本项目着重研究量子非线性参量过程在量子调控、量子信息处理中的所涉及的理论问题。量子非线性参量过程在不同物理分支中均有着重要的理论和应用研究价值，如量子化学中的原子分子转化过程，非线性光系统中的参量下转换等。然而由于实验条件的限制，对这一非线性过程在量子效应增强情况下的模拟和调控研究还处于初步。近年来光力和冷原子系统中的理论和实验进展，为模拟和调控这一机制提供了理想的平台。本项目中，我们结合在量子光学中的研究背景，具体在光腔杂糅系统及冷原子系统中，考虑与量子非线性参量过程相关的物理机制的实现和调控，并以此为基础,利用具体理论分析和数值相结合的方法研究其中相关物理过程的调控，量子相变，及动力学等。进一步地，我们将在理论探索的基础上考察这一效应在量子光学和量子信息处理中的相关应用问题。

This project focuses on theoretical problems related to quantum nonlinear parametric process encountered in quantum simulation and quantum information process. Quantum nonlinear parametric process plays important roles within different branches of physics, ranging from coherent transfer between atoms and molecula, parametric down-conversion of photons, and et.al.. However, due to the limitation of experimental constraints, detailed investigation of this effect related to quantum simulation in quantum regime remains largely unexplored in previous studies. The recent experimental and theoretical progresses in opto-mechanics and cold atoms provides new platforms of investigation these effects in highly controllable manner. Based on our previous research background in quantum optics and atomic physics, in this project, we focus on the investigation of various physics effects related to quantum nonlinear parametric process, including its manipulation in hybrid cavities, or cold atoms, various phase transition physics, and its dynamics. Finally, based on these investigations, the relevant applications in quantum optics and quantum information processing will also be considered.