第八屆全國磁學會議課件

DynamicsofDipolarSpinorBose-EinsteinCondensatesYunboZhang

InstituteofTheoreticalPhysics,ShanxiUniversity,Taiyuan

HongKongMeeting13-16Dec2005?DynamicsofDipolarSpinorBos1CollaborationJiu-QingLiang,ShanxiUniversity,ChinaLiYou,GeogiaTech,USAKalle-AnttiSuominen,UniversityofTurku,FinlandShuChen,IOP,CAS,ChinaH.J.W.Müller-Kirsten,UniversityofKaiserslautern,Germany/yunbo/index.html?CollaborationJiu-QingLiang,S2OUTLINESpinorDipolarCondensatesTunnelingandSelf-TrappingModelandSpin-mixingDynamicsSummary?OUTLINESpinorDipolarCondensa3LaserCooling

EvaporativeCooling

BEC?LaserCoolingEvaporativeCo4Onlylow-fieldseekersaremagneticallytrappable!Hyperfine-Zeemanstates(Breit-RabiFormula)?Onlylow-fieldseekersareHyp5??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)spinrotationsymmetryPhysicalPrinciplesGaugetransformationspinrotation?TwoconservedquantitiesTwo9Theintrinsicmagneticdipolemomentofanatomisrelatedtoitstotalangularmomentumas,withFbeingtheangularmomentumoperator.Magneticdipole-dipoleinteractionThemagneticdipole-dipoleinteractionMDDIis

unitvectormagneticpermeabilityofthevacuum?Theintrinsicmagneticdipole10DipolarSpinorCondensatesSincethespindegreeoffreedombecomesaccessible,MDDIwhicharisefromintrinsicorinducedfieldofmagneticdipolemomentshouldbetakenintoaccountinadditiontotheusuals-wavecontactinteractions.S.Yi,L.YouandH.Pu,Phys.Rev.Lett.93,040403(2004).Long-rangevectorizationand?DipolarSpinorCondensatesSinc11ExperimentalAdvancesA.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=3?ExperimentalAdvancesA.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!?HigherHyperfineSpinCondensa13conjugatevariablesequationofmotionclassicalHamiltonianMacroscopicQuantumSelfTrapping?conjugatevariablesequationof14??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).ExperimentalObservation?M.Albiez,R.Gati,J.Folling17Spinmixingdynamics:Modelsinglemodeapproximationcanonicalvariables

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

-1?Spinmixingdynamics:Modelsin18EquationofMotionDefineHamiltonianbecomescyclicinthecoordinatesand.?EquationofMotionDefineHamilt19Non-rigidpendulum?Non-rigidpendulum?20timetimeSpin-MixingDynamics?timetimeSpin-MixingDynamics?21timetimeSpin-MixingDynamics?timetimeSpin-MixingDynamics?22Thedistinctionbetweenthetwodynamicalregimes--MQTandMQST--becomesapparenthere.Intheformerregimethedynamicalvariablesfollowaclosedphasespacetrajectory,while,inthelattertheyfollowanopentrajectorywithanunboundphase.Constantenergycontours?Thedistinctionbetweenthetw23Weshow,thedynamicsissensitivenotonlytothespin-exchangeinteraction(SEI)and

