A.-S. F. Obada

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.

Entanglement degree of a nonlinear multiphoton Jaynes-Cummings model

We extend our earlier investigations (Furuichi S and Abdel-Aty M 2001 J. Phys. A: Math. Gen. 34 6851) on the entanglement degree of a two-level atom to include any forms of nonlinearities of both the field and the intensity-dependent atom-field coupling. We present a derivation of the unitary operator within the frame of the dressed state approach, by means of which we identify and numerically demonstrate the region of parameters where significantly large entanglement can be obtained. The influences of the nonlinearity, Stark shifts and detuning on the degree of entanglement are examined. It is shown that features of the degree of entanglement are influenced significantly by the kinds of nonlinearity of the single-mode field. The model presented in this paper can be regarded as a generalization of the Jaynes-Cummings model.

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.

Photon and atomic statistics in generalized Jaynes-Cummings models

The interaction between a single two-level atom and a single mode is studied in some Jaynes-Cummings models. The coupling is supposed to depend on a function of the photon number operator. The evolution operator is calculated; then the probability distribution is obtained. Different statistical quantities are computed for the two states of the atom and different initial distributions for the radiation mode. Three modes are taken and studied, namely thermal, coherent and squeezed coherent light.

Aspects on entropy squeezing of a two-level atom in a squeezed vacuum

Abstract The entropy squeezing and variance squeezing for the entangled state of a single two-level atom interacting with a single electromagnetic field mode in a squeezed vacuum with a broad bandwidth are studied. The exact results are employed to perform a careful investigation of the influence of the various parameters of the system on the atomic inversion as well as the entropy squeezing and variance squeezing. It is shown that features of the quantum entropy are influenced significantly by the photon number, the two-photon correlation strength, and the squeezed phase.

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.