The interaction of a V-type three-level atom with a single mode of electromagnetic field via multi-photon transitions is analytically solved via supersymmetric unitary operator approach. We have constructed the corresponding supersymmetric generators and performed the diagonalization of the Hamiltonian of the atomic system. The time evolution of the atom-field wave functions is derived in an exact form. We studied some quantum effects of the considered system, namely the evolution of both the second-order correlation function of the radiation field and the quasi-probability distribution Q-function is investigated. We conclude that the used method of solution is very simple and can be applied on a variety of similar atomic systems.

通过超对称unit算子方法解析地解决了V型三能级原子与单模电磁场通过多光子跃迁的相互作用。我们构造了相应的超对称生成器，并对原子系统的哈密顿量进行了对角化。原子场波函数的时间演化以精确形式导出。我们研究了所考虑系统的一些量子效应，即辐射场的二阶相关函数和拟概率分布Q函数的演化。我们得出的结论是，所使用的求解方法非常简单，可以应用于各种相似的原子系统。