magneticdipole-dipoleinteraction(MDDI)butalsototheinitialatomnumberdistributionandrelativephaseamongthreecomponentsofthecondensate.Wedemonstrate,thecharacteristicsofthedynamicssuchas``macroscopicquantumself-trapping''effect(MQST)areaccessibleandcontrollablebymodifyingthetrappinggeometry.Summary?Weshow,thedynamicsissensi24Thanks!?Thanks!?25每一次的加油，每一次的努力都是為了下一次更好的自己。12月-2212月-22Thursday,December29,2022天生我材必有用，千金散盡還復(fù)來。10:47:1810:47:1810:4712/29/202210:47:18AM安全象只弓，不拉它就松，要想保安全，常把弓弦繃。12月-2210:47:1810:47Dec-2229-Dec-22得道多助失道寡助，掌控人心方位上。10:47:1810:47:1810:47Thursday,December29,2022安全在于心細，事故出在麻痹。12月-2212月-2210:47:1810:47:18December29,2022加強自身建設(shè)，增強個人的休養(yǎng)。2022年12月29日10:47上午12月-2212月-22擴展市場，開發(fā)未來，實現(xiàn)現(xiàn)在。29十二月202210:47:18上午10:47:1812月-22做專業(yè)的企業(yè)，做專業(yè)的事情，讓自己專業(yè)起來。十二月2210:47上午12月-2210:47December29,2022時間是人類發(fā)展的空間。2022/12/2910:47:1810:47:1829December2022科學，你是國力的靈魂；同時又是社會發(fā)展的標志。10:47:18上午10:47上午10:47:1812月-22每天都是美好的一天，新的一天開啟。12月-2212月-2210:4710:47:1810:47:18Dec-22人生不是自發(fā)的自我發(fā)展，而是一長串機緣。事件和決定，這些機緣、事件和決定在它們實現(xiàn)的當時是取決于我們的意志的。2022/12/2910:47:18Thursday,December29,2022感情上的親密，發(fā)展友誼；錢財上的親密，破壞友誼。12月-222022/12/2910:47:1812月-22謝謝大家！每一次的加油，每一次的努力都是為了下一次更好的自己。12月-26DynamicsofDipolarSpinorBose-EinsteinCondensatesYunboZhang

InstituteofTheoreticalPhysics,ShanxiUniversity,Taiyuan

HongKongMeeting13-16Dec2005?DynamicsofDipolarSpinorBos27CollaborationJiu-QingLiang,ShanxiUniversity,ChinaLiYou,GeogiaTech,USAKalle-AnttiSuominen,UniversityofTurku,FinlandShuChen,IOP,CAS,ChinaH.J.W.Müller-Kirsten,UniversityofKaiserslautern,Germany/yunbo/index.html?CollaborationJiu-QingLiang,S28OUTLINESpinorDipolarCondensatesTunnelingandSelf-TrappingModelandSpin-mixingDynamicsSummary?OUTLINESpinorDipolarCondensa29LaserCooling

EvaporativeCooling

BEC?LaserCoolingEvaporativeCo30Onlylow-fieldseekersaremagneticallytrappable!Hyperfine-Zeemanstates(Breit-RabiFormula)?Onlylow-fieldseekersareHyp31??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)spinrotationsymmetryPhysicalPrinciplesGaugetransformationspinrotation?TwoconservedquantitiesTwo35Theintrinsicmagneticdipolemomentofanatomisrelatedtoitstotalangularmomentumas,withFbeingtheangularmomentumoperator.Magneticdipole-dipoleinteractionThemagneticdipole-dipoleinteractionMDDIis

unitvectormagneticpermeabilityofthevacuum?Theintrinsicmagneticdipole36DipolarSpinorCondensatesSincethespindegreeoffreedombecomesaccessible,MDDIwhicharisefromintrinsicorinducedfieldofmagneticdipolemomentshouldbetakenintoaccountinadditiontotheusuals-wavecontactinteractions.S.Yi,L.YouandH.Pu,Phys.Rev.Lett.93,040403(2004).Long-rangevectorizationand?DipolarSpinorCondensatesSinc37ExperimentalAdvancesA.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=3?ExperimentalAdvancesA.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!?HigherHyperfineSpinCondensa39conjugatevariablesequationofmotionclassicalHamiltonianMacroscopicQuantumSelfTrapping?conjugatevariablesequationof40??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).ExperimentalObservation?M.Albiez,R.Gati,J.Folling43Spinmixingdynamics:Modelsinglemodeapproximationcanonicalvariables

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

-1?Spinmixingdynamics:Modelsin44EquationofMotionDefineHamiltonianbecomescyclicinthecoordinatesand.?EquationofMotionDefineHamilt45Non-rigidpendulum?Non-rigidpendulum?46timetimeSpin-MixingDynamics?timetimeSpin-MixingDynamics?47timetimeSpin-MixingDynamics?timetimeSpin-MixingDynamics?48Thedistinctionbetweenthetwodynamicalregimes--MQTandMQST--becomesapparenthere.Intheformerregimethedynamicalvariablesfollowaclosedphasespacetrajectory,while,inthelattertheyfollowanopentrajectorywithanunboundphase.Constantenergycontours?Thedistinctionbetweenthetw49Weshow,thedynamicsissensitivenotonlytothespin-exchangeinteraction(SEI)and

magneticdipole-dipoleinteraction(MDDI)bu