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Chinese Journal of Physics

Entropy and Entanglement of the Nonlinear Jaynes-Cummings Model

A.‐S. F. Obada, M. M. A. Ahmed, F. K. Faramawy, Eied Mahmoud Khalil

Published Feb 1, 2004• 18 citations
OpenAlex

Abstract

We have studied the influences of the Stark shifts and a Kerr-like medium on the degree of entanglement and the spectrum, for a system in which a two-level atom interaction occurs with a single mode of an electromagnetic field two-photon processes. The analytical expression for the spectrum is obtained from the finite double-Fourier transform of the two-time field correlation function. It is shown that the Stark shift effect changes the quasiperiod of the field entropy and, hence, the entanglement between the particle and the field.

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We have studied the influences of the Stark shifts and a Kerr-like medium on the degree of entanglement and the spectrum, for a system in which a two-level atom interaction occurs with a single mode of an electromagnetic field two-photon processes. The analytical expression for the spectrum is obtained from the finite double-Fourier transform of the two-time field correlation function. It is shown that the Stark shift effect changes the quasiperiod of the field entropy and, hence, the entanglement between the particle and the field.
In this study, we use the quantum entropy to measure the degree of entanglement in the time development of the two-level particle (atom or ion). The influence of atomic coherence on the evolution of the field quantum entropy and the entanglement of the atom-field in the two-photon process, taking into account the level shifts produced by the Stark effect with an additional Kerr-like medium for one mode, are examined. The exact results are employed to perform a careful investigation of the temporal evolution of the entropy. It is shown that the evolution of the field entropy is very sensitive to the relative phase of the particle and field. The effect of both the Stark shift and the presence of a Kerr-like medium on the entropy is analyzed. The results show that the effect of the Kerr-like medium and the Stark shift changes the quasiperiod of the field entropy evolution and the entanglement between the particle and the field. The general conclusions reached are illustrated by numerical results.
An entangled state, as an essential tool in quantum information processing, may be generated through the interaction between light and matter in cavity quantum electrodynamics. In this paper, we study the interaction between two two-level atoms and a two-mode field in an optical cavity enclosed by a medium with Kerr nonlinearity in the presence of a detuning parameter and Stark effect. It is assumed that the atom–field coupling and third-order susceptibility of the Kerr medium depend on the intensity of the light. In order to investigate the dynamics of the introduced system, we obtain the exact analytical form of the state vector of the considered atom–field system under initial conditions which may be prepared for the atoms (in a coherent superposition of their ground and upper states) and the fields (in a standard coherent state). Then, in order to evaluate the degree of entanglement between the subsystems, we investigate the dynamics of the entanglement by employing the entanglement of formation. Finally, we analyze in detail the influences of the Stark shift, the deformed Kerr medium, the intensity-dependent coupling, and also the detuning parameter on the behavior of this measure for different subsystems. The numerical results show that the amount of entanglement between the different subsystems can be controlled by choosing the evolved parameters appropriately.
The interaction between a two-level atom and a single-mode field in the k -photon Jaynes—Cummings model (JCM) in the presence of the Stark shift and a Kerr medium is studied. All terms in the Hamiltonian, such as the single-mode field, its interaction with the atom, the contribution of the Stark shift and the Kerr medium effects are considered to be f -deformed. In particular, the effect of the initial state of the radiation field on the dynamical evolution of some physical properties such as atomic inversion and entropy squeezing are investigated by considering different initial field states (coherent, squeezed and thermal states).
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 interaction between a one-mode electromagnetic field and a two-photon Jaynes-Cummings model in the presence of the classical homogenous gravitational field with an added Kerr-like medium when the atom is prepared initially in the momentum eigenstate. The wave function is calculated by using the Schrodinger equation for a coherent electromagnetic field and an atom in the excited state. The influence of the Kerr-like medium and the classical homogenous gravitational field on the properties of the entropy of the field is examined. Keywords: two-level atom; Kerr-like medium; gravitational field; entropy .
In this communication, two-mode nonlinear coherent states are reviewed and special cases are given. Starting from a three-level atom coupled to two modes of radiation with any form of nonlinearities of the two-mode fields, we derive a Raman-coupled effective Hamiltonian by a unitary transformation, evaluated perturbatively in coupling constants. We use the quantum entropy to measure the degree of entanglement in the time development of an effective two-level atom interacting with two-mode nonlinear-coherent states. The results show that the nonlinearity effect yields the superstructure of atomic Rabi oscillations and the effect of the Stark shift changes the quasiperiod of the field entropy evolution and entanglement between the particle and the field. A possible experimental test of a new effect is proposed.