Observation of Phase Separation in a Strongly-Interacting Im(2)

Thepresenceofacoreregionwithequaldensitiesforthetwocomponentswascorrelatedwiththepresenceofapaircondensate.Thedensitydi erenceatthecen-ternd0alongwiththecondensatefractionisshownasafunctionofthepopulationimbalanceδinFig.4.Asshown,thereisacriticalimbalanceδcwheresuper uid-itybreaksdownduetolargeimbalance[5,7].Inthesuper uidregion,i.e.,δ<δc,nd0vanishes,andforδ>δc,nd0rapidlyincreaseswithasuddenjumparoundδ≈δc.WeobserveasimilarbehaviorthroughoutthestronglyinteractingregimeneartheFeshbachresonance, 0.4<1/kFa<0.6.Thisobservationclearlydemon-

We have observed phase separation between the superfluid and the normal component in a strongly interacting Fermi gas with imbalanced spin populations. The in situ distribution of the density difference between two trapped spin components is obtained using

FIG.4:(Coloronline)Phaseseparationinastronglyinteract-ingFermigas.Normalizedcentraldensitydi erenceη(blackcircle)andcondensatefraction(redtriangle)asfunctionsofimbalanceδforvariousinteractionstrengths.η≡nd0/n0wherend0wasmeasuredastheaverageoverthecentral

regionof7µm×40µmina2D-cutofthe3Ddistribution(Fig.3(c))andn0=3.3×1012cm 3isthecalculatedcentraldensityofafullypolarizedFermigaswithNt=1×107.Theconden-satefractionwasdeterminedfromthebimodaldistributionoftheminoritycomponentafteramagnetic eldsweepandexpansion.Thesolidlineisa tforthecondensatefractiontoathresholdfunction∝(1 |δ/δc|n).Thecriticalimbalanceδcindicatedbytheverticaldashedlineswere96%,77%,and51%forB=780G,B=834GandB=884G,respectively.

stratesthatforthisrangeofinteractionsapairedsuper- uidisspatiallyseparatedfromanormalcomponentofunequaldensities.

Theshellstructureischaracterizedbytheradiusofthemajoritycomponent,theradialpositionRpofthepeakinnd( r),thesizeRcoftheregionwherendisdepleted,andthe“visibility”ofthecoreregionα≡(nd(Rp) nd0)/(nd(Rp)+nd0)(Fig.5).Thesuddendropofαaroundδ≈δchasthesameoriginastheobservedsuddenjumpofnd0:thebreakdownofsuper uidity(compareFig.4).ThecomparisonbetweenRpandRcshowsthattheboundarylayerbetweenthesuper uidandnormalregionisratherthin.Ithasbeensuggestedthatthede-tailedshapeofpro lesintheintermediateregioncouldbeusedtoidentifyexoticstatessuchastheFulde-Ferrell-Larkin-Ovchinnikov(FFLO)state[23,24,25].Thiswillbeasubjectoffutureresearch.

Thesuper uidrequiresequalcentraldensitiesinthestronglyinteractingregimeatourcoldesttemperatures.

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FIG.5:(Coloronline)Characterizationoftheshellstructure.(a)Reconstructed3Dradialpro lesatB=834G.(b)RadiusofthemajoritycomponentR(blackcircle),peakpositionofthedensitydi erenceRp(redcircle),andradiusoftheemptycoreRc(bluetriangle).Rwasdeterminedfromthepro les’wingsusinga ttoazero-temperatureTFdistribution.ThesolidlineindicatestheTFradiusofthemajoritycomponentinanidealnon-interactingcase.Ratδ=0(opencircle)wasmeasuredfromanimagetakenwithaprobefrequencypreferentiallytunedtoonecomponent.Rcisde nedasthepositionofthehalf-peakvalueintheemptycoreregionforδ<δc.(c)Visibilityofthecoreregionisde nedasα≡(nd(Rp) nd0)/(nd(Rp)+nd0).

AnormalimbalancedFermimixturewillhaveunequaldensities.Thus,oneshouldexpectthatavisiblechangeinthedensitydi erenceoccursasthetemperatureisloweredacrossthenormal-to-super uidphasetransi-tion[7,9].Insituphase-contrastimagesofacloudatvarioustemperaturesareshowninFig.6.Thetempera-tureTofthecloudiscontrolledwiththe nalvalueofthetrapdepthintheevaporationprocess.Theshellstruc-tureappearsandbecomesprominentwhenTdecreasesbelowacertaincriticalvalue.Thisshellstructuregivesrisetothebimodaldensitypro leoftheminoritycom-ponentthatweobservedafterexpansionfromthetrapinourrecentwork[7].Hereweshowviainsitumeasure-mentsthattheonsetofsuper uidityisaccompaniedbyapronouncedchangeinthespatialdensitydi erence.ThephasetransitionischaracterizedinFig.7.AsTislowered,nd0graduallydecreasesfromitsplateauvalueandthecondensatefractionstartstoincrease.Fromthepointofcondensation(condensatefraction>1%)anddeformationoftheminorityclouds(χ2inFig.7(b)),wedeterminethecriticaltemperatureTc=0.13(2)TFfortheimbalanceofδ=56(3)%.TF=1.7µKistheFermitemperatureofanon-interactingequalmixturewiththesametotalatomnumber.Theriseinχ2,thedropinnd0andtheonsetofcondensationareallobservedataboutthesametemperature.Betterstatisticsareneededtoaddressthequestion:whethersomeweakexpulsionof

We have observed phase separation between the superfluid and the normal component in a strongly interacting Fermi gas with imbalanced spin populations. The in situ distribution of the density difference between two trapped spin components is obtained using

FIG.6:EmergenceofphaseseparationinanimbalancedFermigas.Thetemperatureofthecloudwascontrolledbyvaryingthe nalvalueofthetrapdepthUfintheevaporationprocess.Phase-contrastimagesweretakenafteradiabaticallyrampingthetrapdepthuptokB×3.7µK(fr=192Hz).ThewholeevaporationandimagingprocesswereperformedatB=834G(N7t≈1.7×10,δ≈56%).The eldofviewforeachimageis160µm×940µm.Theverticalandhorizontalscaleoftheimagesdi erbyafactorof

1.5.

FIG.7:(Coloronline)PhasetransitioninanimbalancedFermigas.ThephasetransitionshowninFig.6wascharac-terizedbymeasuring(a)populationimbalanceδ,(b)temper-atureT(blackcircle),χ2for ttingtheminoritycloudwitha nitetemperatureFermi-Diracdistribution(redtriangle),(c)centraldensitydi erencend0(blackcircle),andcondensatefraction(redtriangle).Thesolidlineisaguidetotheeyeforχ2.WhenUf<kB×1µK,δdecreasedmainlyduetolossofthemajoritycomponent.Thenumberoftheminoritycomponentwasconstant(N2≈3.7×106).Twasdeterminedfromthenon-interactingouterregionofthemajoritycloudafter10msofballisticexpansion[7].Tandnd0wereaveragedvaluesofthreeindependentmeasurements.Theopen(solid)arrowin(c)indicatesthepositionforTc(T ).Seethetextforthede nitionsofTcandT .

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majorityatomsfromthecenteroccursalreadyslightlyaboveTc.

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