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

Results in Physics

Entropy squeezing and atomic Wehrl density for the interaction between SU(1,1) Lie algebra and a three-level atom in presence of laser field

A.‐S. F. Obada, Nawal A. Alshehri, Eied Mahmoud Khalil, S. Abdel‐Khalek, H. F. Habeba

Published Sep 13, 2021• 14 citations
Publisher

Abstract

In this paper, we investigate a system Hamiltonian describing the interaction between SU(1,1) quantum system and a three-level atom in Λ configuration in presence of a classical external field. Appropriate conical transformations are performed for the atom matrices. The analytical solution of the model is obtained by using the Schrödinger equation. Then the atomic density operator of the proposed system is obtained. The effect of the detuning parameter and the classical external field on the atomic levels occupation, atomic entropy squeezing, variance squeezing, atomic Q-function and atomic Wehrl density are investigated for certain chosen values of the classical field parameter and the detuning parameter. The obtained results has a potential applications to topics related to ideal and real laser.

DOI
10.1016/j.rinp.2021.104759

Related papers

Linear entropy and squeezing of the interaction between two quantum system described by su (1, 1) and su(2) Lie group in presence of two external terms

M. Sebawe Abdalla, Eied Mahmoud Khalil, A.‐S. F. Obada +2 more

A Hamiltonian, that describes the interaction between a two-level atom (su(2) algebra) and a system governed by su(1,1) Lie algebra besides two external interaction, is considered. Two canonical transformations are used, which results into removing the external terms and changing the frequencies of the interacting systems. The solution of the equations of motion of the operators is obtained and used to discuss the atomic inversion, entanglement, squeezing and correlation functions of the present system. Initially the atom is considered to be in the excited state while the other systems is in the Perelomov coherent state. Effects of the variations in the coupling parameters to the external systems are considered. They are found to be sensitive to changing entanglement, variance and entropy squeezing.

AIP Advances•Jan 1, 2017•25 citations

Quantum scheme for N-level atom interacting with a two two-level atom: Atomic Fisher information and entropy squeezing

Eman M. A. Hilal, Sadah Abdullah Alkhateeb, S. Abdel‐Khalek +2 more

In this work, we introduce a model of a two-atom interacting with a multi-level atom governed by su(2) Lie algebra in the presence of external classical field. The influence of the classical field on the system is discussed in detail for certain values for the classical terms. The atomic density matrix of the proposed system is obtained. The dynamical behavior of the atomic Fisher information as an indicator of the nonlocal correlation between a two-atom and su(2) field is discussed. Moreover, we examine the effect of classical field on the evolution of entropy squeezing and the geometric phase induced between the initial and final state of the proposed system. The results outlined some important phenomena as sudden death and sudden birth of entanglement in presence of the classical terms is observed through the dynamics of atomic Fisher information in the presence of classical field for the large number of levels.

Alexandria Engineering Journal•Feb 26, 2020•9 citations

Quantum treatment for three waves mutually interacting with a single two-level atom

M. Sebawe Abdalla, A.‐S. F. Obada, Eied Mahmoud Khalil +1 more

In this paper, we study the interaction between a two-level atom and three types of interaction of three quantized modes of a quantized field, namely: two parametric amplifiers and a frequency converter. The SU(1, 1) algebra is used to represent the combination of the interacting modes. A canonical transformation is used to cast the Hamiltonian into a tangible form. The solution of the Schrodinger equation for the wave function is given analytically. Using this solution we discuss numerically the atomic inversion, the degree of entanglement through the linear entropy and the variance entropy for chosen values of the detuning and coupling parameters. It is shown that the atomic inversion can be controlled through the rotation angle α and the atomic angle θ as well as the Bargmann index k. The degree of entanglement is affected by both α and θ in addition to the ratio ϵ. Variance squeezing is sensitive to changes in the atomic and the phase angles besides the parameter k. For entropy squeezing, the effective parameters are α, θ and k.

Laser Physics•Aug 22, 2014•7 citations

A nonlinear interaction between SU(1,1) quantum system and a three-level atom in different configurations with damping term

A.‐S. F. Obada, M. M. A. Ahmed, Mohamed Abu-Shady +3 more

Abstract The effect of nonlinear medium and phase damping is investigated on an atom of three levels in different forms interacting with the SU(1,1) Lie algebra. The SU(1,1) system starts the interaction from the Perelomov coherent state, while the atom starts the interaction from excited-most state. The time dependent wave function is calculated by using the Schrödinger equation. The density matrix is obtained. The influences of damping, nonlinearity (Kerr-like medium), Perelomov coherent parameter and the Bargmann index on some non-classical properties, such as: revivals-collapses phenomenon, entanglement and atomic variables squeezing, are investigated.

Physica Scripta•Feb 1, 2021•8 citations

Entanglement Quantifier Based on Atomic Wehrl Entropy for Non-Linear Interaction between a Single Two-Level Atom and SU(1,1) Quantum System

S. Abdel‐Khalek, Manal Al-Quthami, M. M. A. Ahmed

In this paper, we study the dynamics of the atomic inversion, scaled atomic Wehrl entropy and marginal atomic Wehrl density for a single two-level atom interacting with SU(1,1) quantum system. We obtain the expectation values of the atomic variables using specific initial conditions. We examine the effects of different parameters on the scaled atomic Wehrl entropy and marginal atomic Wehrl density. We observe an interesting monotonic relation between the different physical quantities for different values of the initial atomic position and detuning parameter.

