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1、PHYSICALREVIEWA79,0334012009Nonlineardynamicsofacigar-shapedBose-EinsteincondensateinanopticalcavityJ.M.Zhang,F.C.Cui,D.L.Zhou,andW.M.LiuBeijingNationalLaboratoryforCondensedMatterPhysics,InstituteofPhysics,ChineseAcademyofSciences,Beijing100080,ChinaReceived3December2008;p
2、ublished3March2009Weinvestigatethenonlineardynamicsofacombinedsystemwhichiscomposedofacigar-shapedBose-Einsteincondensateandanopticalcavitywiththetwosidescoupleddispersively.Thissystemischaracterizedbythecavity-inducednonlinearity;afterintegratingoutthefastdegreeoffreedomofth
3、ecavitymode,thepotentialfeltbythecondensatedependsonthecondensateitself.Adoptingadiscrete-modeapproximationforthecondensate,wemapoutthesteadyconÞgurationsofthesystem.Itisfoundthatduetothenonlinearityofthesystem,thenonlinearlevelsofthesystemmayfoldupinsomeparameterregimes.Thatw
4、illleadtothebreakdownofadiabaticevolutionofthesystem.Analysisofthedynamicalstabilityofthesteadystatesindicatesthatthesamelevelstructurealsoresultsinopticalbistability.DOI:10.1103/PhysRevA.79.033401PACSnumbers:37.10.Jk,37.10.Vz,42.50.Pq,42.65.PcI.INTRODUCTIONcondensate-cavity
5、systemmapsontothegenericcavityopto-mechanicalsystemperfectly.InthisworkweapproachtheRecently,alotofinvestigationshavebeendevotedtothesameproblemfromtheperspectiveofdiffractionofmattercombinationofultracoldatomphysicsandcavityquantumwavebyanopticallattice.Wewillnotrestricttothe
6、weakexcitationlimit.Wewilldevelopadiscrete-modeapproxima-electrodynamics.Experimentally,theeffortsculminateinthetionDMAforthecondensatewiththeideathatthedynam-successfulcouplingofaBose-EinsteincondensateBEC,icsofthecondensateconÞnestosomediscretemodes.Bythatis,asinglematte
7、r-waveÞeldmode,toasinglecavitycomparingwiththefulldescriptionofGross-PitaevskiiGPmodeinahighÞnesseopticalcavity1,2.Thoughofaveryequation,weÞndthattheÞnite-modeapproximationisquan-shorthistory,thistypeofcombinedsystemhasdemonstratedtitativelygoodinthecaseofweakatom-atominte
8、raction.manyinterestingphenomena,suchasvacuumRabisplittingThe
