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Results in Physics

On the degenerate and non-degenerate two-photon interaction between a two-level atom and a quantized two-modes: Entanglement and Pancharatnam phase

Eman M. A. Hilal

Published Jan 1, 2017• 3 citations
Publisher

Abstract

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.

DOI
10.1016/j.rinp.2017.09.017

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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.
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.
In this paper, we present the interaction between a five-level [Formula: see text]-configuration atom and a two-mode quantized field in the presence of the damping with the nonlinearity. According to the generalized nonlinear Jaynes–Cummings model (JCM) and the analytical solution of the Schrödinger equation, the general formula of the wave function for this system under special conditions, where the atom (the field) is initially prepared in the excited state (coherent state), has been found. Under some particular conditions, the five-level [Formula: see text]-type atom can be reduced to the three-level [Formula: see text]-type atom. Some physical aspects of the atom-field entangled state showing the entanglement degree, such as the field entropy. Moreover, we evaluate some of their non-classical statistical aspects such as atomic inversion. The effects of the physical parameters such as a Kerr medium, detuning parameter and the intensity-dependent coupling on the temporal behavior of the latter mentioned non-classical statistical aspects have been explored. We show that by choosing the evolved parameters in the interaction process, each of the above non-classical statistical features can be treated. We found that the parameters have an important influence on the properties of these phenomena.
In this paper we introduce a new Hamiltonian which represents the interaction between a two-level atom and two modes of an electromagnetic field injected simultaneously within a cavity. Field–field interaction of the parametric converter type is taken into consideration. Under certain conditions the solution to the Schrödinger equation is obtained exactly. By using this solution we discuss numerically the degree of entanglement through the entropy of the field, for chosen values of the detuning and coupling parameters.
Abstract In this paper, we consider the interaction between two two-level atoms and a two-mode binomial field with a general intensity-dependent coupling regime. The outlined dynamical problem has explicit analytical solution, by which we can evaluate a few of its physical features of interest. To achieve the purpose of the paper, after choosing a particular nonlinearity function, we investigate the quantum statistics, atomic population inversion and at last the linear entropy of the atom-field system which is a good measure for the degree of entanglement. In detail, the effects of binomial field parameters, in addition to different initial atomic states on the temporal behavior of the mentioned quantities have been analyzed. The results show that, the values of binomial field parameters and the initial state of the two atoms influence on the nonclassical effects in the obtained states through which one can tune the nonclassicality criteria appropriately. Setting intensity-dependent coupling function equal to 1 reduces the results to the constant coupling case. By comparing the latter case with the nonlinear regime, we will observe that the nonlinearity disappears the pattern of collapse-revival phenomenon in the evolution of Mandel parameter and population inversion (which can be seen in the linear case with constant coupling), however, more typical collapse-revivals will be appeared for the cross-correlation function in the nonlinear case. Finally, in both linear and nonlinear regime, the entropy remains less than (but close to) 0.5. In other words the particular chosen nonlinearity does not critically affect on the entropy of the system.
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 the present paper we consider a nonlinear interaction between two electromagnetic field modes and a two-level atom. A new Hamiltonian model is introduced to represent such an interaction, where three coupling parameters are involved. We assume that the two-level atom interacts with each mode separately as well as with the two modes nonlinearly. Thus degenerate and non-degenerate processes are considered. Using a suitable canonical transformation and integrability condition the system is reduced to a single mode case. The density matrix is calculated and used to study the photon distribution, the atomic occupation probabilities, the von Neumann entropy and the entropy squeezing.