Bose-Bose mixture in a three-dimensional optical lattice
J. Catani, L. De Sarlo, G. Barontini, F. Minardi1,2 and M. Inguscio1,2
LENS - European Laboratory for Non-Linear Spectroscopy and Dipartimento di Fisica,
Universit`a di Firenze, via N. Carrara 1, I-50019 Sesto Fiorentino - Firenze, Italy
1CNR-INFM, via G. Sansone 1, I-50019 Sesto Fiorentino - Firenze, Italy
2INFN, via G. Sansone 1, I-50019 Sesto Fiorentino - Firenze, Italy
(Dated: February1, 2008)
We produce a heteronuclear quantum degenerate mixture of two bosonic species, 87Rb and 41K,
in a three-dimensional optical lattice. On raising the lattice barriers, we observe the disapperance
8 oftheinferencepatternoftheheavier87Rb,shiftingtowardshallowerlatticedepthsinthepresence
0 of a minor fraction of 41K. This effect is sizable and requires only a marginal overlap between the
0 two species. We compare our results with similar findings reported for Fermi-Bose mixtures and
2
discuss the interpretation scenarios proposed to date, arguing that the explanation may be linked

n totheincreased effective mass dueto theinterspecies interactions.
a
J PACSnumbers: 03.75.-b,05.30.Jp,73.43.Nq

9
2
Quantum degenerate gases are formidable systems to Surprisingly enough, we find that the effect is sizable

] shine light on fundamental quantum phenomena occur- (see Fig. 1), not only for small fractions of the minority
r
e ring at extremely low temperatures, such as supercon- species, but even for marginal spatial overlap between
h ductivity and superfluidity. In combination with opti- the two.
t
o cal lattices and scattering resonances, degenerate gases Theexperimentalsetuphasbeendescribedearlier[11,
. give rise to strongly correlated systems, enriching even 12]. Here we briefly outline the production of a dou-
t
a further the breadth of phenomena that can be directly ble Bose-Einstein condensate (BEC), first demonstrated
m
probed. Indeed, the pioneering experiment on the su- in [13]. We capture 2 108 87Rb atoms and a variable
- perfluid to Mott-insulator transition [1] has shown how number of 41K atoms i×n the stretched F = 2,m = 2
d | F i
n physical models long studied in the field of condensed states in a Ioffe millimetric trap (MMT) [12, 14] and we
o matter can be realized almost ideally. With two differ- start evaporationby lowering the MMT depth from 5 to
c ent atomic species, the wealth of quantum phases grows 3.5 mK, with final harmonic frequencies (ω ,ω ,ω ) =
x y z
[ to a daunting complexity [2], only marginally explored 2π (16.8,202,202) Hz [15]. We then cool 87Rb only
2 by experiments. Actually, experiments with heteronu- by ×microwave evaporation, while 41K is cooled sympa-
v clear mixtures in three-dimensional (3D) optical lattice thetically. A single sideband, 10 dB below the carrier,
1 have been performed very recently only for Fermi-Bose selectively removes 87Rb atoms in the F = 2,m = 1
8 systems [3, 4], while Fermi-Fermi and Bose-Bose mix- state,whichwouldquicklydepletethe4|1KsampleF. BECi
7
2 tures are yet uncharted territory. The importance of isachievedfirstfor41Kat250nKandthenfor87Rb: con-
. mixtures in optical lattices is hardly overstated: asso- densates contain typically 4(2) 104 87Rb(41K) atoms,
6 ×
ciation of dipolar molecules [5], mapping of spin arrays with Thomas-Fermiradii of 2.4(2.2)µm and peak densi-
0
7 [6], schemes for quantum calculation [7], and implemen-
0 tationofdisorder[8]representonlyafew majorresearch
: lines that potentially will greatly benefit from such sys-
v
i tems. Inparticular,Bose-Bosemixturesseemwellsuited
X
forallthesepurposes,providedthatcollisionallossesare
r adequately suppressed.
a
This work reports the first realization of a degenerate
Bose-Bose heteronuclear mixture in a 3D optical lattice.
Exploiting the large mass difference, we investigate the
regime where one species lies well in the superfluid do-
main, while the other exhibits the disappearence of the
interference pattern usually associated with the transi-
tionfromasuperfluidtoaMottinsulator. Wefocusonly
on the interference pattern and do not probe the shell FIG. 1: (Color online): Interference pattern of 87Rb for s =
structure characteristic of a Mott-insulator for trapped 6, 11, 16 (left to right). Upper row: 87Rb only; lower row:
systems [9, 10]. We observe that the presence of the 87Rbmixedwith41K(notshown). Eachpanelrepresentsthe
superfluid enhances the loss of phase coherence of the column density overan area 175µm ×135µm.
second species occurring for increasing lattice strengths.
2
ties of 1.4(0.9) 1014 cm−3.
