M. Sebawe Abdalla

Dynamics of a non-linear Jaynes-Cummings model

Abstract A non-linear Jaynes-Cummings model is presented. The atom interacts with two modes non-linearly. One- and multiphoton processes are considered. The Heisenberg equations of motion are solved exactly with detuning present. The evolution operator is calculated for the general case. Different statistical quantities pertaining to either the atom or the fields are computed. Numerical investigations are carried out for the phenomena of collapses and revivals, bunching and antibunching, modes correlation and squeezing for different initial values of the mean number of photons.

Multimode and multiphoton processes in a non-linear Jaynes-Cummings model

Abstract Exact operator solutions for the generalized Jaynes-Cummings model (JCM) of a two-level atom interacting with a non-linear bosonic field with multimodes has been given. Two different methods have been applied, the Heisenberg equations and the evolution operator. The photon numbers have been given through the characteristic function. Different statistical quantities have been computed. The phenomenon of collapses and revivals in the atomic inversion and the photon number as well as squeezing have been investigated.

Entropy and entanglement of time dependent two-mode Jaynes–Cummings model

In this communication we examine the field entropy and the degree of entanglement for a time dependent Jaynes–Cummings model. We have allowed the amplitude of the laser field irradiating a trapped ion to be modulated. A sinusoidal modulation depending on a quadratic function in the argument is considered. At exact resonances the analytic solution for the wave function is given, and the density matrix operator is obtained. We show that for a small value of the acceleration the entanglement between the field and the atom would delay, while for a large value of the acceleration the entanglement decreases its value. We have also shown that the effect of the velocity is different from that of the acceleration where the value of the entropy decreases as we increase the value of its parameter.

Quantum information and entropy squeezing of a two-level atom with a non-linear medium

In the language of quantum information theory we study the entropy squeezing of a two-level atom in a Kerr-like medium. A definition of squeezing is presented for this system, based on information theory. The utility of the definition is illustrated by examining the entropy squeezing of a two-level atom with a Kerr-like medium. The influence of the non-linear interaction of the Kerr medium, the atomic coherence and the detuning parameter on the properties of the entropy and squeezing of the atomic variables is examined.

Quantum entropy of isotropic coupled oscillators interacting with a single atom

Abstract In this communication we introduce a new model of Hamiltonian which represents the interaction between a two-level atom and two electromagnetic fields injected simultaneously within a cavity. By using the canonical transformation the model can be regarded as a generalization of the Jaynes–Cummings model (JCM). The relationship between the original and new states has been established, and the exact expression for the wave function in Schrodinger picture is obtained. The atomic inversion and the degree of entanglement are considered. We find that the revival time is different from what has been observed in the JCM case.

Pair entanglement of two-level atoms in the presence of a nondegenerate parametric amplifier

The problem of two two-level atoms in interaction with a nondegenerate parametric amplifier is considered. The analytical solution of the wavefunction is obtained and used to derive the density matrix operator. The temporal evolution of the atomic inversion, the degree of entanglement, as well as the variance and entropy squeezing are discussed. In our analysis, we assumed that the atomic systems are in the excited states and the fields in the squeezed-pair coherent state. It has been shown that the coupling parameter, λ3 (the coupling between the two fields), gets more effective for the case in which the q-parameter is not equal to zero. Also for a strong coupling parameter λ3 the superstructure phenomenon can be observed. In the meantime, as we increase the value of the coupling parameter, the entanglement between the atoms and the fields gets stronger. Also it has been shown that in the presence of the parametric amplifier term, the system never reaches the pure state except during revival periods.

Entropy and variance squeezing for time-dependent two-coupled atoms in an external magnetic field

A model of a two-coupled two-level atom under the action of an external magnetic field is introduced. The system is assumed to be isotropic and the coupling between the atoms is taken to be explicitly time dependent. Direct solution for the equations of motion in the Heisenberg picture is used to obtain the explicit expression for the dynamical operators when we assumed the coupling parameter is constant. In the meantime we have employed the rotating wave approximation for the case in which the coupling parameter is time dependent. The variance and entropy squeezing for both cases are discussed. It has been shown that the variance squeezing and entropy squeezing are sensitive to any change in the atomic states, so that there is no variance squeezing reported for the case in which one or both the atoms are in the pure states (e.g., lower or excited states). Further, the phenomenon of squeezing is also affected by the value of the coupling parameter, where we have noted that for a strong coupling parameter the squeezing is pronounced for a long period of time.

Entropy squeezing of a two-mode multiphoton Jaynes-Cummings model in the presence of a nonlinear medium

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.

Uncertainty relation and information entropy of a time-dependent bimodal two-level system

In this paper we consider a nonlinear interaction between a two-level atom and two modes of the electromagnetic field within a cavity. As the instantaneous position of the particle inside the cavity depends on both velocity and acceleration, we have assumed the coupling parameter to be explicitly time dependent. We have obtained the dynamical operators by solving the Heisenberg equations of motion and then constructed the density operator. The Heisenberg uncertainty relation is used to examine the entropy squeezing for this system. We have studied the effects of the phase, velocity and acceleration on entropy squeezing and atomic inversion. In addition the possibility of Bell-state production is discussed.

Degree of entanglement for anisotropic coupled oscillators interacting with a single atom

In this paper we introduce a new Hamiltonian which represents the interaction between a two-level atom and two modes of an electromagnetic field injected simultaneously within a cavity. Field–field interaction of the parametric converter type is taken into consideration. Under certain conditions the solution to the Schrodinger equation is obtained exactly. By using this solution we discuss numerically the degree of entanglement through the entropy of the field, for chosen values of the detuning and coupling parameters.