Study On Ground States And Nonlinear Dynamics Of Ultracold Atom With Spin-orbit-coupling

Ultracold atom,as a new quantum simulation platform,is of great significance inbasic physics research and technology application.This dissertation studies the physical properties of ultracold atoms and its application in precise measurement physics,and closely links the basic theoretical research with the experimental application,aiming at the frontier researches of ultracold atom gases in quantum frequency standard,so as to provide the theoretical basis for practical application.Scientists have long been interested in studying the light-matter interaction,revealing novel quantum phenomenon and designing new quantum states by their peculiar properties.The experimental realization of spin-orbit coupling in ultracold atomic system breaks through the bottleneck that neutral atoms cannot simulate the response of charged particles to external electromagnetic field,which provides the possibility to find new states,and has greater application potential in quantum simulation,quantum information,quantum computing and other areas.Although this dissertation focuses on the physical properties of ultracold atomic gases,it provides theoretical basis for the subsequent study of higher-order effects,including spin-orbit coupling,multiple collision,quantum noise,the interaction between atomic multipole moment and external field,and the impact on the uncertainty and stability of the frequency of cold atomic clocks,and also deepens the understanding of the physical mechanism,to measure the factors accurately and control them effectively.In this dissertation,we study the ground state and nonlinear dynamics of spin-orbit coupled ultracold atoms in detail.Firstly,we consider a Bose–Einstein condensate with spin–orbit coupling and trapped in radially periodic potentials.Based on the Gross-Pitaeviskii equation within mean field theory,we obtain the complete ground state phases of system in global space.For the case that the center of radially periodic potential is a barrier and a potential well,we study the influence of the controllable parameters such as the depth of potential,spin-orbit coupling,and the contact interaction on the ground state of the system in detail,which provides theoretical basis for the further study of the physical properties of ultracold atomic gases in optical lattice.Furthermore,we consider the miscibility-immiscibility transition of a binary ultracold Bose gases with imbalanced population of atoms in harmonic potential.Most previous studies focused on the influence of the parameters such as the atomic interaction,the external potential,there are few studies on the number of atoms.It is found that all the phase diagrams include the miscible,symmetric immiscible,and asymmetric immiscible phases,and there exists a tricritical point where those three different phases merge for the ideal model without intraspecies interactions,and for the ³Na-²³Na mixture and the ⁸⁷Rb-⁸⁷Rb mixture.Inspired by the stabilization of the Bose gases in free space by the time-dependent atomic interaction,we consider a binary pseudospin-1/2 Bose-Einstein condensate with Rashba spin-orbit coupling in two-dimensional free space,and assume that the spin-orbit coupling varies with time periodically.It is found that dynamically stabilized ultracold atom system can be formed with appropriate parameters including ramp schemes and spin-orbit coupling,and its motional trajectory and stability show nontrivial behavior and strong dependence on the force generated by the SOC from time-dependent variational analysis.Finally,we investigate the ring dark solitons in a binary Bose-Einstein condensate with tunable intercomponent interaction.Our results show that in the presence of periodic modulation of the inter-component interaction not only the stability of the ring dark solitons enhanced effectively but also their decaying dynamics and pattern are dramatically affected during the dyamical process.Our results further enrich our knowledge on the dynamics of ring dark solitons in ultracold atomic systems.