本项目基于Floquet态理论和多重尺度微扰法研究如何利用周期驱动调控光学系统的Parity-Time（PT）对称性。利用更高阶的近似分析方法揭示和预言一些容易被忽视的新的量子现象，为设计光学器件提供理论依据；探索非线性、维度、周期驱动、PT对称性等相互作用下的系统动力学机制；直观理解PT对称性系统中的几何相位，阐明非厄密系统中的几何相位在耦合光波导中的观测效应和应用。本项目开展的理论研究不仅有助于人们理解周期驱动系统的PT概念，而且在量子技术、光学通信和冷原子领域有着潜在的应用价值。

In this project, we will conduct theoretical study on the topics of how to employ periodic modulations to manipulate Parity-Time (PT) symmetry in optical systems. Our planned projects include: First, we will present an analysis of the driven PT optical system in a more accurate way by a multiple scale asymptotic expansion method. This more accurate method allows us to predict some novel and important physical phenomenon which is easily neglected in the exactly numerical simulations and totally lost in the commonly used high-frequency averaging approximation. Second, we will explore the combined effects of nonlinearity, periodic driving and PT symmetry on the system's dynamics. Third, we will propose some experimental schemes to observe and demonstrate the berry phase and its applications in driven PT optical systems. Our work is of broad interest as the underlying idea may become fruitful in other ?elds, and promises versatile applications in quantum technology and optical device.