Wang Huan-Yu, Zhao Xiao-Ming, Zhuang Lin, Liu Wu-Ming
Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, People's Republic of China.
Department of Physics, Institute of Theoretical physics, University of Science and Technology Beijing, Beijing, 100083, People's Republic of China.
J Phys Condens Matter. 2022 Jul 5;34(36). doi: 10.1088/1361-648X/ac7c4e.
Floquet engineering plays a key role in realizing novel dynamical topological states. The conventional Floquet engineering, however, only applies to time-periodic non-dissipative Hermitian systems, and for the open quantum systems, non-Hermitian processes usually occur. So far, it remains unclear how to characterize the topological phases of time-periodic open quantum systems via the frequency space Floquet Hamiltonian. Here, we propose the non-Floquet theory to solve the problem and illustrate it by a continuously time-periodic non-Hermitian bipartite chain. In non-Floquet theory, a temporal non-unitary transformation is exercised on the Floquet states, and the transformed Floquet spectrum restores the form of the Wannier-Stark ladder. Besides, we also show that different choices of the starting points of the driving period can result in different localization behavior, effects of which can reversely be utilized to design quantum detectors of phases in dissipative oscillating fields. Our methods are capable of describing topological features in dynamical open quantum systems with various driving types and can find its applications to construct new types of dynamical topological materials.
弗洛凯工程在实现新型动态拓扑态方面起着关键作用。然而，传统的弗洛凯工程仅适用于时间周期非耗散厄米系统，而对于开放量子系统，通常会出现非厄米过程。到目前为止，尚不清楚如何通过频率空间弗洛凯哈密顿量来表征时间周期开放量子系统的拓扑相。在此，我们提出非弗洛凯理论来解决该问题，并通过一个连续时间周期非厄米二分链进行说明。在非弗洛凯理论中，对弗洛凯态进行时间非酉变换，变换后的弗洛凯谱恢复了万尼尔 - 斯塔克阶梯的形式。此外，我们还表明驱动周期起始点的不同选择会导致不同的局域化行为，其效果可反过来用于设计耗散振荡场中的相位量子探测器。我们的方法能够描述具有各种驱动类型的动态开放量子系统中的拓扑特征，并可应用于构建新型动态拓扑材料。