Journal of Quantum Information Science•Jan 1, 2014•1 citation

Influence of classical field on entanglement and photon statistics of n-level atom interacting with a two two-level atom

Hammad Alotaibi, Eied Mahmoud Khalil, S. Abdel‐Khalek +1 more

In this study, we consider three interacting atoms, one of them represented by N-level atom based on SU(2) Lie algebra and the other represented by a two two-level atom in presence of the external field. The effect of the external field on the dynamics of the proposed system is discussed in detail for certain values for the external field. The dynamical expression of the observable operators is obtained by using the Heisenberg equation of motion. The general solution via solving Schrodinger equation is obtained. The fidelity and concurrence formula as a measure of entanglement between two two-level atom are calculated and discussed in detail. We explore the sudden death and sudden birth phenomena with and without the presence of external field. Finally, we compare the results of the fidelity, concurrence and second-order correlation function for some values of the initial state and the external field parameters.

Thermal Science•Jan 1, 2020•2 citations
In this paper, we investigate a system Hamiltonian describing the interaction between SU(1,1) quantum system and a three-level atom in Λ configuration in presence of a classical external field. Appropriate conical transformations are performed for the atom matrices. The analytical solution of the model is obtained by using the Schrödinger equation. Then the atomic density operator of the proposed system is obtained. The effect of the detuning parameter and the classical external field on the atomic levels occupation, atomic entropy squeezing, variance squeezing, atomic Q-function and atomic Wehrl density are investigated for certain chosen values of the classical field parameter and the detuning parameter. The obtained results has a potential applications to topics related to ideal and real laser.
A Hamiltonian, that describes the interaction between a two-level atom (su(2) algebra) and a system governed by su(1,1) Lie algebra besides two external interaction, is considered. Two canonical transformations are used, which results into removing the external terms and changing the frequencies of the interacting systems. The solution of the equations of motion of the operators is obtained and used to discuss the atomic inversion, entanglement, squeezing and correlation functions of the present system. Initially the atom is considered to be in the excited state while the other systems is in the Perelomov coherent state. Effects of the variations in the coupling parameters to the external systems are considered. They are found to be sensitive to changing entanglement, variance and entropy squeezing.
In this work, we introduce a model of a two-atom interacting with a multi-level atom governed by su(2) Lie algebra in the presence of external classical field. The influence of the classical field on the system is discussed in detail for certain values for the classical terms. The atomic density matrix of the proposed system is obtained. The dynamical behavior of the atomic Fisher information as an indicator of the nonlocal correlation between a two-atom and su(2) field is discussed. Moreover, we examine the effect of classical field on the evolution of entropy squeezing and the geometric phase induced between the initial and final state of the proposed system. The results outlined some important phenomena as sudden death and sudden birth of entanglement in presence of the classical terms is observed through the dynamics of atomic Fisher information in the presence of classical field for the large number of levels.
In this paper, we study the interaction between a two-level atom and three types of interaction of three quantized modes of a quantized field, namely: two parametric amplifiers and a frequency converter. The SU(1, 1) algebra is used to represent the combination of the interacting modes. A canonical transformation is used to cast the Hamiltonian into a tangible form. The solution of the Schrodinger equation for the wave function is given analytically. Using this solution we discuss numerically the atomic inversion, the degree of entanglement through the linear entropy and the variance entropy for chosen values of the detuning and coupling parameters. It is shown that the atomic inversion can be controlled through the rotation angle α and the atomic angle θ as well as the Bargmann index k. The degree of entanglement is affected by both α and θ in addition to the ratio ϵ. Variance squeezing is sensitive to changes in the atomic and the phase angles besides the parameter k. For entropy squeezing, the effective parameters are α, θ and k.
Abstract The effect of nonlinear medium and phase damping is investigated on an atom of three levels in different forms interacting with the SU(1,1) Lie algebra. The SU(1,1) system starts the interaction from the Perelomov coherent state, while the atom starts the interaction from excited-most state. The time dependent wave function is calculated by using the Schrödinger equation. The density matrix is obtained. The influences of damping, nonlinearity (Kerr-like medium), Perelomov coherent parameter and the Bargmann index on some non-classical properties, such as: revivals-collapses phenomenon, entanglement and atomic variables squeezing, are investigated.
In this paper, we study the dynamics of the atomic inversion, scaled atomic Wehrl entropy and marginal atomic Wehrl density for a single two-level atom interacting with SU(1,1) quantum system. We obtain the expectation values of the atomic variables using specific initial conditions. We examine the effects of different parameters on the scaled atomic Wehrl entropy and marginal atomic Wehrl density. We observe an interesting monotonic relation between the different physical quantities for different values of the initial atomic position and detuning parameter.
In this study, we consider three interacting atoms, one of them represented by N-level atom based on SU(2) Lie algebra and the other represented by a two two-level atom in presence of the external field. The effect of the external field on the dynamics of the proposed system is discussed in detail for certain values for the external field. The dynamical expression of the observable operators is obtained by using the Heisenberg equation of motion. The general solution via solving Schrodinger equation is obtained. The fidelity and concurrence formula as a measure of entanglement between two two-level atom are calculated and discussed in detail. We explore the sudden death and sudden birth phenomena with and without the presence of external field. Finally, we compare the results of the fidelity, concurrence and second-order correlation function for some values of the initial state and the external field parameters.