第八届全国磁学会议.ppt

DynamicsofDipolarSpinorBose EinsteinCondensates YunboZhangInstituteofTheoreticalPhysics ShanxiUniversity Taiyuan HongKongMeeting13 16Dec2005 Collaboration Jiu QingLiang ShanxiUniversity ChinaLiYou GeogiaTech USAKalle AnttiSuominen UniversityofTurku FinlandShuChen IOP CAS ChinaH J W M ller Kirsten UniversityofKaiserslautern Germany OUTLINE SpinorDipolarCondensatesTunnelingandSelf TrappingModelandSpin mixingDynamicsSummary LaserCoolingEvaporativeCoolingBEC Onlylow fieldseekersaremagneticallytrappable Hyperfine Zeemanstates Breit RabiFormula T L Ho Phys Rev Lett 81742 1998 T OhmiandK Machida J Phys Soc Jpn 671822 1998 Spinor 1condensate density densitycollisionalinteraction spin spincollisionalinteraction s wavescatteringlengthforthetwospin 1atomsinthecombinedsymmetricchanneloftotalspinf C K Law H PuandN P Bigelow Phys Rev Lett 815257 1998 Twoconservedquantities 1 totalatomnumbers 2 totalhyperfinespin Twosymmetries 1 U 1 symmetry 2 SO 3 spinrotationsymmetry PhysicalPrinciples Gaugetransformationspinrotation Theintrinsicmagneticdipolemomentofanatomisrelatedtoitstotalangularmomentumas withFbeingtheangularmomentumoperator Magneticdipole dipoleinteraction Themagneticdipole dipoleinteractionMDDIis unitvector magneticpermeabilityofthevacuum DipolarSpinorCondensates Sincethespindegreeoffreedombecomesaccessible MDDIwhicharisefromintrinsicorinducedfieldofmagneticdipolemomentshouldbetakenintoaccountinadditiontotheusuals wavecontactinteractions S Yi L YouandH Pu Phys Rev Lett 93 040403 2004 Long range vectorization and ExperimentalAdvances A Griesmaier J Werner S Hensler J StuhlerandT Pfau Phys Rev Lett 94 160401 2005 J Stuhler A Griesmaier T Koch M Fattori T Pfau S Giovanazzi P Pedri andL Santos Phys Rev Lett 95 150406 2005 Cr 52 Tc 700nKN 50 000 MDDIofisafactorof36higherthanthatforalkaliatoms MDDIbreaksSO 3 symmetryintoaxialsymmetry BoththesignandthemagnitudeofMDDIarehighlytunable 52Cr spin 3BosonJ 3 I 0F 3 HigherHyperfineSpinCondensates Spin 1 87Rb 23NaFM AFMSpin 2 85RbFM AFM CyclicSpin 3 133Cs 52CrBiaxialorUniaxialSpinNematic Ho cond mat 0511751Machida cond mat 0511052Santos cond mat 0511634 Whyinteresting Non Abeliantopologicaldefects BiaxialNematicLiquidCrystalSpin 2CyclicphaseSpin 3 definitely conjugatevariables equationofmotion classicalHamiltonian MacroscopicQuantumSelfTrapping MQT macroscopicquantumtunneling theatomicpopulationisperiodicallyexchangedwhichisanalogoustotheJosephsonsinusoidaloscillation MQST macroscopicquantumself trapping whenthenonlinearityexcessessomecriticalvalue populationimbalanceisself lockedtotheinitialvalue whichcorrespondstothelocalizationoftheatomicpopulationinoneofcomponentsintheformofsmall amplitudeoscillations M Albiez R Gati J Folling S Hunsmann M Cristiani andM K Oberthaler Phys Rev Lett 95 010402 2005 ExperimentalObservation Spinmixingdynamics Model singlemodeapproximation canonicalvariables RongCheng Jiu QingLiang YunboZhang J Phys B At Mol Opt Phys 38 2005 2569 2578 mean fieldtheory time dependentvariationalprinciple EquationofMotion Define Hamiltonianbecomescyclicinthecoordinatesand Non rigidpendulum time time Spin MixingDynamics time time Spin MixingDynamics Thedistinctionbetweenthetwodynamicalregimes MQTandMQST becomesapparenthere Intheformerregimethedynamicalvariablesfollowaclosedphasespacetrajectory while inthelattertheyfollowanopentrajectorywithanunboundphase Constantenergycontours Weshow thedynamicsissensitivenotonlytothespin exchangeinteraction SEI andmagneticdipole dipoleinteraction MDDI butalsototheinitialatomnumberdistributionandrelativephaseamongthreecomponen