Four-level double V-type atomic system solved by virtue of supersymmetric unitary transformation

Abstract

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.