周期调制量子格点体系的拓扑物态及其表征

Topological physics, a tight combination of topology and physics, mainly investigates non-local physical properties of systems under continuous transformation. It not only is of great fundamental interests in quantum geometric phases, quantum hall effects and non-local quantum entanglement, etc, but also has potential applications in quantum materials, quantum devices and quantum computing, etc. Attribute to their ultralong coherence time and high controllability, ultracold atoms in optical lattices have been an excellent platform for exploring topological states. Regarding the periodically modulated quantum lattice systems, this project will study the key problems on topological transport, topological multipole moments and detecting topological invariants within ultracold atoms in optical lattices. The main research contents include: (1) high efficient topological transport and detecting large Chern number in one dimensional periodically modulated optical lattices. (2) novel topological states of multipole moments and their characterization in high dimensional periodically modulated optical lattices. This project will provide theoretical direction for exploring topological transport, novel topological states of multipole moments and detecting topological invariants.

拓扑物理学是拓扑学与物理学的有机结合，主要研究特定体系在连续变形下保持不变的非局域物性。它不仅在量子几何相位、量子霍尔效应和非局域量子纠缠等领域有重要的基础研究价值，而且在量子材料、量子器件和量子计算等方面有广泛的应用价值。归功于其稳固的量子相干性和高度的可控性，光学晶格中的超冷原子体系已成为研究拓扑物态的一个新平台，特别是为探测拓扑不变量和探索非平衡拓扑物态等方面提供了新的机遇。针对周期调制量子格点体系，本项目将研究光学晶格中超冷原子体系的拓扑输运、拓扑多极矩以及拓扑不变量的探测等关键问题。主要研究内容包括：（1）一维周期调制光晶格中超冷原子体系的高效拓扑输运与大陈数探测；（2）高维周期调制光晶格中超冷原子体系的新奇多极矩拓扑物态及其表征。本项目将为探索周期调制体系的拓扑输运、新奇多极矩拓扑物态和拓扑不变量的测量等提供理论导向。

本项目按计划顺利完成，达到了预期的研究目标。本项目主要研究周期调制量子格点体系中的新奇拓扑物态及其刻画，探索高阶拓扑角态以及拓扑输运新方案。具体包括：提出利用布洛赫振荡实现无需均匀能带填充的拓扑泵浦新方案；探索相互作用对布洛赫振荡协助的拓扑泵浦的影响；将布洛赫振荡协助的拓扑输运推广到二维；提出利用无序的周期调制体系实现纠缠态的制备和分发；提出相互作用诱导的拓扑泵浦；理论提出并实验观测非傍轴效应诱导的非对称拓扑输运；理论提出并实验观测非傍轴效应诱导的拓扑泵浦中的朗道-齐纳隧穿，理论提出并实验观测到拓扑角态；同时，我们提出了动力学绕数、约化陈数、矢量陈数的新概念，发展了在无序体系计算实空间绕数的新方法；发现了相互作用诱导的拓扑边缘态、辐射束缚拓扑边缘态等新现象；这些理论结果和方法有助于理解非平衡拓扑物态的刻画、调控和应用。