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Journal of Optics B Quantum and Semiclassical Optics

Entropy and phase properties of isotropic coupled oscillators interacting with a single atom: one-and two-photon processes

Mahmoud Abdel‐Aty, M. Sebawe Abdalla, A.‐S. F. Obada

Published Apr 5, 2002• 39 citations
Publisher

Abstract

We investigate a modified model of the Jaynes–Cummings model involving multimode and multiphoton processes. The interaction part of the Hamiltonian consists of a two-level atom interacting with two isotropic fields injected simultaneously within a perfect cavity. The equation governing the system are solved and the relevant wave functions for one-and two-photon processes are obtained. In the two-photon case we invoked the SU (1, 1) Lie algebra to reach this solution. The density matrix elements are calculated and the entropy and the atomic inversion are computed. The influence of the mean photon numbers and the detuning on these quantities are studied. Comparison between the present model and the usual nonlinear model is given. The phase properties are also discussed.

DOI
10.1088/1464-4266/4/3/367

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We investigate a modified model of the Jaynes–Cummings model involving multimode and multiphoton processes. The interaction part of the Hamiltonian consists of a two-level atom interacting with two isotropic fields injected simultaneously within a perfect cavity. The equation governing the system are solved and the relevant wave functions for one-and two-photon processes are obtained. In the two-photon case we invoked the SU (1, 1) Lie algebra to reach this solution. The density matrix elements are calculated and the entropy and the atomic inversion are computed. The influence of the mean photon numbers and the detuning on these quantities are studied. Comparison between the present model and the usual nonlinear model is given. The phase properties are also discussed.
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.
From a quantum information point of view we study the entropy squeezing of a two-level atom interacting with two modes with intensity-dependent coupling. The Hamiltonian we consider consists of all acceptable forms of nonlinearities. A definition of squeezing is presented for this system, based on information theory. The utility of the definition is illustrated by examining squeezing in the information entropy of a two-level atom in the presence of a nonlinear medium. We examine the influence of the nonlinear interaction, the atomic coherence and the detuning parameter on the properties of the entropy and squeezing of the atomic variables. It is shown that features of the quantum entropy are influenced significantly by the kinds of intensity-dependent atom-field coupling and the nonlinearities of the two-mode fields.
In terms of a new Hamiltonian we introduce a modified Jaynes–Cummings model to represent the interaction between a two-level atom and two electromagnetic fields injected simultaneously within a perfect cavity. The field–field interaction is assumed to be in the frequency converter form. Exact expressions of the dynamical operators is given by solving the equations of the motion in the Heisenberg picture. The entropy squeezing is examined in the framework of Shannon information entropy. Using the entropic uncertainty relation, one can be able to show that there is a new kind of quantum squeezing in the entropy.
Photon statistics in some fully quantized models of the interaction of a two-level atom with a single-mode radiation field have been studied using the operator equations of motion. Expressions for the photon number distribution and the mean photon number are presented for various initial conditions. It is found that the mean photon number may show decays and revivals of coherence similar to those of the atomic inversion in the coherent-state Jaynes-Cummings model. Application of these models to the study of multiphoton laser, absorption, and emission processes is also discussed.
In this paper, effective Hamiltonian of the two-mode multiphoton Jaynes-Cummings model is given via the intensity-dependent coupling in the rotating wave approximation. Under strong field, the atom-field entanglement and the entanglement between two modes of coherent field, according to the above model, are investigated by using the quantum reduced entropy and the quantum relative entropy, respectively. It is showed that properties of these two types of entanglements are considerably relevant to the absorption or emission photon number k, per atomic transition. Different properties of entanglements in the processes of two-photon (k=1) and mutiphoton (k>2) are revealed respectively. The preparation of entangled states is discussed. The Einstein-Podolsky-Rosen states of atom-field irrelevant to time, as well as entangled states between two models of the coherent field are prepared, respectively.