高阶拓扑量子物态自从2016年发现以来吸引了广泛的关注，成为了凝聚态以及超冷原子物理等领域的一个研究热点。由于这是一个刚兴起的领域，目前，虽然实验和理论方面都有一定的进展，但仍然有更丰富的物理值得发现。另外，超冷原子实验虽然在拓扑观测方面取得了很大的进展，但在高阶拓扑量子物态方面仍没有实验进展。本项目基于申请人以往在拓扑物态方面的研究，拟围绕超冷原子气体高阶拓扑量子物态展开以下理论研究：（1）探索超冷原子中实现和观测高阶拓扑量子物态可行的实验方案；另外，通过紧束缚近似方法，探索新的高阶量子物态和它们的性质。（2）通过含时演化的方法，研究高阶拓扑量子物态的非平衡动力学；另外，探索调控该拓扑物态的方法；（3）通过平均场方法，研究高阶拓扑量子物态能带中玻色爱因斯坦凝聚体的非线性性质。该项目的研究将拓展和加深人们对高阶拓扑相的认识和理解，并为超冷原子实现和观测高阶拓扑相奠定理论基础。

Since their discovery in 2016, higher order topological matters have attracted considerable attention ranging from condensed matter physics to ultracold atomic gases. Even though the field has seen a rapid progress in both experiments and theory, many interesting and significant physics phenomena deserve to explore. While ultracold atomic gases have made significant progress in observing topological matters, higher order topological phases have not been observed there. Based on our previous research, this proposal will investigate the higher order topological phenomena in ultracold atomic gases. Specific projects include: (1) We will explore feasible experimental proposals for observing the higher order topological matters in cold atoms. In addition, we will explore new higher order topological phases and their properties by tight-binding methods. (2) We will study the non-equilibrium dynamics of the higher order topological matters by time evolution of the Schrodinger equation. Moreover, we will explore the method to control the topological matters. (3) We will use the mean field approximation to study the nonlinear properties of Bose-Einstein condensates in the higher order topological band. This proposal aims to lay the theoretical foundation for experimental observation of higher order topological phenomena in cold atoms, to deepen our understanding on these phenomena and discover new higher order phenomena.