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单击此处编辑母版标题样式,单击此处编辑母版文本样式,第二级,第三级,第四级,第五级,#,Dynamics of Dipolar Spinor Bose-Einstein Condensates,Yunbo Zhang,Institute of Theoretical Physics,Shanxi University,Taiyuan,Hong Kong Meeting,13-16 Dec 2005,Collaboration,Jiu-Qing Liang,Shanxi University,China,Li You,GeogiaTech,USA,Kalle-Antti Suominen,University of Turku,Finland,Shu Chen,IOP,CAS,China,H.J.W.M,ller-Kirsten,University of Kaiserslautern,Germany,http:/ Dipolar Condensates,Tunneling and Self-Trapping,Model and Spin-mixing Dynamics,Summary,Laser Cooling,Evaporative Cooling,BEC,Only low-field seekers are,magnetically trappable!,Hyperfine-Zeeman states,(Breit-Rabi Formula),T.-L.Ho,Phys.Rev.Lett,81 742(1998).,T.Ohmi and K.Machida,J.Phys.Soc.Jpn.67 1822(1998).,Spinor-1 condensate,density-density collisional interaction,spin-spin collisional interaction,s-wave scattering length for the two spin-1 atoms in the,combined symmetric channel of total spin,f,.,C.K.Law,H.Pu and N.P.Bigelow,Phys.Rev.Lett,81 5257(1998).,Two conserved quantities,(1)total atom numbers,(2)total hyperfine spin,Two symmetries,(1),U(1)symmetry,(2)SO(3)spin rotation symmetry,Physical Principles,Gauge transformation spin rotation,The intrinsic magnetic dipole moment of an atom is related to its total angular,momentum as ,with,F,being the angular momentum operator.,Magnetic dipole-dipole interaction,The magnetic dipole-dipole interaction,MDDI,is,unit vector,magnetic permeability of the vacuum,Dipolar Spinor Condensates,Since the spin degree of freedom becomes accessible,MDDI,which arise from intrinsic or induced field of magnetic dipole moment should be taken into account in addition to the usual s-wave,contact,interactions.,S.Yi,L.You and H.Pu,Phys.Rev.Lett.93,040403(2004).,Long-range,vectorization,and,Experimental Advances,A.Griesmaier,J.Werner,S.Hensler,J.Stuhler and T.Pfau,Phys.Rev.Lett.94,160401(2005);J.Stuhler,A.Griesmaier,T.Koch,M.Fattori,T.Pfau,S.Giovanazzi,P.Pedri,and L.Santos,Phys.Rev.Lett.95,150406(2005);,Cr-52,T,c,700nK,N50,000,MDDI of is a factor of,36,higher than that for alkali atoms.,MDDI breaks SO(3)symmetry into,axial,symmetry.,Both the sign and the magnitude of MDDI are highly tunable.,52,Cr,spin-3 Boson J=3,I=0,F=3,Higher Hyperfine Spin Condensates,Spin-1:,87,Rb,23,Na FM,AFM,Spin-2:,85,Rb FM,AFM,Cyclic,Spin-3:,133,Cs,52,Cr Biaxial or Uniaxial Spin Nematic,Ho,cond-mat/0511751,Machida,cond-mat/0511052,Santos,cond-mat/0511634,Why interesting?,Non-Abelian topological defects,Biaxial Nematic Liquid Crystal,Spin-2 Cyclic phase,Spin-3:definitely!,conjugate variables,equation of motion,classical Hamiltonian,Macroscopic Quantum Self Trapping,MQT(macroscopic quantum,tunneling,):,the,atomic population is periodically exchanged which is analogous to the Josephson sinusoidal oscillation.,MQST(macroscopic quantum self-trapping):,when the nonlinearity excesses some critical value,population imbalance is self-locked to the initial value,which corresponds to the localization of the atomic population in one of components in the form of small-amplitude oscillations.,M.Albiez,R.Gati,J.Folling,S.Hunsmann,M.Cristiani,and M.K.Oberthaler,Phys.Rev.Lett.95,010402(2005).,Experimental Observation,Spin mixing dynamics:Model,single mode approximation,canonical variables,Rong Cheng,Jiu-Qing Liang,Yunbo Zhang,J.Phys.B:At.Mol.Opt.Phys.38(2005)25692578,mean-field theory,time-dependent variational principle,m,f,=+1,0,-1,Equation of Motion,Define,Hamiltonian becomes cyclic in the coordinates and .,Non-rigid pendulum,time,time,Spin-Mixing Dynamics,time,time,Spin-Mixing Dynamics,The distinction between the two dynamical regimes-MQT and MQST-becomes apparent here.In the former regime the dynamical variables follow a,closed,phase space trajectory,while,in the latter they follow an,open,trajectory with an unbound phase.,Constant energy contours,We show,the dynamics is sensitive not only to the spin-exchange interaction(SEI)and,magnetic dipole-dipole interaction(MDDI)but also to the,initial atom number distribution,and,relative phase,among three components of the condensate.,We demonstrate,the characteristics of the dynamics such as macroscopic quantum self-trapping effect(MQST)are accessible and controllable,by modifying the trapping geometry,.,Summary,Thanks!,投入多一点，方法好一点，绩效自然高一点。,10月-24,10月-24,Tuesday,October 1,2024,未来的成功属于质量领先者。,19:41:50,19:41:50,19:41,10/1/2024 7:41:50 PM,若要产品好，个人品质要提高。,10月-24,19:41:50,19:41,Oct-24,01-Oct-24,老毛病，要根治。小问题，要重视。,19:41:50,19:41:50,19:41,Tuesday,October 1,2024,管理基础打得牢安全大厦层层高。,10月-24,10月-24,19:41:50,19:41:50,October 1,2024,宁愿事前检查，不可事后修改。,2024年10月1日,7:41 下午,10月-24,10月-24,搞好安全有责任，永为国家做贡献。,01 十月 2024,7:41:50 下午,19:41:50,10月-24,抓好产品质量，必须从我做起。,十月 24,7:41 下午,10月-24,19:41,October 1,2024,ISO9000-,主客共享乐在其中。,2024/10/1 19:41:50,19:41:50,01 October 2024,安全第一，人人牢记。,7:41:50 下午,7:41 下午,19:41:50,10月-24,确保质量安全。,10月-24,10月-24,19:41,19:41:50,19:41:50,Oct-24,船到江心补漏迟，事故临头后悔晚。,2024/10/1 19:41:50,Tuesday,October 1,2024,安全在于心细，事故出自大意。,10月-24,2024/10/1 19:41:50,10月-24,谢谢大家！,
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