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The European Physical Journal Plus

Supersymmetric approach to the interaction of a V-type three-level atom with a single mode of electromagnetic field via multi-photon transitions

N. H. Abd El-Wahab, R. A. Zait

Published Aug 1, 2020• 3 citations
Publisher
DOI
10.1140/epjp/s13360-020-00620-4

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A generalized atomic system of N-level atom within the framework of ($$N-1$$) JCM interacting with one-mode field solved via supersymmetric approach

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We study a generalized atomic system of N-level atom within the framework of ([Formula: see text]) JCM interacting with one-mode field in the presence of Kerr medium and multi-photon transitions. We solve this system via supersymmetric approach. We show that the system possesses supersymmetric structure and construct its supersymmetric generators and their properties and diagonalize its Hamiltonian using supersymmetric unitary transformation. The atom-field eigenfunctions and eigenvalues of the system are obtained in two different cases of the initial conditions of the atom and the field mode. The evolution of the quasi-probability distribution Q-function and the atomic inversion is investigated for one case of the initial conditions. Their graphical results are presented and discussed for three special cases of the level number N, namely, [Formula: see text] which represents the three-level Λ-type system, [Formula: see text] which represents the four-level m-configuration system, and [Formula: see text] which represents the five-level double Λ-type system. The influence of the detuning and Kerr medium parameters on the behavior of these nonclassical quantities is presented graphically and discussed and found that they have important effects. We end by discussion and conclusions and some features and comments.

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Intensity-dependent and multi-photon Hamiltonian of two two-level atoms and two-mode field in a Kerr medium solved by virtue of supersymmetric unitary transformation

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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.

Modern Physics Letters A•Mar 4, 2021•5 citations
A generalized atomic system of N-level atom within the framework of (N−1N-1N−1) JCM interacting with one-mode field solved via supersymmetric approach
We study a generalized atomic system of N-level atom within the framework of ([Formula: see text]) JCM interacting with one-mode field in the presence of Kerr medium and multi-photon transitions. We solve this system via supersymmetric approach. We show that the system possesses supersymmetric structure and construct its supersymmetric generators and their properties and diagonalize its Hamiltonian using supersymmetric unitary transformation. The atom-field eigenfunctions and eigenvalues of the system are obtained in two different cases of the initial conditions of the atom and the field mode. The evolution of the quasi-probability distribution Q-function and the atomic inversion is investigated for one case of the initial conditions. Their graphical results are presented and discussed for three special cases of the level number N, namely, [Formula: see text] which represents the three-level Λ-type system, [Formula: see text] which represents the four-level m-configuration system, and [Formula: see text] which represents the five-level double Λ-type system. The influence of the detuning and Kerr medium parameters on the behavior of these nonclassical quantities is presented graphically and discussed and found that they have important effects. We end by discussion and conclusions and some features and comments.
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.