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International Journal of Modern Physics B

QUANTUM TREATMENT OF A TIME DEPENDENT SINGLE-TRAPPED ION INTERACTING WITH A BIMODAL CAVITY FIELD

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

Published Dec 30, 2003• 12 citations
Publisher

Abstract

In the present communication we consider a time dependent ion-field interaction. Here we discuss the interaction between a single trapped ion and two fields taking into account the coupling parameter to be time dependent and allowing for amplitude modulation of the laser field radiating the trapped ion. At exact resonances the analytic solution for the Heisenberg equations of motion is obtained. We examine the effect of the velocity and the acceleration on the Rabi oscillations by studying the second order correlation function. The phenomenon of squeezing for single and two fields cases is considered. The cross correlation between the fields is discussed.

DOI
10.1142/s0217979203023628

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In the present communication we consider a time dependent ion-field interaction. Here we discuss the interaction between a single trapped ion and two fields taking into account the coupling parameter to be time dependent and allowing for amplitude modulation of the laser field radiating the trapped ion. At exact resonances the analytic solution for the Heisenberg equations of motion is obtained. We examine the effect of the velocity and the acceleration on the Rabi oscillations by studying the second order correlation function. The phenomenon of squeezing for single and two fields cases is considered. The cross correlation between the fields is discussed.
The time evolution of the atomic Wehrl entropy and long-lived entanglement generation using a single trapped ion interacting with a laser field are analyzed. Starting from the Heisenberg equation of motion, an exact solution of the system is obtained by indicating that there are some interesting features when a time-dependent modulating function is considered. We demonstrate that the long-living quantum entanglement can be obtained using the time-independent interaction when the field is initially in a pair cat states.
The problem of the interaction between a two-level atom and a two-mode field in the parametric amplifier-type is considered. A similar problem appears in an ion trapped in a two-dimensional trap. The problem is transformed into an interaction governed by su(1,1) Lie algebraic operators with phase and coupling parameter depending on time. Under an integrability condition, that relates phase and coupling, a solution to the wavefunction is obtained using the Schrödinger equation. The effects of the functional dependence of the coupling and the initial state of the two-level atom on atomic inversion, the degree of entanglement, the fidelity and the Glauber second-order correlation function are investigated. It is shown that the acceleration term plays an important role in controlling the function behavior of the considered quantities.
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.
Starting from the Jaynes-Cummings(J-C) model describing the interaction of a trapped ion with a standing wave laser field,we derive the interaction Hamiltonian on the nonlinear J-C model of the trapped ion excited resonantly with single quantum vibrational mode.After solving the time dependent states of this model,we study the ion centroid motion of squeezing effects by utilizing the ion numerical model.It is shown that the ion squeezing effects is related with the Lamb-Dicke parameter and the position of the ion in the standing wave laser field.