用不变量方法解具有非线性场和原子与场非线性耦合的Jaynes-Cummings模型(英文)

Invariant method for solving Jaynes-Cummings model with field nonlinearity and strong atom-field coupling

采用Lewis-Riesenfeld不变量方法研究了具有非线性场和任意形式原子与场相互作用的Jaynes-Cummings模型.该模型由于具有超对称代数结构,因此其Hamiltonian量可用超对称算符的线性组合表示.在算符N′的本征值子空间,用生成元算符构造出系统的不变量后,利用不变量方法求得了系统的一般波函数和时间演化算符,同时也计算了原子布居数和光子数的时间演化表达式.

Single-mode Jaynes-Cumrnings model with any forms of intensity-dependent atom-field coupling and the nonlinearity of the quantized photonic field are studied by using the invariant method. Due to the fact that this model possessing a supersymmetric structure, an invariant is constructed by the supersymmetric generators in the eigenspace of the conserved supersymmetric generator N＇. We then obtain the general wave function, time evolution operator and the time evolution expressions of both the atomic inversion and the photon number for the system.