中文摘要：

根据光和频产生过程的动力学演化总是保持闲置光和信号光的光子数之和守恒这一性质,构建出了光学谐振腔中频率转换系统的含时不变量.并运用此不变量及Lewis-Riesenfeld量子不变量方法,在失谐情形下,对这一双模量子化电磁场耦合系统相应的薛定谔方程进行了求解.得到了系统随时间演化的量子态和演化算符的显示解析表达式.此解对于进一步研究系统各种量子性质是有用的.

英文摘要：

The time-dependent invariant of a quantum frequency conversion system in an optical cavity is found from the simple observation that the dynamical evolution of a sum-frequency generation process preserves the total number of the idler photons and the signal photons involved in the process. By using this invariant and the Lewis-Riesenfeld quantum invariant approach, the Schrt~dinger equation for the coupled system of the two quantized modes of the electromagnetic field is solved under detuned condition. The explicitly analytical formulae of the quantum states and the evolution operators of the system are obtained. It should be useful for further studies on the various quantum properties of the quantum system.