We consider a generalized multi-photon interaction of two collectively two-level atoms with two-mode of electromagnetic field in the presence of Kerr medium and intensity-dependent coupling. We show that this atomic system possesses supersymmetric structure. We solved this system by virtue of supersymmetric unitary transformation. The supersymmetric generators of this atomic system are constructed. The diagonalization of the corresponding Hamiltonian is performed by introducing a supersymmetric unitary transformation. Accordingly, the eigenvalues and eigenfunctions of the Hamiltonian of the atomic system are obtained. The time evolution of the atom–field wave functions is derived in an exact form for two cases of the initial states of the atoms and the field modes. Some quantum effects such as the second-order correlation function, cross-correlation, purity and Husimi Q-function are investigated. The effects of the Kerr medium, detuning parameter, intensity-dependent coupling and multi-photon transition on the evolution of these quantum effects are examined. We conclude that the supersymmetric unitary transformation method is very simple and can be applied to a variety of atomic systems which possess a supersymmetric structure.

中文翻译：

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利用超对称酉变换求解克尔介质中两个两能级原子和双模场的强度相关和多光子哈密顿量

我们考虑了在存在克尔介质和强度相关耦合的情况下，两个共同的两能级原子与两种模式的电磁场的广义多光子相互作用。我们证明了这个原子系统具有超对称结构。我们通过超对称酉变换解决了这个系统。构造了这个原子系统的超对称发生器。相应哈密顿量的对角化是通过引入超对称酉变换来执行的。从而得到原子系统哈密顿量的特征值和特征函数。对于原子的初始状态和场模式两种情况，原子场波函数的时间演化以精确的形式推导出来。一些量子效应，例如二阶相关函数，问-功能进行了调查。研究了克尔介质、失谐参数、强度相关耦合和多光子跃迁对这些量子效应演化的影响。我们得出结论，超对称酉变换方法非常简单，可以应用于各种具有超对称结构的原子系统。