×
Inthepresenceof2 103 41Katomsclearlycondensed
×
(inverted ellipticity after expansion), since no thermal
cloud can be detected, our sensitivity places an upper
bound of 50% on the thermal fraction of this species:
this sets an upper bound on the temperature of 73 nK.
Since the evaporation is stopped at the same level also
in the absence of 41K, the same temperature boundary
applies also for 87Rb alone. At 73 nK, the peak density
of the 41K thermal atoms is lower than 1/60 that of the
condensate. For this reason, we will throughout neglect
the 41K thermal fraction in the following.
The clouds are only partially overlapped: due to dif-
ferential gravity sag, the 87Rb condensate lies 3.2 µm
below 41K. Also, numerical integration of the 3D Gross-
Pitaevskii equation (GPE) shows that both density dis-
tributionsaredeformedandalmostcompletelyphasesep-
arated, due to the strong K-Rb repulsion [16]. Indeed,
the interspecies scattering length aK−Rb = 163a0 [17] is
much larger than both aRb = 99a0 [18] and aK = 65a0
[19], with a0 the Bohr radius.
Once double BEC is achieved, we ramp three retrore-
FIG. 2: (Color online) Visibility and width of the central
flected optical lattice beams at λL = 1064 nm, with peak of the 87Rb interference pattern, for partial (a,c) and
frequencies differing by tens of megahertz, propagating zero(b,d)overlapwiththe41Kcondensate. Ineachpanelwe
along the x,y, and z axes and focusing at the center of comparedataandfit(dashedlines)with41Katoms(red)and
theMMTwithwaistsequalto(90,180,160)µm. Thelat- without(black),i.e. with NK =2(1)×103 and 0. Theinsets
tice strengthis calibratedby means ofBraggoscillations show: howvisibilityof87Rbisextractedfrom images(e)and
and Raman-Nath diffraction [20], yielding a systematic theinterference pattern of 41K visible for s=20 (f).
uncertaintyof10%,whichmustbe addedtothe statistic
uncertainties quoted hereafter. We choose the duration
and time constant of the exponential turn-on profile, 50
Fig. 1, augment those of similar experiments carriedout
and 20 ms, respectively, by maximizing the visibility of
the87Rbinterferencepattern. Wewaitfor5mswiththe with the mutually attractive 40K-87Rb Fermi-Bose mix-
ture [3, 4].
optical lattice at full power and abruptly switch off the
latticebeams(<1µs)andtheMMTcurrent( 100µs). To quantify the shift of the transition point, we plot
We image both species after a typical time o∼f flight of the visibility and the width of the central peak versus
15 to 20 ms with resonant absorption: the interference the lattice strength in units of the 87Rb recoil energy
peaks of 87Rb are progressively smeared as the lattice s [21]. We compare data taken with 41K and when
strength is ramped at higher values. 41K was not even loaded in the MMT (Fig. 2). We
fit the visibility with a phenomenologicalFermi function
We measure the width of the central peak and the
visibility v of the interference pattern, defined as [22] v =v0/[1+exp(α(s sc))],whichhastheexpectedflatbe-
−
haviorbelowthecriticallatticestrengths anddecreases
v =(N N )/(N +N ), where N and N denote, re- c
p d p d p d
− exponentially for s s . From the fit, we find that, for
spectively, the summed weights of the first lateral peaks c
and of equivalent regions at the same distance from the NRb =3 104, the≫critical s value is sc =16.8 0.4 for
central peak along the diagonals [see Fig. 2(e)]. At 87Rbonly×,whilesc =12.4 0.3withNK =(2 ±1) 103.
our lattice wavelength, the optical potential is the same Using the formula η =±0.696s−0.1exp(2.07√±s)(×a/λL)
within 10% for 87Rb and 41K. However,due to the their [22], we relate s with the ratio of interaction to tunnel-
largermassandscatteringlength,87Rbatomstunnelless ing matrix elements, η =U/(6J), in terms of the lattice
and repel each other more: the combined effect is that wavelength λL and the scattering length a. From the
87Rb loses phase coherence at lower lattice power than fit values, we derive both the critical value ηc and the
41K. exponents of the visibility decay for s sc, v η−ν:
Themainexperimentalresultofthisworkistheobser- without 41K we find ηc = 12.3+−64..23 and ≫ν = 2.3+−00∼..64, but
vation that the lattice strength at which the 87Rb inter- with 41K we have ηc = 3.9+−11..62 and ν = 3.4+−00..85 (error
ference pattern starts washing out is greatly shifted not bars are dominated by the calibrationuncertainty of the
only by a minor admixture of 41K atoms, but also with lattice strength).
