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Transylvanian Review

Some entanglement aspects of two-two level atoms interacting with three modes of electromagnetic fields in finite trio coherent state

Ali S.I, T Emam, T Salah

Published Jan 1, 2018• 1 citation
OpenAlex

Abstract

AIM: The aim of  this contribution, was to investigate the interaction of two two-level atoms with three-modes of radiation field in finite trio coherent state. The field-field and the atom-field interaction are taken into account. Methods: In this paper, We obtained an exact solution of the wave function in the Schrodinger picture by using some canonical transformation. Which used to study some entanglement phonomena. Results: Some statistical aspects to describe the system Hamiltonian are calculated. The temporal evolution of the atomic inversion, the entropy squeezing, variance squeezing and scaled atomic Wehrl entropy phenomena are discussed. Discussion: This paper concludes that the  entanglement degree measure (EDM) between subsystem are investigated for cosiderable system. The results shown that all these phenomena are controlled of entanglement degree by trio finite state parameters and photon number operators.

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AIM: The aim of  this contribution, was to investigate the interaction of two two-level atoms with three-modes of radiation field in finite trio coherent state. The field-field and the atom-field interaction are taken into account. Methods: In this paper, We obtained an exact solution of the wave function in the Schrodinger picture by using some canonical transformation. Which used to study some entanglement phonomena. Results: Some statistical aspects to describe the system Hamiltonian are calculated. The temporal evolution of the atomic inversion, the entropy squeezing, variance squeezing and scaled atomic Wehrl entropy phenomena are discussed. Discussion: This paper concludes that the  entanglement degree measure (EDM) between subsystem are investigated for cosiderable system. The results shown that all these phenomena are controlled of entanglement degree by trio finite state parameters and photon number operators.
In this paper, we investigate the entanglement of the interaction of three modes of radiation field with moving and unmoving two-level atom. The time evolution of the von Neumann entropy, entropy squeezing and marginal atomic Wehrl entropy is investigated. The marginal atomic Wehrl entropy as squeezing indicator of the entanglement of the system is suggested. The results beacon the important roles played by both the atomic motion parameters in the evolution of entanglement, entropy squeezing and marginal atomic Wehrl entropy. Using special values of the photon number of transition and atomic motion parameter, the entanglement phenomena of sudden death and long living entanglenment can be appeared. The results show that there is atomic motion monotonic harmonization atomic Wehrl entropy (WE). It is illustrated that the amount of the above-mentioned phenomena can be tuned by controlling the evolved parameters appropriately.
In this paper, we study the interaction between an effective two-level atom and a three-mode field. The atom and the field are initially in the excited state and finite dimensional trio-coherent state, respectively. For this sytem, we investigate the atomic inversion, the von Neumann entropy, and the atomic Wehrl entropy. We show that there is a connection between all of these quantities. Also, we prove that the atomic Wehrl entropy exhibits a temporal evolution similar to the von Neumann entropy. It is observed that the Stark shift parameter plays an important role on the evolution of these quantities.
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.
We consider the interaction between a two-level atom and a quantum system that consists of three electromagnetic fields. An analytic solution is provided for the wave function of a pairwise mutual interaction between a two-level atom and three modes using a frequency converter. SU(2) group generators are used to describe these field mode interactions. In addition, a canonical transformation is employed in order to convert the Hamiltonian model into a Jaynes–Cumming-like model, which is used to solve the Schrödinger equation. Statistical properties related to the atomic inversion, entanglement, and squeezing phenomena are discussed. Superstructure patterns and partial disentanglement, as well as squeezing swapping between quadratures, are displayed for selected parameters.
In this paper, we study the interaction between a two-level atom and a three types of nonlinear interaction of two modes, two as a degenerate two photon and the third of the converter form. The solution to the Schrodinger equation is obtained exactly under a certain specific condition. By using this solution we discuss numerically the atomic inversion, the degree of entanglement through the atomic Wehrl entropy, the geometric phase entropy for chosen values of the detuning and coupling parameters. Statistical properties of the investigated system is discussed by the evolution of the Mandel parameter.
We study in this paper the dynamics of two electromagnetic (EM) fields and their entanglement in the interaction with a 3-level atom (Λ-configuration). We investigate the interaction when initially one of the fields is in a single mode coherent state, and the other one is in a Fock(number) state. We have calculated the mean photon numbers of the fields and their entanglement by means of the fields entropy as a measure of it. The results show the synchronization between entanglement beats and collapses-revivals of the fields, which cause the field in the Fock state (noncoherent) to behave coherently during the interaction. Also the results offer a way to generate coherent fields and achieve any desired degree of entanglement with specified dynamics via controlling the parameters of the atomic system.