自旋轨道耦合偶极玻色-爱因斯坦凝聚体中的孤子及涡旋动力学研究

自旋轨道耦合和偶极玻色凝聚体的实验实现，丰富了超冷原子系统的调控自由度，也拓展了超冷原子气体作为量子仿真和模拟平台的研究视野，为探索孤子及涡旋动力学开辟了新途径。本项目紧密结合国内外冷原子物理最新研究进展，通过李群方法、达布变换法、含时变分法等解析方法，并配合数值模拟，深入探讨自旋轨道耦合、偶极-偶极相互作用以及外势等可调控参数对玻色-爱因斯坦凝聚体中的孤子及涡旋动力学性质的影响。主要内容包括孤子和涡旋存在的参数区间、稳定性、动力学演化及碰撞，具有周期性调制自旋轨道耦合玻色-爱因斯坦凝聚体动力学研究，自旋轨道耦合高自旋玻色-爱因斯坦凝聚体的孤子动力学等。描绘孤子在自旋轨道耦合、偶极-偶极相互作用下呈现出的新奇动力学规律，阐明内外自由度对系统动力学的影响机制，实现对系统动力学的精确量子调控；研究结果将与已知实验相对照，解释实验，为新的实验提供理论依据。

The experimental realizations of spin-orbit coupling and dipolar Bose condensates have enriched the degrees of freedom in ultracold atomic system, broaden the research visual field of ultracold atomic gas as the platform of quantum simulation, and offered us a new avenue to explore the dynamics of soliton and vortex. In this project, combing with the latest research progress of cold atomic physics at home and abroad closely, we will research the effects of adjustable parameters, such as spin orbit coupling, dipole-dipole interaction and external potential, on the dynamics of soliton and vortex in Bose-Einstein condensates by analytical methods including Lie group method, Darboux transformation method, Time-dependent variational method, combining with numerical simulation. The main contents include the parameter range, stability, dynamical evolution and collision of solitons and vortices, the dynamics of Bose Einstein condensate with periodic modulation spin-orbit coupling, the dynamics of soliton in spin-orbit-coupled high spin Bose Einstein condensates,and so on. Moreover, we will describe the novel dynamics of solitons on the affection of spin-orbit coupling and dipole-dipole interaction, expound the influence mechanism of internal and external degrees of freedom on system dynamics, and realize the precise quantum control of system dynamics. The research results will be compared with known experiments, to explain experiments and provide theoretical basis for new experiments.