Investigation On The Ground States And The Dynamics Of Multi-Component Spin-Orbit-Coupled Bose-Einstein Condensates

The experimental realization of Bose-Einstein condensates(BECs)is a milestone breakthrough in modern physics.It has opened a new era in the study of macroscopic quantum many-body phenomena.Especially in recent years,spin-orbit coupling(SOC)in ultracold atomic gases has been realized experimentally,which has attracted great interest on the study of spin-orbit-coupled quantum gases.This new and controllable artificial SOC not only offers new possibilities for quantum simulations of spin quantum Hall effect,topological superconductors and topological superfluids,but also provides a new direction for exploring exotic quantum phenomena and novel states of matter in the fields of ultracold atomic and molecular physics and condensed matter physics.By using quantum many-body theory,mean-field theory,and numerical calculations as well as simulations,we investigate the ground-state structures and dynamic properties of multi-component spin-orbit-coupled BECs.Some interesting quantum phases,novel topological excitations and unique dynamic properties have been revealed respectively.The present work provides theoretical basis and reference for relevant cold atom experiments.The main contents of this dissertation are as follows:Firstly,we have investigated the ground-state structures of dipolar spin-orbit-coupled BECs in a toroidal trap.Using the imaginary-time propagation method based on the Peaceman-Rachford algorithm,we have obtained the ground-state wave function of the system by numerically solving the coupled Gross-Pitaevskii equations.Combined effects of DDI and SOC on the ground states of the system have been discussed.A ground-state phase diagram has been obtained as a function of the SOC and DDI strengths.As two new degrees of freedom,the DDI and SOC can be used to obtain the desired ground-state phases and to control the phase transition between various ground states.In particular,the system displays exotic topological structures and spin textures.Secondly,we have studied the topological excitations of rotating two-component BECs with Rashba-Dresselhaus spin-orbit coupling(RD-SOC)in a two-dimensional(2D)optical lattice plus a 2D harmonic trap.The effects of SOC,rotation frequency and interparticle interaction on the ground-state structures and spin textures of the system have been investigated for the 2D isotropic RD-SOC case,the 2D anisotropic RD-SOC one,and the 1D RD-SOC one,respectively.It is shown that the system favors novel vortex patterns,spin textures and skyrmion excitations including an exotic skyrmion-half-skyrmion lattice(skyrmion-meron lattice),a complicated meron lattice,a skyrmion chain,and a Bloch domain wall.Thirdly,we have investigated the topological excitations of rotating SU(2)as well as SU(3)spin-orbit-coupled spin-1 BECs with ferromagnetic spin interaction in an in-plane quadrupole field.The effects of the multicomponent order parameters,in-plane quadrupole field,SU(2)SOC,SU(3)SOC,spin-exchange interaction,and rotation on the topological structure of the system have been analyzed and discussed.In the absence of rotation,we find that the spin-1 BEC with SU(2)SOC experiences a transition from a coreless polar-core vortex to a singular polar-core vortex when the quadrupole field strength increases.Whereas for the case of SU(3)SOC,the enhancing quadrupole field can lead to the transition of the system from a vortex-antivortex cluster state to a polar-core vortex state.Without rotation but with fixed quadrupole field,when the SU(2)SOC strength increases,the system transforms from a central Mermin-Ho vortex into a criss-crossed vortex-antivortex string lattice.By contrast,increasing SU(3)SOC strength can induce a phase transition from a vortex-antivortex cluster into a bending vortex-antivortex chain.In particular,for the rotating case,we have given a phase diagram with respect to the quadrupole field strength and the SU(2)SOC strength.It is shown that the rotating system supports four typical quantum phases:rotationally symmetric vortex necklace,diagonal vortex chain cluster,single diagonal vortex chain,and few vortex state.Furthermore,the system favors novel spin textures and skyrmion configurations including a criss-crossed half-skyrmion-half-antiskyrmion(meron-antimeron)lattice,a bending half-skyrmion-half-antiskyrmionchain,a skyrmion-half-skyrmion necklace,a symmetric half-skyrmion lattice,and an asymmetric skyrmion-half-skyrmion lattice.Finally,we have investigated the dynamics of spin-orbit-coupled F=1 BECs in a rotating toroidal trap.In order to study the dynamics,the system is rotated suddenly after the system has been prepared to the ground state.Thus we may obtain the steady structure when the rotating spin-orbit-coupled F=1 BECs reaches the equilibrium state,and can study the dynamics of the whole time evolution of the system.It is shown that during the early evolution period there are drastic turbulent oscillation and ghost vortices on the surface of the component densities due to the surface wave excitations.With the time evolution,ghost vortices enter the atom cloud and become visible vortices which display irregular distribution.Next,the component density distributions gradually become more regular.At the same time,the phase defects gradually gather to trap center to form a multi-quantum vortex.For given parameters,the system finally forms a steady and symmetrical giant vortex structure,where the giant vortices in the three components differ by one quantum number in turn.