Cooling quantum gases with entropy localization 2017 F Nur ünal.pdf

该【Cooling quantum gases with entropy localization 2017 F Nur ünal 】是由【dt83088549】上传分享，文档一共【8】页，该文档可以免费在线阅读，需要了解更多关于【Cooling quantum gases with entropy localization 2017 F Nur ünal 】的内容，可以使用淘豆网的站内搜索功能，选择自己适合的文档，以下文字是截取该文章内的部分文字，如需要获得完整电子版，请下载此文档到您的设备，方便您编辑和打印。PAPER?ESSYoumayalsolike-ApplicabilityoftheminimumentropyCoolingquantumgaseswithentropylocalizationgenerationmethodforoptimizingyclesXue-TaoCheng,,Xin-:FNurü-EntropyProfilesDecrypted:QuantifyingandUnderstandingtheInfluenceofCrystallineDefectsthroughExperimentandModellingMichaelPeterMercer,SteffenSchlueter,.-:(2017)023045https:///-2630/aa5e7bPAPERCoolingquantumgaseswithentropylocalizationESSFNurünal1,2andErichJMueller1RECEIVED1LaboratoryofAtomicandSolidStatePhysics,CornellUniversity,Ithaca,NY14853,UnitedStatesofAmerica13June20162DepartmentofPhysics,BilkentUniversity,06800Ankara,TurkeyREVISED24January2017E-mail:******@:disorder,cooling,entropylocalization6February2017PUBLISHED23February2017AbstractOriginalcontentfromthisWestudythedynamicsofentropyinatimedependentpotentialandexplorehowdisorderin?uencesworkmaybeusedunder?-(s)andthetitleofthework,,oftentreatedasanuisancetobeavoided,,thequantumHalleffectiswidelybelievedtoonlybeobservablebecauseofdisorder[1].Morerecently,therehavebeenproposalstousedisordertostabilizetopologicalordersagainsttemperature[2,3].Here,weproposeadisorder-enabledcoolingtechniqueforcoldatoms,whichtakesadvantageofthetheoretical[4–6]andexperimental[7,8]developmentsinvolvingmany-‘cooling’ofcoldatomicsystems,therelevantquantityisoftenentropyratherthantemperature[9–18].Temperaturecanberadicallyreducedbyadiabaticallychangingsystemparameters[19–22](forexamplethedepthofanopticallattice),but,?eldinvolvescoolingbyspatiallysegregatingtheentropy[23].Thisapproachismostthoroughlyworkedoutinthecontextofdimpletraps[10],whereadeeppotentialwellyieldsalow-,-,aFermilatticegaswithabandinsulatingcorewillhavemostofitsentropyattheedge,-entropyregion,however,?-entropyatomswhilesimultaneouslychangingthecon?ningpotential[9,10].Here,weproposeanalternative,,Andersonshowedthat,intheabsenceofinteractions,suf?cientlystrongdisorderpreventstransport,andwouldfreezethespatialdistributionofentropy[24,25].Halfacenturylater,Baskoetalcoinedthephrase‘many-bodylocalization’showingthatthisinsulatingbehaviorsurvivesweakinteractionsat?nitetemperature[26].Furtherexperimentalandtheoreticalstudiescon?rmedtheseresults,andshowedtheypersistunderverygeneralconditions[6–8,27–31].Oneexpectsthatgenericallydisordercanbeusedtoprevententropy?ow,,weinvestigatethedynamicsofasimplemodelofharmonicallytrappedone-dimensionalspin-,,intheabsenceofdisorder,,on?nement,entropy?,for?(2017)023045FNünalandEJMueller?nitesweeprates,?ndthatsuf?cientlystrongdisorderpreventstheentropy?ow,,?()t??122?i??=-?()aaii+1+ai+1ai+wziaaii+D-+()()()t1,1aaiiiiaaiJiN=-22ω?withnearest-()aicreates(annihilates),?1,one?,uniformlydistributedwith∣zzi∣?,()?,?ndingsingle-particleeigenstatesYandeigenvaluesen.()emn--kT1TheentropyofthesystemisSfff=-?nnnln()+-(1n)ln(1-fn)wherefn=+()1eistheFermi–?nditconvenienttonotincludeBoltzmann’()n2Sffffi=-?∣∣(()(Yinnln+1-n)(ln1-n)),()2n?sothatSS=?,,however,itisagoodde?,wetakeN?=?200sites,hegapΔ,(interactingornon-interacting)thetotalentropycannotchange:,,,-interactinggas,upationfactorsfninequation(2)willbeconstant,()n–-dependentHartreeFockapproximation,whichwas?rstproposedbyDirac[32],isexactforanon-,eveninthecaseofinteractions,,givenenoughdegreesoffreedom,anisolatedquantumsystemshouldbecapableofthermalizing[33–38].Thermalizationrequiresentropygrowth,([39]).Forgenericquantumstatestheentanglemententropyofasmallsubregionisproportionaltothevolumeofthatregion,ode?,asconventionallyde?ned,?neentropydensitieswhichincreasewithtimeinisolatedsystems[40–42].,weexploretheentropyredistribution,ascapturedbyequation(2).,?ningentropydensity,?nitionofentropy,?,,,,wecanusethesingle-particleSchr?dingerequationtoevolvethewavefunctions,upationfactors?,(2017)023045FNü?nedbyequation(2)forsuperlatticestrengthD=,trapfrequencyw=,chemicalpotentialm=?=?=600.(a)Inthedisorderfreecase,entropy?owsinfromtheedgesasthesuperlatticepotentialisturnedoff.(b)Strongdisorderpreventsthis?owbylocalizingtheentropyattheedges.?D?D-0tt,0??t,D=()t?0()3?t?0,t>-freecase,entropyde?nedbyequation(2)?,,however,,,asanticipated,strongdisorder(z=),thestateisnominallynon-()natthe?,inthecentralregion,??ndthattheentropyevolutionissensitivetosweeprate(1t).Inafastsweep(smallτ)wherethewavefunctionsdonothaveenoughtimetoadjustthemselvestothenewHamiltonian,theentropydistributionimmediatelyafterthesweepwouldbesimilartotheinitialcon?guration,=tfortwodifferentdisorderstrengths,z=1(dots)andz=2(diamonds),(-60<<i60forN?=?200sites).Thiscentralregionholds75%(z=2),forweakerrandomness(z=1),thecentralentropyseemstoincreaseinitiallyaswemakethesweepslowerandthensaturatestoa?,weletthesystemevolveforanother10tafterthesweeppleted,,theentropyevolvessigni?,thecentralentropydensityisnearlyindependentofsweeprate,saturatingnear18%forz=,theentropy,asde?nedbyequation(2),,theamountofentropywhich?(2017)023045FNü(-<<60i60forN?=?200sites).Here,thesuperlatticestrengthisD=3,trapfrequencyisw=,chemicalpotentialism=?=?=tandthesolidlinescorrespondtot=,z=1(dark)andz=2(light).Forweakerdisorder,thereissigni?cantentropy?owfollowinganabruptramp,?nalentropyinthecentralregionofthetrap(-<<60i60forN?=?200sites)=3,trapfrequencyisw=,temperatureisT?=?,andchemicalpotentialis?xedatm==,56%