自旋轨道耦合费米气体的物理性质研究

规范场理论是研究基本粒子相互作用的基本原理。电磁场作为最简单的例子，通过引入标量势和矢量势来描述带电粒子与电磁场之间的耦合。超冷原子作为模拟量子模型的良好实验平台，2009年美国的I.Spielman小组在87^Rb超冷原子体系中，通过利用梯度磁场下光和原子的相互作用实现了模拟人造规范势场。紧接着，山西大学张靖小组和MIT的M.Zwierlein小组都在费米原子气体中实现了自旋轨道耦合。自旋轨道耦合的实现，为在冷原子体系中寻找拓扑态奠定了基础。基于实验的进展，我们拟开展关于自旋轨道耦合费米原子体系的课题研究。我们将在设计的外势场和构型中寻找马约拉纳费米子，并且从时间和空间上寻找量子操控方法。我们还将利用量子光学的手段，设计探测拓扑态的方案，用以区分拓扑态和平庸态。此外，我们还将针对窄Feshbach共振自旋轨道耦合费米气体，研究该体系的拓扑相变。

Gauge theories are fundamental principles in our understanding interactions between elementary particles. Electromagnetism is the simplest example, where the scalar and vector potentials together describe the coupling between charged matter and electromagnetic field. As a good platform of quantum simulation, in 2009, I.Spielman’s group in the US realized synthetic gauge field in 87^Rb atoms system by using interaction between light and atoms with gradient magnetic field. Soon after that, Zhang Jing’s group in Shanxi University and M.Zwierlein’s group in MIT realized spin orbit coupling in Fermi gas respectively. The realization of spin-orbit coupling laid foundation for searching topological state in ultracold system. Based on the progress in experiments, we plan to carry out research on spin-orbit coupling Fermi atoms system. We will search majorana fermions in designed external potentials and configurations, and seek quantum control methods in time and space. We will propose detecting schemes by quantum optics methods to distinguish between topological state and trivial state. In addition, we will investigate topological phase transition for spin-orbit coupling Fermi system near narrow Feshbach resonance.