Dynamics Of Spin-Orbit Coupled Spinor Bose-Einstein Condensates

As a macroscopic quantum phenomenon,Bose-Einstein condensation has attracted much attention since its experimental realization in 1995.The controllability of Bose-Einstein condensate(BEC)makes it an ideal platform for the study of topological defects and quantum phase transition.The experimental realization of the artificial spin-orbit(SO)coupling opens a new window for spinor BEC to investigate the topological excitation and novel quantum states,such as skyrmions,nematic phases,and supersolid states.A brief overview of the development process of BEC is given firstly.The basic theory of ideal gas and the Gross-Pitaevskii equation for interacting Boson gas are then introduced,together with the topological structure and the ground-state properties of spinor BEC especially under SO coupling.Later,the time-splitting Fourier spectrum method and Bogoliubov excitation spectrum are described in detail.In chapter 2,the splitting process of a multiply quantized vortex state in a highly oblate BEC in or in the absence of an optical lattice is studied.The splitting pattern shows four-periodicity(six-periodicity)behavior in a square(triangular)optical lattice.The relaxation time and angular momentum are also investigated to explore the properties of splitting.One singly quantized vortex or antivortex can be finally stabilized at the trap center.In chapter 3,the surface excitations,shape deformation,and the formation of persistent current for a Gaussian obstacle potential rotating in a highly oblate BEC are investigated.A vortex dipole can be produced and trapped in the center of the stirrer even for the slow motion of the stirring beam.When the angular velocity of the obstacle is above some critical values,the surface wave excitations would induce remarkable deformation of the condensate shape at the corresponding rotation frequency.After a long enough time,a small number of vortices are found to be either trapped in the condensate or pinned by the obstacle,which provides another way to manipulate the vortex.In chapter 4,we study the dynamics of a quasi-two-dimensional(2D)spin-orbitcoupled ferromagnetic BEC under a linear Zeeman magnetic field disturbed by a moving obstacle.The Bogoliubov excitation spectrums and corresponding critical excitations in different situations are analyzed.The structure of the coreless vortex or antivortex generated by the moving obstacle has been investigated.When the Zeeman field is parallel to the 2D system plane,the vortex cores for the three components of a(an)vortex(antivortex)could be arranged into a line which is vertical to the Zeeman field,and their order would be reversed as the spin-orbit coupling increases.When the Zeeman field is perpendicular to the plane,a skyrmionlike vortex ground state could be induced via spin-orbit interaction even by a static obstacle and thus becomes unique in contrast with the scalar BECs or spinor BECs without spin-orbit coupling.This topological structure is also found to be dynamically stable if the obstacle is moving at a relatively small velocity.In chapter 5,we demonstrate the dynamics of a spin-1 quasi-one-dimensional BEC with Rashba SO coupling in a narrow box trap as an obstacle potential is moving in it.The energy spectrum and the Bogoliubov excitation spectrum are firstly investigated.The dependence of the critical velocity for excitation on the trap geometry and SO coupling is then discussed.When the obstacle moves along the plane wave direction of ground state,a long density belt accompanied by density islands are found ahead the obstacle potential,which are mainly determined by the trap geometry.Under a sufficiently large SO coupling,there exists another velocity threshold for different density excitation.Furthermore,the density belt would be replaced by a series of density islands arranged closely when the obstacle moves against the plane wave direction.In the last chapter,we summarize our work briefly and introduce the prospect of future research.