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Physica Scripta

Effects of Stark shift and decoherence terms on the dynamics of phase-space entropy of the multiphoton Jaynes Cummings model

A.‐S. F. Obada, S. Abdel‐Khalek, Eied Mahmoud Khalil, S. I. Ali

Published Oct 26, 2012• 25 citations
Publisher

Abstract

The time evolution of the Wehrl entropy and Wehrl phase distribution for the multiphoton Jaynes Cummings model, where the dynamics is described by the phase-damped terms, is studied. Analytical and numerical results under certain parametric conditions are obtained by means of which we analyze the influence of dissipation on the dynamics of Husimi Q-function, Wehrl entropy and Wehrl phase distribution for different values of the Stark shift parameter. Our results show that information about the dynamical properties of the system can be obtained through the Wehrl entropy and Wehrl phase distribution from the point of view of phase-space information. An interesting relation between the correlation, Stark shift and decoherence effect is observed.

DOI
10.1088/0031-8949/86/05/055009

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The time evolution of the Wehrl entropy and Wehrl phase distribution for the multiphoton Jaynes Cummings model, where the dynamics is described by the phase-damped terms, is studied. Analytical and numerical results under certain parametric conditions are obtained by means of which we analyze the influence of dissipation on the dynamics of Husimi Q-function, Wehrl entropy and Wehrl phase distribution for different values of the Stark shift parameter. Our results show that information about the dynamical properties of the system can be obtained through the Wehrl entropy and Wehrl phase distribution from the point of view of phase-space information. An interesting relation between the correlation, Stark shift and decoherence effect is observed.
The concept of the classical-like Wehrl entropy is shown to be a very sensitive and informative measure describing the time evolution of a quantum system. Its applications to the Jaynes-Cummings model reveal relevant aspects of the field dynamics. The Wehrl entropy provides a compact one-parameter description giving, among other things, a clear signature for the splitting of the Q function. It gives also a clear indication of the phase randomization of the coherent electromagnetic field states during the interaction with a two-level atom.
The time evolution of the linear entropy of an atom in k-photon Jaynes–Cummings model is investigated taking into consideration Stark shift and Kerr-like medium. The effect of both the Stark shift and Kerr-like medium on the linear entropy is analyzed using a numerical technique for the field initially in coherent state and in even coherent state. The results show that the presence of the Kerr-like medium and Stark shift has an important effect on the properties of the entropy and entanglement. It is also shown that the setting of the initial state plays a significant role in the evolution of the linear entropy and entanglement.
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.
By using the multiphoton Jaynes-Cummings model,the dynamical properties of the field entropy in the system that consists of a two-level atom interacting with a single-mode field via multiphoton transition are studied.The frequency of the field varying with time in the form of u sin wt has been considered.The results show that the time-evolution behavior of the field entropy is modulated by the frequency variation of field using the numerical.The modulation intensity is enchanced as the amplitude u of frequency variation of field increases.When the amplitude u of the time varying fields is larger than a fixed value,the time-evolution behavior of the field entropy will display periodic oscillation behavior.Its oscillation period agrees with the period of frequency varying.It shows that the evolution of field entropy is influenced by the frequency parameters w and u of the field varying with time.
In this paper we consider the influence of phase damping on the Jaynes?Cummings model (JCM) in the presence of the classical laser field. It is shown that for the temporal evolution of the atomic inversion a detuning parameter plays a role in delaying the effect of the damping. Our consideration is also extended to discuss the atomic Wehrl entropy and entropy squeezing. For the case of the marginal distribution, it is noted that the damping factor plays a considerable role in reducing the number of the fluctuations in the function behavior. On the other hand the damping factor removes the phenomenon of squeezing from both quadratures of the entropy squeezing.