Jaynes-Cummings模型的一种精确代数解法

An exact algebraic solution of Jaynes-Cummings model

基于Jaynes-Cummings模型的SU(2)群结构,用代数方法求得该模型的时间演化算符。作为该解法的应用,精确给出了初始态为|e,n>情况下系统随时间演化到任一时刻t的状态|ψ(t)>,并求出了系统初始态为|g,α>的情况下,系统在任一时刻t处于激发态的几率P_e(t)。最后讨论了该解法的优越性。

Based on the SU（2） group structure of Jaynes-Cummings model, its time evolution operator were obtained by using the algebraic method. As an application of the solution, the exact result of state of the system evoluting with time at any given time t in the condition that the initial state of system is le, n） was given. Then, the probability Pc（t） of finding the atom in excited state le） at time t was obtained in the condition that the initial state of the system is 1g, a）. The superiority of the solution was discussed lastly.