旋量玻色-爱因斯坦凝聚中的拓扑缺陷

This project studies the topological defects and dynamical properties of the spinor Bose-Einstein condensates (BECs). Spinor BECs can host rich topological structures due to their internal degree of freedom. We have developed a method to obtain the exact solutions to the coupled nonlinear Gross-Pitaevskii equations which govern the motion of the spinor BECs. The method was extended from one-dimensional to two- and three-dimensional systems. A series of novel quantum states, such as fractioanl vortices, skyrmion lattices, and knots are constructed, which help us to understand the topological structures. We are planning to extend this method to the more complicated F>1 BECs. Furthermore, we will consider the effects of the spin-orbital couplings to explore the structures of monopoles, 3D Skyrion, as well as other more complex knots. Our method is general and can be applied to other nonlinear systems, e.g., the nonlinear Klein-Gordan equations in quantum field theory, to obtain the spatiotemporal skyrmions. The stability and dynamical properties of the topological defects will be investigated by numerical simulations. Special attentions will be payed to the dynamics of the fractional non-Abelian vortices.

本项目研究旋量玻色-爱因斯坦凝聚(BEC)中的拓扑缺陷及其动力学性质。旋量凝聚体由于其内部自由度，因而具有丰富的拓扑结构。我们发展了一种解析方法，可以获得旋量BEC所满足的耦合非线性方程组的精确定态解，将这种解析方法从一维推广到二维和三维系统，得到一系列具有奇异拓扑结构的量子态，比如分数涡旋、skyrmion晶格、纽结等，加深了对这些拓扑缺陷的理解。我们计划将这一方法应用到自旋F>1的复杂旋量系统，并且进一步考虑自旋-轨道耦合的效应，探索诸如单极子、三维Skyrmion、以及其它复杂的纽结结构。我们的方法具有普适性，可以应用于其它的耦合非线性系统，比如量子场论中的非线性克莱因-戈登方程，得到时空Skyrmion孤子。我们还将采用数值方法模拟研究这些拓扑缺陷的稳定性和动力学特性，其中特别关注分数（非阿贝耳）涡旋的动力学性质。

本项目研究了旋量玻色-爱因斯坦凝聚中的拓扑缺陷及相关的物理性质。旋量凝聚体由于其内部自由度，因而具有丰富的拓扑结构和相结构。我们提出了一种新的具有扭结结构的3D dimeron，并研究了它的稳定性和实现条件；对于自旋-轨道耦合的二组分玻色凝聚，研究了孤子结构和流形混合动力学；研究了环形势阱中自旋-1玻色凝聚体的相结构；采用变分序参量的方法研究了光格子中自旋-轨道耦合玻色系统的基态及超固体相。另外，我们还研究了在光格子中操控冷原子的方法，提出利用交变外驱动场实现在一维和高维光格子中有效地定向移动中性原子，为未来的冷原子量子操控打下基础。我们还研究了能带的拓扑性，提出了利用表面声波实现量子化的电荷pumping方法；揭示了在磁性梯子光格子中手征布洛赫振荡与能带拓扑性的关系。