原子的自旋不被外场极化、而具有自旋自由度的玻色爱因斯坦凝聚体称为旋量玻色爱因斯坦凝聚体。由于其自旋自由度的引入，旋量玻色爱因斯坦凝聚体在弱磁场测量、量子模拟等领域具有广泛的应用前景。本项目根据当前旋量玻色爱因斯坦凝聚体实验研究的最新进展，选择自旋1、自旋2的旋量玻色爱因斯坦凝聚体为主要研究对象，通过理论分析和数值模拟等，拟集中开展以下三方面的研究（1）通过考虑自旋轨道耦合效应等，探索旋量玻色爱因斯坦凝聚体中的新奇拓扑激发以及研究其稳定性; (2)利用统计映射Gross-Pitaevskii方程，研究有限温度下旋量玻色爱因斯坦凝聚体的非平衡动力性质及拓扑缺陷的形成，发现新的物理现象和物理机制；（3）研究旋量玻色爱因斯坦凝聚体混合物的基态和拓扑激发。本项目将加深人们对旋量玻色爱因斯坦凝聚体中各种新颖量子激发以及其产生机理的认识。

The spinor Bose-Einstein condensate (BEC), where the spin of the atoms is not frozen by the external potential, has the spin degree of freedom. The spinor BEC has extensive application prospects on the measurement of the weak magnetic field, simulation of the quantum system, etc, due to the introduction of the spin degree of freedom. This project bases on the latest development of the experiments on spinor BEC, and chooses the spin-1 and spin-2 BEC as the main investigated object. With the numerical simulation and theoretical analysis, we will focus on the following three subjects: (1) by considering the spin-orbit coupling and others, we study the exotic topological excitations as well as their stability in the spinor BEC. (2) by solving the stochastic projected Gross-Pitaevskii equation numerically, we investigate the non-equilibrium dynamics and the formation of topological defects in spinor BEC with the non-zero temperature, and we aim to discover some new physics and the mechanism. (3) we study the ground state and the topological excitation in the mixtures of the multi-component spinor BEC. This project will enhance our understanding of various exotic quantized excitations and their generating mechanism in the spinor BEC.