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Communications in Theoretical Physics

Properties of Entropy and Entanglement of Two-Mode Nonlinear Coherent States

Mahmoud Abdel‐Aty, Tarek M. El-Shahat, A.‐S. F. Obada

Published Dec 15, 2002• 5 citations
Publisher

Abstract

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.

DOI
10.1088/0253-6102/38/6/715

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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.
Starting from a three-level atom coupled to two modes of a radiation field, we derive a Raman-coupled Hamiltonian. The exact results are employed to carry out a careful investigation of the temporal evolution of the entropy. A factorization of the initial density operator is assumed, with the privileged field modes being in a coherent state. We invoke the mathematical concept of the maximum variation of a function to construct a measure for entropy fluctuations. It is shown that when the individual modes of the field are far detuned from the intermediate atomic level, there is a dynamical Stark shift induced by the Kerr-like medium. The results show that the Kerr effect creates the superstructure of atomic Rabi oscillation and changes the quasiperiod of the field entropy evolution and entanglement between the atom and the field. The dynamic behavior of the mean atomic level occupation probabilities are investigated numerically as functions of time. A number of novel phenomena are discovered and discussed.
In this paper, we use the quantum field entropy to measure the degree of entanglement in the time development of a three-level atom interacting with two-mode fields including all acceptable kinds of nonlinearities of the two-mode fields. This model describes a very general situation in which the system admits two detuning parameters and includes an arbitrary form of the nonlinearity of the two modes. It is shown that when the individual modes of the field are detuned far from the intermediate atomic level, the dynamic Stark shift is induced by the nonlinear medium. The results show that the non-linearity effect yields the superstructure of atomic Rabi oscillations and changes the quasiperiod of the field entropy evolution and entanglement between the atom and the field. The general conclusions reached are illustrated by numerical results.
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.
The problem of a two-level atom interacting with single mode cavity field is considered, however, the optical cavity is filled with new structure of a generalized nonlinear Stark shift via Ξ configuration. One starts with a three-level trapped atom interacting with the quantized field of center of mass motion thus a Hamiltonian for one-phonon process with nonlinearities is derived. Through the elimination of the intermediate level by using the adiabatic elimination method, we generate a new structure of effective Hamiltonian for a two-level atom with a nonlinear Stark shift. The temporal evolution of the atomic inversion is studied, we introduce that in the presence of the Stark shift parameter the atom leaves in a maximal entangled sate. We use the von Neuman entropy to measure the degree of entanglement between the atom and the field. After adding the nonlinear Stark shift the system never reaches the pure state. Also we study the Q-function for obtaining more information in phase space for this system. These aspects are sensitive to changes in the Stark shift parameter. The results shows that the effect of the nonlinearity in the Stark shift 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.
We investigate the evolution of the atomic quantum entropy and the atom–field entanglement in a system of a Λ-configuration three-level atom interacting with a two-mode field with additional forms of nonlinearities of both the field and the intensity-dependent atom–field coupling. With the derivation of the unitary operator within the frame of the dressed state and the exact results for the state of the system we perform a careful investigation of the temporal evolution of the entropy. A factorization of the initial density operator is assumed, considering the field to be initially in a non-correlated two-mode squeezed coherent or binomial state. The effects of the mean photon number, detuning, Kerr-like medium and the intensity-dependent coupling functional on the entropy are analysed.