a marginal spatial overlap. These findings, displayed in The width of the central peak measures the inverse
3
correlation length: it signals the transition with a stark 50ms alsointhe presenceof41K (see Fig.4) andindeed
climb at s 10 in the presence of 41K and s 14 in the visibility difference is roughly constant at 15%. We
≃ ≃
the absence thereof [see Figs. 2(c) and 2(d)]. After the conclude that, while in principle one could expect that
transition, the width increase is steeper in the presence inthe presence of41K the lattice rampshouldbe slower,
of 41K even for null overlap (Fig. 2(d)): this behavior there is no evidence that this is indeed the case, at least
is unexpected and so far unexplained. While the transi- as far as the loss of visibility is concerned. Moreover,
tion points detected by the width and the visibility are we do not observe a significant change in the number of
different, the shift is the same, ∆s 4. atoms with the duration of the ramp; hence three-body
c
≃
Such a shift is surprising, given the little overlap be- losses play a negligible role, consistently with the small
tween the two species. Numerical integration of the 3D overlapof the two clouds.
GPE with an s = 11 vertical lattice shows that the As mentioned, our experimental findings extend those
overlap is restricted to one lattice site out of 11 (see of Refs. [3, 4] to bosonic impurities and help to shine
Fig. 3). Generalizing to a 3D lattice, we expect that somelightonthe inducedlossofcoherence,whoseorigin
approximatelyonly10%ofsitesaresimultaneouslyfilled has so far remained unclear, if not controversial. Gu¨nter
with both 87Rb and 41K atoms. In order to check that et al. report that the transition point, extracted from
the shift is genuinely related to the interspecies interac- the visibility data with a fitting procedure equivalent to
tion, we repeat the experiment with larger differential ours and expressed in terms of η , shifts from 6.5 to 2.5
c
sag of the two samples. Once the double-species BEC for an 8% admixture. Both values are lower than ours.
is achieved, we relax the MMT harmonic frequencies to Ospelkauset al. insteadquantifytheshiftintermsofs ,
c
~ω =2π (9.2,108,108)Hz, thereby increasingthe verti- as we do, and fit the visibility with the Fermi function.
×
calseparationto11µm,sothattheoverlapistotallyneg- The reported shift ∆s = 3(1.5) for a 7 % fraction of
c
ligible even for any undetected 41K thermal cloud (1/e2 impurities agrees with our result. With the same data,
radius = 7.7 µm). Figures 2(b) and 2(d) show that, al- but measured from the width of the central peak, the
though the visibility is slightly lower in the presence of transitionpointshiftsfromη =9to4.5[3]andby∆s =
c c
41K, the transition point is the same within our error 1(1) [4].
bars: sc =15.8(0.5). Several different scenarios have been proposed to ex-
Asafurthertest,weinvestigatetheeffectofthelattice plain the impurities-induced loss of coherence. We dis-
turn-onramps. Asmentioned,for87Rbalone,thevisibil- cussheretheimpactofourexperimentonthesescenarios.
ity ismaximumforarampof50ms. A priori, this ramp First, we notice that one would naively expect that
duration could be insufficient in the presence of 41K im- stronglyinteractingimpuritieswouldlocallyincreasethe
purities. Therefore, we monitor the visibility versus the 87Rbatomfillingfactorandhencethechemicalpotential,
rampduration. Theturn-onprofilefollowsessentiallyan byexpelling orattractingthem. However,increasingthe
exponentialfunctionwithatime constantequalto0.4of chemical potential leads to an enhancement of the su-
the total ramp duration, smoothed at the end. We find perfluid fraction, which is indeed the result predicted by
thatthevisibilitydecreasesforturn-ontimeslongerthan Ref. [5], but opposite to what we observe. Ospelkaus et
al. argue that fermionic atoms act like randomly local-
ized scatterers for the boson order parameter, thereby
6 nits] splitting it into isolated superfluid domains unable to
m] b. u maintain a single coherent phase throughout the sample
µon, y [ 24 2ψ|| [ar -6 -4 y-2 [µ0m]2 4 6 [st4uo]nr.elToofchatelhizseua4tg0igoKens,itmeddpepuperhnitedinesos,mcrleeunacdoianinl,lgyretoomnlionthcisaecleifznearttmiooifonnA.inHcdonewar---
siti ever,bosonic41Katomsareexpectedtolocalizeless,not
po 0 more,than 87Rb. Therefore,the interpretationbased on
al
c Andersonlike localization does not hold in our case and
erti -2 might be unnecessary for the Fermi-Bose experiments.
