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Journal of Quantum Information Science

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

Published Jan 1, 2014• 1 citation
Publisher

Abstract

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.

DOI
10.4236/jqis.2014.41004

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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 paper, we study the dynamics of the atomic inversion, scaled atomic Wehrl entropy and marginal atomic Q-function for a single two-level atom interacting with SU(1,1) quantum system. We obtain the wave function and system density matrix using specific initial conditions. We examine the effects of different parameter s on the scaled atomic Wehrl entropy, atomic Q-function and their marginal distribution. We observe an interesting monotonic relation between the different physical quantities for different values of the initial atomic position and detuning parameter
We study the dynamics of the atomic inversion, scaled atomic Wehrl entropy, and marginal atomicQ-function for a single two-level atom interacting with a one-mode cavity field taking in the presence of atomic damping. We obtain the exact solution of the master equation in the interaction picture using specific initial conditions. We examine the effects of atomic damping parameter and number of multiphoton transition on the scaled atomic Wehrl entropy, atomicQ-function, and their marginal distribution. We observe an interesting monotonic relation between the different physical quantities in the case of different values of the number of photon transition during the time evolution.
Abstract The effect of nonlinearity, initial atomic state, and different resonance cases on the interaction between nonlinear SU (1, 1) quantum states and a two-level atom is discussed. The optimal behaviours of decoherence, entanglement and quantum coherence are predicted via using the skew information, tomographic entropy, and the relative entropy of coherence, respectively. It is shown that the detuning parameter has a destructive effect on the coherence and consequently on the entanglement if the quantum system is regulated in the ideal SU (1, 1) quantum systems. For the nonlinear SU (1, 1) quantum systems, the ability to suppress the decay of entanglement induced by the detuning may be increased by preparing the initial atomic state in its excited state.
Abstract The effect of nonlinearity, initial atomic state, and different resonance cases on the interaction between nonlinear SU (1, 1) quantum states and a two-level atom is discussed. The optimal behaviours of decoherence, entanglement and quantum coherence are predicted via using the skew information, tomographic entropy, and the relative entropy of coherence, respectively. It is shown that the detuning parameter has a destructive effect on the coherence and consequently on the entanglement if the quantum system is regulated in the ideal SU (1, 1) quantum systems. For the nonlinear SU (1, 1) quantum systems, the ability to suppress the decay of entanglement induced by the detuning may be increased by preparing the initial atomic state in its excited state.
We propose the use of atomic Wehrl entropy associated to the reduced atomic density operator as an entanglement indicator of bipartite systems. This is applied to a two-level system (one single harmonically trapped ion) by taking into account the linear center-of-mass-motional degree of freedom. Detailed analytical and explicit expressions are given, taking into account different configurations. The results show the important roles played by the laser phase and initial state setting in the evolution of the atomic Q-function, atomic Wehrl entropy and marginal atomic Q-function. Our procedure of using atomic Wehrl entropy may be applied to a system with Hilbert space of high dimension.
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.