腔QED系统中基于Lyapunov控制的量子态操控

基于腔量子电动力学（腔QED）系统设计有效的控制场来操控量子态演化不仅对探索量子力学基本问题具有重要意义，而且对量子信息处理也有实际的应用价值。本项目拟在腔QED系统中采用Lyapunov控制理论设计控制场，快速制备具有高保真度的量子态和快速执行量子逻辑门。首先考虑一个三能级原子囚禁在一个腔中的模型，研究该系统的动力学特性。然后通过Lyapunov控制理论提出有效的方法设计控制场加速系统演化以及实现布居数的完美转移。接着，进一步通过结合Lyapunov控制方法和脉冲逆向设计方法来操控腔中多个原子。基于此，然后研究多个腔多个原子构成的多体复杂系统中多粒子纠缠态快速制备以及快速执行多比特量子逻辑门等量子信息处理。本项目将详细讨论腔场耗散，原子自发辐射以及实验参数波动对系统演化的影响。因此该项目对深入研究场-物质相互作用的基础物理有重要促进作用。

Based on cavity quantum electrodynamic (QED) system, design effective control field to manipulate quantum state is not only important for exploration of fundamental issues of quantum mechanics, but also have practical applications in quantum information processing. In this project, we will employ Lyapunov theory to design control fields for fast generation of target quantum state and fast implementation of quantum logic gates in cavity QED systems. We first consider a three-level atom trapped in a cavity, and investigate the dynamics of such a cavity QED system. Then, based on Lyapunov control theory, we propose an effective method to design control field for speeding up the evolution of system and realizing perfect population transfer. We further combine the Lyapunov control method and pulse-reverse engineering to manipulate multiple atoms in a cavity. On this basis, we will study the generation of multiparticle entangled state, fast implementation of quantum logic gates and other quantum information processing, in a more complex systems which consist of multiple cavities and atoms. In this project, we will also consider the influences of the decay of cavity, spontaneous emission of atom and variation of system parameters. This project will play an important role in the study of the basic physics of field-matter interaction.