1、Dynamics of Dipolar Spinor Bose-Einstein CondensatesYunbo Zhang Institute of Theoretical Physics, Shanxi University, Taiyuan Hong Kong Meeting13-16 Dec 2005.CollaborationJiu-Qing Liang, Shanxi University, ChinaLi You, GeogiaTech, USAKalle-Antti Suominen, University of Turku, FinlandShu Chen, IOP, CA

2、S, ChinaH.J.W. Mller-Kirsten, University of Kaiserslautern, G/yunbo/index.html.OUTLINESpinor Dipolar CondensatesTunneling and Self-TrappingModel and Spin-mixing DynamicsSummary.Laser Cooling Evaporative Cooling BEC.Only low-field seekers are magnetically trappable!Hyperfine-Zeeman s

3、tates(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 condensatedensity-density collisional interactionspin-spin collisional interactions-wave scattering length for the two spin-1 atoms in the combined symmetric channe

4、l 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 symmetryPhysical PrinciplesGauge transformation spin rotation.The intrinsic magnetic

5、 dipole moment of an atom is related to its total angular momentum as , with F being the angular momentum operator.Magnetic dipole-dipole interactionThe magnetic dipole-dipole interaction MDDI is unit vectormagnetic permeability of the vacuum.Dipolar Spinor CondensatesSince the spin degree of freedo

6、m 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-rangevectorizationand.Experimental AdvancesA. Griesmaie

7、r, 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-52Tc700nKN50,000 MDDI of is a factor of 36 higher than that for alkali atoms.

8、MDDI breaks SO(3) symmetry into axial symmetry. Both the sign and the magnitude of MDDI are highly tunable.52Cr, spin-3 Boson J=3, I=0F=3.Higher Hyperfine Spin CondensatesSpin-1: 87Rb, 23Na FM, AFMSpin-2: 85Rb FM, AFM, CyclicSpin-3: 133Cs, 52Cr Biaxial or Uniaxial Spin NematicHo, cond-mat/0511751Mac

9、hida, cond-mat/0511052Santos, cond-mat/0511634Why interesting?Non-Abelian topological defectsBiaxial Nematic Liquid CrystalSpin-2 Cyclic phaseSpin-3: definitely!.conjugate variablesequation of motionclassical HamiltonianMacroscopic Quantum Self Trapping. MQT (macroscopic quantum tunneling): the atom

10、ic 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 ato

11、mic 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: Modelsingle mode approximationcanonical variables Rong Che

12、ng, Jiu-Qing Liang, Yunbo Zhang, J. Phys. B: At. Mol. Opt. Phys. 38 (2005) 25692578mean-field theorytime-dependent variational principlemf = +1 0 -1.Equation of MotionDefineHamiltonian becomes cyclic in the coordinates and .Non-rigid pendulum.time timeSpin-Mixing Dynamics.time timeSpin-Mixing Dynami

13、cs.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 compo