周期驱动量子系统中的拓扑物态及其输运性质研究

Periodically driven quantum systems possess many exotic nonequilibrium states of matter, such as quantum time crystals and Floquet topological phases. The latter are formed by eigenstates of the system’s time evolution operator over a complete driving period. Compared with equilibrium topological states of matter, nonequilibrium Floquet states are usually subject to distinct symmetry classifications and characterized by topological invariants that are different from their static counterparts. Furthermore, they possess anomalous edge states under open boundary conditions, whose topological properties are characterized by new types of bulk-boundary correspondence. Due to their robustness, fast-tunability and flexibility, Floquet topological states have shown huge potential in a broad range of applications, such as quantum simulation, quantum control, and quantum information processing..In recent years, higher-order and non-Hermitian topological insulators have become focuses of investigation in a wide range of research areas, such as quantum physics, condensed matter physics and optics. However, the Floquet counterparts of these exotic topological states of matter have been rarely explored. The discovery of these higher-order and non-Hermitian Floquet states will help us to advance the classification of nonequilibrium topological phases, and recognizing the potential applications of these new phases. By designing the periodic driving fields coupling to particles in lattices, we plan to search for higher-order and non-Hermitian Floquet topological states of matter with large topological invariants and high adjustability. We further uncover the topological properties and bulk-boundary (corner) correspondence of the found higher-order/non-Hermitian Floquet topological phases by investigating their quasienergy spectrum, symmetry classification, topological invariants and topological edge (corner) states. To establish connections with experiments, we study the dynamical and transport properties of the found Floquet topological states with the help of quantum pumps, scattering matrix, and Green’s function methods. Finally, we discuss the potential applications of these higher-order/non-Hermitian Floquet topological states in areas such as quantum transport and quantum information science.

量子系统在周期含时外场驱动下能产生多种新奇的非平衡物态，例如时间晶体和Floquet拓扑物态。后者由系统在一个驱动周期中演化算符的本征态构成。与静态系统中的拓扑物态相比，Floquet物态具有独特的对称分类和拓扑不变量、反常的体-边缘态对应关系，并因其高速便捷的可调性而在量子模拟、量子调控、量子信息等领域具有重大的应用潜力。近年来，更高阶和非厄米拓扑绝缘体成为了拓扑物态研究中的热点问题。对与之相应的Floquet物态的发现将有助于扩展对非平衡物相的拓扑分类，并提升其应用潜力。申请人拟通过设计作用于量子系统的周期驱动场，来寻找具有大拓扑量子数且拓扑性质高度可调的更高阶与非厄米Floquet拓扑物态，探索其准能带结构、对称分类、几何相位、拓扑不变量、拓扑边缘态、体-边缘对应关系，揭示其体态和边缘态的量子输运与动力学特征，并讨论这些物态的实验实现和在量子输运、量子信息等领域中的潜在应用。

量子系统在周期含时外场驱动下能产生多种新奇的非平衡物态，如时间晶体和Floquet拓扑物态。后者由系统在一个驱动周期中演化算符的本征态构成。与静态系统中的拓扑物态相比，Floquet物态具有独特的对称分类和拓扑不变量、反常的体-边缘态对应关系，并因其高速便捷的可调性而在量子模拟、量子调控、量子信息等领域具有重大应用潜力。近年来，更高阶、非厄米和准周期拓扑相成为拓扑物态研究中的热点问题。对与之相应的Floquet物态的探索有助于扩充对非平衡物相的对称与拓扑分类，并提升其应用潜力。..在资助期间，项目主持人围绕非厄米Floquet拓扑物态、高阶Floquet拓扑物态、非厄米准晶和动力学量子相变开展了系统的理论研究，发现了非厄米Floquet系统中的拓扑绝缘体、拓扑超导体、拓扑准晶、二阶拓扑绝缘体等新型非平衡物相，揭示了这些物相的对称分类、拓扑表征、体-边缘对应关系和非厄米趋肤效应，提出了基于平均手性位移和时间平均自旋纹理来刻画这些物相的动力学方案，构建了非厄米拓扑物态和动力学量子相变之间的联系，并探索了不同驱动方案对Floquet系统中动力学量子相变的影响。基于这些发现，项目主持人在Physical Review A、Physical Review B、Physical Review Research、New Journal of Physics、Scipost Physics等SCI期刊发表科研论文20余篇，被引用280余次（Google Scholar）。相关成果在理论上扩展了驱动与开放系统中非平衡物态与相变的可能存在形式与分类框架，在应用上为量子计算方案的设计、拓扑物态的制备与调控和新型量子器件的研发提供了新思路。