Abstract We introduce a generalized atomic system of N -level
(N−2) V -configuration atom, with integer
N>2 , interacting with a single mode field in the presence of multi-photon transitions and Kerr medium. We solve this system by virtue of supersymmetric (SUSY) unitary transformation and show that it possesses SUSY structure and define its SUSY generators and perform the diagonalization of the corresponding Hamiltonian. We construct the eigenstates and eigenvalues of this system when the atom and the field mode are initially prepared in two different cases. We investigate some quantum aspects of the considered system, namely, the time evolution of the atomic population inversion of the system, the evolution of the Mandel M -parameter and the distribution Husimi Q -function of the field. We show the influence of the detuning and Kerr medium parameters on their behavior for some different N , where e.g., for
N=5 we obtain the results of the five-level triple V -type system. We end with some discussions and conclusion.
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.
Analytical description for a Su(2)-quantum system interacting with a damped Su(1, 1)-cavity, which is filled with a non-linear Kerr medium, is presented. The dynamics of non-classicality of Su(1, 1)-state is investigated via the negative part of the Wigner function. We show that the negative part depends on the unitary interaction and the Kerr-like medium and it can be disappeared by increasing the dissipation rate and the detuning parameter. The phase space information of the Husimi function and its Wehrl density is very sensitive not only to the coupling to the environment and the unitary interaction but also to the detuning as well as to the Kerr-like medium. The phase space information may be completely erased by increasing the coupling to the environment. The coherence loss of the Su(2)-state is investigated via the Husimi Wehrl entropy. If the effects of the detuning parameter or/and of the Kerr-like medium are combined with the damping effect, the damping effect of the coupling to the environment may be weaken, and the Wehrl entropy is delayed to reach its steady-state value. At the steady-state value, the phase space information and the coherence are quickly lost.