随着人造规范场和自旋轨道耦合在费米冷原子体系中的实现，研究自旋轨道耦合这个新的自由度在冷原子体系中所带来的奇异拓扑量子相将具有十分现实的意义。我们计划研究一维连续和晶格体系中自旋轨道耦合所带来的拓扑超流现象和其中存在的Majorana费米子；分析speckle长程无序, 非磁杂质与相互作用等对拓扑超流的影响，以及准无序带来的迁移率边界对Majorana费米子的影响。我们计划利用解析分析和数值求解Bogoliubov de Gennes方程以及严格对角化，数值重整化群等严格的数值方法，通过对能谱,局域态密度,无序参与度等物理量的计算分析得出相应的量子相图, 并进一步分析自旋轨道耦合对自旋-电荷分离以及拓扑淬火带来的影响。以上的理论分析与正在进行的具有自旋轨道耦合的冷原子实验密切相关。相比较于在固体材料中研究拓扑性质, 冷原子体系具有参数高度精确可调等优势。

With the realization of the synthetic gauge field and spin-orbit coupling in ultracold fermionic system, it is of realistic importance to study the novel topological quantum phases brought by this new degrees of freedom. We are planning to study the topological superfluid, and the Majorana fermions in one-dimensional continuum and optical-lattice systems. We are interested in the effects of the long-range speckle disorder, non-magnetic disorder and interactions on the delocalized supefluid and localized topological superfluid. By means of the analytical and numerical methods, like solving the Bogoliubov de Gennes mean-field equations and using the exact diagnolization, and the numerical density-matrix renormalization method, the phase diagram will be obtained by analyzing the energy spectrum, local density of states, and the inverse of disorder participation ratio, etc.The effect of the spin-orbit coupling on spin-charge separation and the novel physics due to topological quench will be further discussed. The above theoretical study is closely relevant to the present cold atomic experiment related to the spin-orbit coupling. Comparing to the study of the topological properties in the solid-state material, the advantage in cold atomic system is that almost all the parameters in the system are precisely adjustable in a large range.