Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Modern Physics Letters A

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

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

Published Mar 4, 2021• 5 citations
Publisher

Abstract

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.

DOI
10.1142/s0217732321500607

Related papers

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

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

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.

Modern Physics Letters A•Aug 30, 2021•3 citations

A generalized N-level $$(N-2)$$ V-configuration atomic system interacting with a single-mode field in the presence of k-photon transition and Kerr medium: SUSY approach

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

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.

Optical and Quantum Electronics•Dec 3, 2025•0 citations

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

R. A. Zait

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.

Scientific Reports•Jan 8, 2026•0 citations

Supersymmetry as an Algebraic Approach to the Jaynes-Cumming Model with Stark Shift and Kerr-Like Medium

Rasha M. Farghly, Mohamed Abdal-Mubark, Sara Mohamed

Supersymmetry arguments are used to derive the wave function of a two-level atom interacts with a single mode cavity field through a multi-photon transition in the presence of a Kerr-like medium and Stark term. The supersymmetric operators related to the atomic system are introduced to diagonalize the Hamiltonian with a canonical transformation technique. Also, the eigenvalues spectrum and eigenvectors are exactly given.

Assiut University Journal of Multidisciplinary Scientific Research•May 1, 2023•1 citation

Dynamics of Kerr-like medium with two-mode intensity-dependent cavity fields

Sudha Singh, C. H. Raymond Ooi

Abstract The dynamics of an effective two-level atom coupled to two-mode intensity-dependent quantized cavity fields via a ladder process in the presence of a Kerr medium has been investigated. Eigenfunctions and eigenvalues of the Hamiltonian of the interacting system have been obtained using a unitary transformation method. The cavity field statistics and non-classical properties are investigated numerically through second-order correlation functions. The effect of detuning and the Kerr medium on the non-classical features of the atom-field state has been analyzed. We find that the presence of Kerr non-linearity enhances the non-classical correlation between the correlated beams at short time intervals and increases antibunching at short time intervals.

Laser Physics•Nov 29, 2018•3 citations

Entropy of a general three-level atom interacting with a two mode

A.‐S. F. Obada, Sadek Ahmed Hanoura, A. A. Eied

A model of a three-level atom in the Λ-configuration interacting with a two-mode field under a multi-photon process is considered. The effects of the mean photon numbers, detuning, Kerr-like medium parameters and various forms of the intensity-dependent coupling functional are considered. Analytical expressions for the time unitary operator, the density operator and the final state of the system are analyzed via the framework of the dressed states. The atom is prepared in its upper excited state, and the fields are prepared in binomial states. The general conclusions reached are illustrated by numerical results displaying the effects of photon-number, detuning and nonlinearities of both the field and intensity-dependent atom–field couplings.

Laser Physics•Jan 11, 2013•20 citations
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.
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.
A generalized N-level (N−2)(N-2)(N−2) V-configuration atomic system interacting with a single-mode field in the presence of k-photon transition and Kerr medium: SUSY approach
Abstract We introduce a generalized atomic system of N -level (N−2)(N-2)(N−2) V -configuration atom, with integer N>2N>2N>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=5N=5N=5 we obtain the results of the five-level triple V -type system. We end with some discussions and conclusion.
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.
Abstract The dynamics of an effective two-level atom coupled to two-mode intensity-dependent quantized cavity fields via a ladder process in the presence of a Kerr medium has been investigated. Eigenfunctions and eigenvalues of the Hamiltonian of the interacting system have been obtained using a unitary transformation method. The cavity field statistics and non-classical properties are investigated numerically through second-order correlation functions. The effect of detuning and the Kerr medium on the non-classical features of the atom-field state has been analyzed. We find that the presence of Kerr non-linearity enhances the non-classical correlation between the correlated beams at short time intervals and increases antibunching at short time intervals.
A model of a three-level atom in the Λ-configuration interacting with a two-mode field under a multi-photon process is considered. The effects of the mean photon numbers, detuning, Kerr-like medium parameters and various forms of the intensity-dependent coupling functional are considered. Analytical expressions for the time unitary operator, the density operator and the final state of the system are analyzed via the framework of the dressed states. The atom is prepared in its upper excited state, and the fields are prepared in binomial states. The general conclusions reached are illustrated by numerical results displaying the effects of photon-number, detuning and nonlinearities of both the field and intensity-dependent atom–field couplings.