Study On Soliton Dynamics In Ultracold Atom With Spin-Orbit-Coupling

Ultracold atom,as a new quantum simulation platform,is of great significance in basic physics research and applied science.The study of ultracold atoms will not only deepen our understanding of the basic concepts,but also promote the intersection and integration of atomic and molecular physics,optics physics,condensed matter physics,quantum optics and other disciplines.At the same time,ultracold atoms also have broad application prospects in the fields of atomic clocks,precise measurement,quantum computation and quantum information.The experimental realization of spinorbit coupling in Bose-Einstein condensation(BEC)provides a platform for the study of novel macroscopic quantum phenomena in gauge field,which is another significant breakthrough in the field of cold atoms after Feshbach resonance and optical lattice.Studying the singularity and novel quantum states of spin-orbit coupled Bose-Einstein condensates and their quantum regulation has become one of the hot topics in the cross-field of ultracold atomic physics and quantum information.Firstly,this thesis gives a brief introduction to the realization,research status and development trend of spin-orbit coupling in cold atomic condensates.The spin-orbit coupling has important influence on the ground state,dynamics,and excited states of the condensate,and also plays an important role in realizing the spin Hall effect and topological insulator.And a brief analyze the research of the spin-orbit coupling in the optical lattice atomic clock.Compared to the realization of spin-orbit coupling in alkali metal atoms,the optical clock system breaks the limitation of life in traditional quantum systems and shows many advantages in the study of spin-orbit-coupled physics.Secondly,the numerical analysis of the two-component ring dark solitons and the vortex pairs formed after decay is carried out in detail.By solving the timecoupled Gross-Pitaevskii equation,the dynamic of vortices followed by the collapse of ring dark solitons in a two-component Bose-Einstein condensate have been studied in detail.It was found that there exsists half-quantum vortex pair in such a twocomponent system compared to the scalar gas,in which the nucleus of the vortexantivortex pair in one component is occupied by the other component.In the case where the initial conditions are the same,the half-quantum vortex increases the time for completing one cycle of motion.In addition,there is a critical depth in the system above which the vortex pair first moves in the vertical direction.Then the vortex pair exhibits complex dynamic behaviors such as recombination.For two ring dark solitons with different initial depths,numerical results show that the number of vortices generated by the split is determined by shallow solitons,and the direction of vortex movement is determined by deeper one.Finally,the properties of the ground state and vortex structure in two-component dipolar Bose-Einstein condensate are also studied.The effects of adjustable parameters,such as dipole-dipole interaction,contact interactions,and rotational frequency on the ground-state properties and vortex structure are studied numerically for harmonic potential plus optical lattice and harmonic plus quartic potential,respectively.Our numerical results show that these controllable parameters significantly affect the number of vortices and its related vortex structure in such a system.