第八届全国磁学会议课件

DynamicsofDipolarSpinorBose-EinsteinCondensatesYunboZhang

InstituteofTheoreticalPhysics,ShanxiUniversity,Taiyuan

HongKongMeeting13-16Dec2005DynamicsofDipolarSpinorBos1CollaborationJiu-QingLiang,ShanxiUniversity,ChinaLiYou,GeogiaTech,USAKalle-AnttiSuominen,UniversityofTurku,FinlandShuChen,IOP,CAS,ChinaH.J.W.Müller-Kirsten,UniversityofKaiserslautern,Germany/yunbo/index.htmlCollaborationJiu-QingLiang,S2OUTLINESpinorDipolarCondensatesTunnelingandSelf-TrappingModelandSpin-mixingDynamicsSummaryOUTLINESpinorDipolarCondensa3LaserCooling

EvaporativeCooling

BECLaserCoolingEvaporativeCo4Onlylow-fieldseekersaremagneticallytrappable!Hyperfine-Zeemanstates(Breit-RabiFormula)Onlylow-fieldseekersareHyp5第八届全国磁学会议课件6

T.-L.Ho,Phys.Rev.Lett,81742(1998).

T.OhmiandK.Machida,J.Phys.Soc.Jpn.671822(1998).T.-L.Ho,Phys.Rev.Lett,817Spinor-1condensatedensity-densitycollisionalinteractionspin-spincollisionalinteractions-wavescatteringlengthforthetwospin-1atomsinthecombinedsymmetricchanneloftotalspinf.

C.K.Law,H.PuandN.P.Bigelow,Phys.Rev.Lett,815257(1998).Spinor-1condensatedensity-den8

Twoconservedquantities

(1)totalatomnumbers

(2)totalhyperfinespin

Twosymmetries

(1)U(1)symmetry

(2)SO(3)spinrotationsymmetryPhysicalPrinciplesGaugetransformationspinrotationTwoconservedquantitiesTwo9Theintrinsicmagneticdipolemomentofanatomisrelatedtoitstotalangularmomentumas,withFbeingtheangularmomentumoperator.Magneticdipole-dipoleinteractionThemagneticdipole-dipoleinteractionMDDIis

unitvectormagneticpermeabilityofthevacuumTheintrinsicmagneticdipole10DipolarSpinorCondensatesSincethespindegreeoffreedombecomesaccessible,MDDIwhicharisefromintrinsicorinducedfieldofmagneticdipolemomentshouldbetakenintoaccountinadditiontotheusuals-wavecontactinteractions.S.Yi,L.YouandH.Pu,Phys.Rev.Lett.93,040403(2004).Long-rangevectorizationandDipolarSpinorCondensatesSinc11ExperimentalAdvancesA.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-52Tc~700nKN~50,000

MDDIofisafactorof36higherthanthatforalkaliatoms.

MDDIbreaksSO(3)symmetryintoaxialsymmetry.

BoththesignandthemagnitudeofMDDIarehighlytunable.52Cr,spin-3BosonJ=3,I=0F=3ExperimentalAdvancesA.Griesm12HigherHyperfineSpinCondensatesSpin-1:87Rb,23NaFM,AFMSpin-2:85RbFM,AFM,CyclicSpin-3:133Cs,52CrBiaxialorUniaxialSpinNematicHo,cond-mat/0511751Machida,cond-mat/0511052Santos,cond-mat/0511634Whyinteresting?Non-AbeliantopologicaldefectsBiaxialNematicLiquidCrystalSpin-2CyclicphaseSpin-3:definitely!HigherHyperfineSpinCondensa13conjugatevariablesequationofmotionclassicalHamiltonianMacroscopicQuantumSelfTrappingconjugatevariablesequationof14第八届全国磁学会议课件15MQT(macroscopicquantumtunneling):

theatomicpopulationisperiodicallyexchangedwhichisanalogoustotheJosephsonsinusoidaloscillation.MQST(macroscopicquantumself-trapping):

whenthenonlinearityexcessessomecriticalvalue,

populationimbalanceisself-lockedtotheinitialvalue,whichcorrespondstothelocalizationoftheatomicpopulationinoneofcomponentsintheformofsmall-amplitudeoscillations.MQT(macroscopicquantumtunn16M.Albiez,R.Gati,J.Folling,S.Hunsmann,M.Cristiani,andM.K.Oberthaler,Phys.Rev.Lett.95,010402(2005).ExperimentalObservationM.Albiez,R.Gati,J.Folling17Spinmixingdynamics:Modelsinglemodeapproximationcanonicalvariables

RongCheng,Jiu-QingLiang,YunboZhang,J.Phys.B:At.Mol.Opt.Phys.38(2005)2569–2578mean-fieldtheorytime-dependentvariationalprinciplemf=+10

