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1、Hubbardmodel(s)EugeneDemlerHarvardUniversity$$NSF,AFOSR,MURI,DARPA,CollaborationswithexperimentalgroupsofI.Bloch,T.EsslingerCollaborationwithE.Altman(Weizmann),R.Barnett(Caltech),A.Imambekov(Yale),A.M.Rey(JILA),D.Pekker,R.Sensarma,M.Lukin,andmanyothersOutlin
2、eBoseHubbardmodel.SuperfluidandMottphasesExtendedHubbardmodel:CDWandSupersolidstatesTwocomponentBoseHubbardmodel:magneticsuperexchangeinteractionsintheMottstatesBoseHubbardmodelforF=1bosons:exoticspinstatesFermiHubbardmodel:competingordersHubbardmodelbeyondc
3、ondensedmatterparadigms:nonequilibriummany-bodyquantumdynamicsBoseHubbardmodelAtomsinopticallatticesTheory:Jakschetal.PRL(1998)Experiment:Kasevichetal.,Science(2001);Greineretal.,Nature(2001);Phillipsetal.,J.PhysicsB(2002)Esslingeretal.,PRL(2004);manymore…Bo
4、seHubbardmodeltunnelingofatomsbetweenneighboringwellsrepulsionofatomssittinginthesamewellUt4BoseHubbardmodel.Mean-fieldphasediagram020M.P.A.Fisheretal.,PRB40:546(1989)MottN=1N=2N=3SuperfluidSuperfluidphaseMottinsulatorphaseWeakinteractionsStronginteractionsM
5、ottMottOpticallatticeandparabolicpotential420N=1N=2N=3SFMIMIJakschetal.,PRL81:3108(1998)SuperfluidtoInsulatortransitionGreineretal.,Nature415:39(2002)t/USuperfluidMottinsulatorShellstructureinopticallatticeS.Foellingetal.,PRL97:060403(2006)Observationofspati
6、aldistributionoflatticesitesusingspatiallyselectivemicrowavetransitionsandspinchangingcollisionssuperfluidregimeMottregimen=1n=2ExtendedHubbardmodel ChargeDensityWave andSupersolidphasesExtendedHubbardModel-onsiterepulsion-nearestneighborrepulsionCheckerboar
7、dphase:Crystalphaseofbosons.BreakstranslationalsymmetryExtendedHubbardmodel.MeanfieldphasediagramvanOtterloetal.,PRB52:16176(1995)Hardcorebosons.Supersolid–superfluidphasewithbrokentranslationalsymmetryExtendedHubbardmodel. QuantumMonteCarlostudySenguptaetal
8、.,PRL94:207202(2005)Hebertetal.,PRB65:14513(2002)DipolarbosonsinopticallatticesGoraletal.,PRL88:170406(2002)Twocomponent BoseHubbardmodel.MagnetismttTwocomponentBosemixtureinopticallatticeExampl
