基于超冷原子系统的高维拓扑物质态的理论研究

Ultracold atoms trapped in optical lattices nowadays are widely recognized as a powerful quantum simulator for mimicking a wide range of systems originally stemming from condensed-matter physics. Meanwhile, searching topological states of matter has now become a forefront of current research in condensed-matter physics. The project proposed here will study how to employ ultracold atoms to simulate, manipulate and detect various exotic high-dimensional topological states of matter, including three-dimensional topological insulators and semimetals. In particular, this project will focus on studying simulation and detection of high-dimensional topological states of matter with lower-dimensional optical lattice, the influence of the interaction between atoms on topological states, and the topological properties of high-dimensional Floquet topological states of matter and its quantum simulation with ultracold atoms. Different from the conventional methods simulating topological states by realizing artificial magnetic field and spin-orbital coupling, our method only requires tuning a particular parameter in the optical lattice system. So, this project not only provides a conceptually simple method to study high-dimensional topological states, but also opens an experimentally feasible route to realize topological states with ultracold atoms system.

超冷原子系统现今已经被广泛的作为一种量子模拟器，用来研究凝聚态物理中的许多物理现象。当前凝聚态物理中的一个前沿方向是寻找各种奇异的拓扑物质态。本项目提出如何基于囚禁在光晶格中的超冷原子体系来模拟，调控以及探测各种奇异的高维拓扑物质态，包括三维拓扑绝缘体和拓扑半金属。本项目主要集中研究(1)基于维度约化的方法来利用低维光晶格体系模拟和探测高维拓扑物质态；(2)原子之间的相互作用引入后对拓扑物质态的影响；(3)高维Floquet拓扑物质态的拓扑特性和超冷原子量子模拟。不同于通常的利用激光诱导原子隧穿实现人工磁场和自旋轨道耦合的方法，来模拟拓扑物质态，本项目采用的方法仅需要周期性的调控光晶格的某一参数。因此，本项目的研究不仅为高维拓扑物质态的理论研究提供了一种简单的理论方法，也为超冷原子体系模拟拓扑物质态提供了一种可行的实验途径。

基于光和原子相互作用体系来产生和调控拓扑物态，不仅可以帮助人们加深对拓扑保护的多体量子态的理解，也可以进一步促进拓扑量保护的量子计算机的研发。本项目主要研究超冷原子，人造原子以及光子量子模拟器中产生和调控各种奇异拓扑物态的新技术，包括拓扑绝缘体和拓扑半金属物态。具体的研究内容包括(1) 如何在超导量子比特体系里实现和探测拓扑物态；如何基于这些拓扑物态来实现拓扑保护的量子信息传递；量子纠缠是如何影响拓扑保护的量子化泵浦；(2) 如何在有原子相互作用的超冷原子量子模拟器中的产生和调控拓扑磁振子物态；(3) 如何在光波导体系里面实现和探测光子拓扑绝缘体，以及研究如何利用拓扑物态对光量子态的拓扑保护来进行量子信息处理。本项目的研究不仅可以为在光和原子相互作用体系中产生和调 控拓扑物态提供了新的技术手段，也能为拓扑保护的量子信息处理提供了新的路线。