-1Spinmixingdynamics:Modelsin18EquationofMotionDefineHamiltonianbecomescyclicinthecoordinatesand.EquationofMotionDefineHamilt19Non-rigidpendulumNon-rigidpendulum20timetimeSpin-MixingDynamicstimetimeSpin-MixingDynamics21timetimeSpin-MixingDynamicstimetimeSpin-MixingDynamics22Thedistinctionbetweenthetwodynamicalregimes--MQTandMQST--becomesapparenthere.Intheformerregimethedynamicalvariablesfollowaclosedphasespacetrajectory,while,inthelattertheyfollowanopentrajectorywithanunboundphase.ConstantenergycontoursThedistinctionbetweenthetw23Weshow,thedynamicsissensitivenotonlytothespin-exchangeinteraction(SEI)and

magneticdipole-dipoleinteraction(MDDI)butalsototheinitialatomnumberdistributionandrelativephaseamongthreecomponentsofthecondensate.Wedemonstrate,thecharacteristicsofthedynamicssuchas``macroscopicquantumself-trapping''effect(MQST)areaccessibleandcontrollablebymodifyingthetrappinggeometry.SummaryWeshow,thedynamicsissensi24Thanks!Thanks!25演讲完毕，谢谢观看！演讲完毕，谢谢观看！26DynamicsofDipolarSpinorBose-EinsteinCondensatesYunboZhang

InstituteofTheoreticalPhysics,ShanxiUniversity,Taiyuan

HongKongMeeting13-16Dec2005DynamicsofDipolarSpinorBos27CollaborationJiu-QingLiang,ShanxiUniversity,ChinaLiYou,GeogiaTech,USAKalle-AnttiSuominen,UniversityofTurku,FinlandShuChen,IOP,CAS,ChinaH.J.W.Müller-Kirsten,UniversityofKaiserslautern,Germany/yunbo/index.htmlCollaborationJiu-QingLiang,S28OUTLINESpinorDipolarCondensatesTunnelingandSelf-TrappingModelandSpin-mixingDynamicsSummaryOUTLINESpinorDipolarCondensa29LaserCooling

EvaporativeCooling

BECLaserCoolingEvaporativeCo30Onlylow-fieldseekersaremagneticallytrappable!Hyperfine-Zeemanstates(Breit-RabiFormula)Onlylow-fieldseekersareHyp31第八届全国磁学会议课件32

T.-L.Ho,Phys.Rev.Lett,81742(1998).

T.OhmiandK.Machida,J.Phys.Soc.Jpn.671822(1998).T.-L.Ho,Phys.Rev.Lett,8133Spinor-1condensatedensity-densitycollisionalinteractionspin-spincollisionalinteractions-wavescatteringlengthforthetwospin-1atomsinthecombinedsymmetricchanneloftotalspinf.

C.K.Law,H.PuandN.P.Bigelow,Phys.Rev.Lett,815257(1998).Spinor-1condensatedensity-den34

Twoconservedquantities

(1)totalatomnumbers

(2)totalhyperfinespin

Twosymmetries

(1)U(1)symmetry

(2)SO(3)spinrotationsymmetryPhysicalPrinciplesGaugetransformationspinrotationTwoconservedquantitiesTwo35Theintrinsicmagneticdipolemomentofanatomisrelatedtoitstotalangularmomentumas,withFbeingtheangularmomentumoperator.Magneticdipole-dipoleinteractionThemagneticdipole-dipoleinteractionMDDIis

unitvectormagneticpermeabilityofthevacuumTheintrinsicmagneticdipole36DipolarSpinorCondensatesSincethespindegreeoffreedombecomesaccessible,MDDIwhicharisefromintrinsicorinducedfieldofmagneticdipolemomentshouldbetakenintoaccountinadditiontotheusuals-wavecontactinteractions.S.Yi,L.YouandH.Pu,Phys.Rev.Lett.93,040403(2004).Long-rangevectorizationandDipolarSpinorCondensatesSinc37ExperimentalAdvancesA.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-52Tc~700nKN~50,000

MDDIofisafactorof36higherthanthatforalkaliatoms.

MDDIbreaksSO(3)symmetryintoaxialsymmetry.

BoththesignandthemagnitudeofMDDIarehighlytunable.52Cr,spin-3BosonJ=3,I=0F=3ExperimentalAdvancesA.Griesm38HigherHyperfineSpinCondensatesSpin-1:87Rb,23NaFM,AFMSpin-2:85RbFM,AFM,CyclicSpin-3:133Cs,52CrBiaxialorUniaxialSpinNematicHo,cond-mat/0511751Machida,cond-mat/0511052Santos,cond-mat/0511634Whyinteresting?Non-AbeliantopologicaldefectsBiaxialNematicLiquidCrystalSpin-2CyclicphaseSpin-3:definitely!HigherHyperfineSpinCondensa39conjugatevariablesequationofmotionclassicalHamiltonianMacroscopicQuantumSelfTrappingconjugatevariablesequationof40第八届全国磁学会议课件41MQT(macroscopicquantumtunneling):

theatomicpopulationisperiodicallyexchangedwhichisanalogoustotheJosephsonsinusoidaloscillation.MQST(macroscopicquantumself-trapping):

whenthenonlinearityexcessessomecriticalvalue,

populationimbalanceisself-lockedtotheinitialvalue,whichcorrespondstothelocalizationoftheatomicpopulationinoneofcomponentsintheformofsmall-amplitudeoscillations.MQT(macroscopicquantumtunn42M.Albiez,R.Gati,J.Folling,S.Hunsmann,M.Cristiani,andM.K.Oberthaler,Phys.Rev.Lett.95,010402(2005).ExperimentalObservationM.Albiez,R.Gati,J.Folling43Spinmixingdynamics:Modelsinglemodeapproximationcanonicalvariables

RongCheng,Jiu-QingLiang,YunboZhang,J.Phys.B:At.Mol.Opt.Phys.38(2005)2569–2578mean-fieldtheorytime-dependentvariationalprinciplemf=+10

-1Spinmixingdynamics:Modelsin44EquationofMotionDefineHamiltonianbeco