V
-4 The loss of phase coherence could follow from heating
-20 -10 0 10 20 -20 -10 0 10 20
of the two clouds when the lattice ramps up. In addi-
Axial position, x [µm]
tion to technical noise, which plays a role only at longer
time scales,we considerthe effect of the thermodynamic
FIG.3: (Coloronline): densitydistributionof87Rb(red,left)
and 41K (blue, right) atoms, in the plane z = 0, calculated transformation involved. With two species, the effective
by numerical integration of the GPE: NRb = 3×104, NK = masseschangeatdifferentratesandthermalequilibrium
2×103,vertical lattice strength s=11. Shadedarea (green) requires an interspecies redistribution of entropy. In our
highlights the overlap, while the inset plot reports density experiment,thisincreasestheentropyof87Rbandthere-
profiles along thevertical line through x=0. fore its thermal component. Quantitatively, due to the
small overlap,we neglect the interspecies interaction en-
4

Ref.[26]reliesonsuitablyweakinterspeciesinteractions.
Rb only In our experiment the effective interspecies interactions
0.7 Rb+K are reduced by the low density of 41K in the overlap re-
difference
0.6 gionbut the approximationsof Ref. [26] are only weakly
satisfied. The order of magnitude of the above value,
y0.5
bilit however, proves that the inhibition of tunneling due to
si0.4 incoherent scattering of phonons deserves a deeper anal-
Vi ysis.
0.3
Finally,weaddressthequestionofwhytheshiftissub-
0.2 stantialevenwiththesmalloverlapshownbyFig.3. We
conjecturethat,owingtotheinhomogeneousdensity,the
0.1
lossofcoherencestartsfromthebordersofthe87Rbcon-
50 100 150 200 250 300
densatewherethe filling factorislower;the overlapwith
Ramp Time (ms) 41K,althoughsmall, occursinthis criticalregion. Alter-
FIG.4: (Coloronline)Visibilityofthefringesats=12versus natively,onecouldcalloncollisionsoccurringduringthe
theduration of thelattice ramp up.
expansion: since we do not observe any degradation of
the 87Rb Raman-Nath diffraction pattern caused by the
presence of 41K,time-of-flight collisionsbetween the two
species seem unable to significantly alter the 87Rb mo-
ergy and calculate the total entropy as the sum of two
mentum distribution, at least in the superfluid regime.
independent contributions. At s = 0, we calculate the
In summary, we have created a degenerate Bose-Bose
contributionofeachcomponentfromthe formulaforthe
mixture in a 3D optical lattice and studied the influence
totalenergy: E/N =3k T ζ(4)t4/ζ(3)+µ(1 t3)2/5(5+
16t3)/7, with t = T/T ,Bwhcere T and µ deno−te the crit- of a minor admixture of superfluid 41K on the loss of
c c 87Rbphasecoherence. Wefindthatthislossisfurthered
ical temperature and the chemical potential [23]. At
in the presence of 41K, even if the two clouds overlap
s = 20 the contribution of 41K is given by the above
only at their boundaries. Our results agree qualitatively
formula (replacing the atomic mass with the effective
with similar observations carried out with a Fermi-Bose
mass of the lowest energy band), while for the contribu-
mixture, notwithstanding the different statistics of im-
tion of 87Rb we take that of a deep Mott insulator [24]:
purities and the opposite sign of the strong interspecies
Sshell/kB = 32π3kBT PjRj/(3mω2λ3L), where Rj and interactions. Following a recent theoretical analysis, we
m indicate the radii of the superfluid layers of the Mott
findthatthe activationenergyofpolaronsis ofthe same
shell structure and the atomic mass. For an initial tem-
orderastheestimatedtemperatureinouropticallattice.
perature of 73 nK (87Rb thermal fractionequalto 0.21),
Our degenerate Bose-Bose mixture will also be studied
thepresenceof41Kincreasesthe87Rbentropyandhence
in the double Mott-insulator regime, promising for the
itsthermalfraction,by20%. Asaconsequence,the87Rb
formationofstablemolecules. Tothisend,Feshbachres-
condensate fraction decreases from 79% to 75% and the
onancespredictedatmoderatemagneticfieldsareinstru-
visibility by approximately the same amount [25]. We
mental to control the interspecies interactions.
conclude that this is a minor effect.
This work was supported by Ente CdR in Firenze,
A plausible interpretation of our findings invokes the
INFN through the project SQUAT-Super, and EU un-
dressing of 87Rb atoms by 41K: naively, dressed 87Rb
der Contracts No. HPRICT1999-00111 and No. MEIF-
atoms weigh more, therefore tunnel less. This argument
CT-2004-009939. We thank P. Maioli, who started this
ismadequantitativebyBrudereret al. [26],whoanalyze
experimentwithus,andallthemembersoftheQuantum
the generation of polarons in a Bose-Bose mixture, i.e.,
Degenerate Gas group at LENS for fruitful discussions.
quasiparticles composed of localized atoms (87Rb) plus
a cloud of superfluid phonons of the other species (41K).
The polarons have two different effects: at zero temper-
ature they reduce the tunneling rate of 87Rb atoms ac-
cording to the picture outlined above; at finite tempera- [*] E-mail address: [email protected]fi.it
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