We consider a four-level double V-type atom with two closely-separated top levels and two closely-separated lower levels interacting with a single mode field via multi-photon processes and in the presence of Kerr medium. We show that this atomic system possesses supersymmetric structure and construct its supersymmetric generators. We diagonalize the Hamiltonian of this system using supersymmetric unitary transformation and obtain the corresponding eigenstates and eigenvalues. The atom–field wave functions are obtained when the atom and the field mode are initially in two different cases. The evolution of both the quasi-probability distribution Q-function and the Mandel Q-parameter of the field are studied when the input field is in a coherent state. The influence of the Kerr medium and the detuning parameters on the behavior of these quantum effects is analyzed. The results show that they play a prominent role on the Poissonian statistics of the field. Also, the Kerr medium changes the behavior of the quasi-probability distribution Q-function. We end with discussion and conclusions.

中文翻译：

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超对称酉变换求解四能级双V型原子系统

我们考虑一个四级双五具有两个紧密分离的顶层和两个紧密分离的较低水平的-型原子通过多光子过程和在克尔介质的存在下与单模场相互作用。我们证明了这个原子系统具有超对称结构并构造了它的超对称发生器。我们使用超对称酉变换对该系统的哈密顿量进行对角化，得到相应的本征态和本征值。当原子和场模式最初处于两种不同情况时，获得原子场波函数。准概率分布的演变问-函数和曼德尔问-当输入场处于相干状态时研究场的参数。分析了克尔介质和失谐参数对这些量子效应行为的影响。结果表明，它们在该领域的泊松统计中发挥着突出的作用。此外，克尔介质改变了准概率分布的行为问-功能。我们以讨论和结论结束。