Quantum Phases And Dynamics Of Spin-orbit-coupled Ultracold Bose Gases

Since the experimental realization of Bose-Einstein condensates(BECs)of alkali metal atoms,great progress has been made in both theory and experiment of cold atom physics,which has become one of the most attractive frontier research fields in contemporary physics.In particular,the first experiment of spin-orbit-coupled ultracold quantum gases was realized by using the artificial gauge field in 2011,which provides a new avenue to further explore the novel quantum states and dynamic properties of many-body and few-body systems.On the other hand,the quantum gases with dipole-dipole interaction(DDI),especially the dipolar BECs,have also attracted great research interest recently.Therefore,it becomes particularly interesting to study the physical relation between the SOC,DDI and the quantum phases,stability and dynamics of multi-component BECs.In this dissertation,by using the meanfield theory,quantum many-body theory and numerical calculation methods,we investigate the influence of SOC,DDI,external potential and rotation on the ground state,topological structure and dynamics of multi-component BECs,and thus reveal the non-trivial quantum phases,topological excitations and dynamic behaviors.Our studies can provide theoretical basis and reference for the future experiments.The main contents of this dissertation are as follows:Firstly,we have investigated the ground-state structures and spin textures of pseudo spin-1/2 BECs with DDI and Rashba SOC in a rotating toroidal trap.A nonlinear sigma model was introduced to establish the accurate mathematical relationship between two pseudospins and to understand the topological structure and physical properties of the system.We have systematically analyzed the combined effects of DDI,SOC,rotation and toroidal trap on the ground-state structure and topological defects of the system,and discussed the relevant physical mechanisms.We presented a set of ground-state phase diagrams as a function of the DDI strength and the ratio between inter-and intra-species interactions.The system can show novel quantum phases and topological excitations including triangular(square)vortex lattice with quantum droplets(QDs),criss-cross vortex string lattice,a half-skyrmion(meron)string,and half-skyrmion-half-antiskyrmion necklace.Secondly,we have developed a phenomenological dissipation model,and investigated the steady-state structures and dynamic properties of pseudo spin-1/2 BECs with Rashba SOC in a rotating quasicrystalline optical lattice(QOL).This phenomenological dissipation model has good prediction power and can well explain the relevant experimental results.The system displays exotic dynamic behaviors.For the rotating case,the system evolves from an initial heliciform-stripe phase into a final visible vortex necklace with a giant vortex and a hidden vortex necklace.Simultaneously,the corresponding spin texture undergoes a transition from a meron-antimeron pair to a half-antiskyrmion necklace.For the case of plane-wave phase without external potential,the 1D and 2D elementary excitation spectrums of the system are studied by deriving and solving the Bogoliubov-de Gennes equation.Furthermore,typical quantum phases of rotating two-component BECs with SOC in different external potentials were summarized.Thirdly,we have investigated the dynamics of kicked pseudo spin-1/2 BECs with Rashba SOC in a 1D tightly confined toroidal trap.The combined effects of SOC,kick strength,kick period,initial phase and contact interaction on the evolution of component density distributions and energy of the system are systematically discussed.For fixed kick strength and kick period,with the increase of SOC,the system dynamics experiences a transition from quasiperiodic motion to modulated quantum beating.When the kick period is an even multiple of π,the system tends to form periodic(quasi periodic)motions such as quantum anti-resonance,quantum beating and Rabi oscillation.When the kick period is an odd multiple or half integer multiple of π,the system mainly shows dynamic localization.For given SOC strength and kick period,the increasing kick strength results in the increase of the energy oscillation amplitude,and the system displays quantum beating behavior.Finally,we have studied the ground-state phases of dipolar antiferromagnetic spin-1 BECs with spin-tensor-momentum coupling(STMC)in 2D QOL.The combined effects of DDI,STMC,SOC,density-density interaction,spin-exchange interaction and QOL on the ground-state structures of the system are systematically discussed.In view of the difference and relationship between quasicrystal optical lattice and harmonic oscillator potential,the results obtained in these two cases were compared and analyzed.When the STMC term is included,with the increase of DDI strength,the density distributions in component 1 and component 3 continuously converge while those in the second component gradually disappear for both the QOL case and the harmonic trap case.Eventually,the ground states of the two systems are ferromagnetic phase with odd petal-like density droplets and that with symmetric stripes,respectively.When the system contains both STMC and SOC terms but without DDI,the ground state of the system is a typical ferromagnetic phase.With the increase of DDI,the ferromagnetic phase gradually evolves into an antiferromagnetic phase.In this context,STMC,SOC and DDI can be effectively applied for quantum state engineering and quantum simulation in ultracold atom and molecule physics and condensed matter physics.