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International Journal of Modern Physics B

QUANTUM DYNAMICS OF TWO-LEVEL ATOMS INTERACTING WITH AN ELECTROMAGNETIC FIELD

Nikolay N. Bogolubov, M. Yu. Rasulova, I. A. TISHABOEV

Published Feb 13, 2014• 1 citation
Publisher

Abstract

We consider the dynamics of a system consisting of N two-level atoms interacting with a multi-mode cavity field. For the given system, the generalized kinetic equation (GKE) is obtained and conditions are given under which its solution is reduced to solution of a linear equation, and of the one-dimensional nonlinear Schrödinger equation, respectively.

DOI
10.1142/s021797921450060x

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We consider the dynamics of a system consisting of N two-level atoms interacting with a multi-mode cavity field. For the given system, the generalized kinetic equation (GKE) is obtained and conditions are given under which its solution is reduced to solution of a linear equation, and of the one-dimensional nonlinear Schrödinger equation, respectively.
The paper is devoted to the investigation of dynamics of system, consisting of interacting two-level atoms and cavity field. Such a system also covers the Jaynes–Cummings model. This paper consists of an introduction, Secs. 2 and 3 and conclusion. In the introduction, a short history of the problem is presented and the problem is formulated. In Sec. 2, the generalized kinetic equation for the system is derived. In Sec. 3, the generalized kinetic equation is solved. In conclusion, the result is formulated.
The paper is devoted to the investigation of dynamics of system, consisting of interacting two-level atoms and field (cavity field). To such system covers also Jaynes-Cummings model. In this paper, evolution of two-level many bosons system interacting with a field is investigated by means of generalized kinetic equation. On base of the Bogolyubov's method (method of elimination of bosons), solution of the generalized kinetic equation is determined and explicit expression of average value of physical quantities, characterizing present system is defined. Moreover, solution of the generalized kinetic equation is defined for the system, consisting of a single two-level atom, interacting with a single cavity field mode. Thereby, offered in the work, statistical approach to the problem allows to generalize well-known theoretical and applied results of Jaynes-Cummings model for the systems, consisting of many two-level atoms and cavity field. This paper consists of an introduction, sections 2, 3 and conclusion. In the introduction, a short history of the problem is presented and the problem is formulated. In section 2, the generalized kinetic equation for the system is derived. In section 3, the generalized kinetic equation is solved. In conclusion the result is formulated.
This paper is an extension of Fujii et al (quant--ph/0307066) and in this one we again treat a model of atom with n energy levels interacting with n(n-1)/2 external laser fields, which is a natural extension of usual two level system. Then the rotating wave approximation (RWA) is assumed from the beginning. To solve the Schr{\" o}dinger equation we set the {\bf consistency condition} in our terminology and reduce it to a matrix equation with symmetric matrix QQQ consisting of coupling constants. However, to calculate exp⁡(−itQ)\exp(-itQ)exp(−itQ) {\bfexplicitly} is not easy. In the case of three and four level systems we determine it in a complete manner, so our model in these levels becomes realistic. In last, we make a comment on Cavity QED quantum computation based on three energy levels of atoms as a forthcoming target.
In this paper, we present some properties through two two-level atoms interacting with a two-mode quantized cavity field. We study this system in the presence of detuning parameter, Kerr nonlinearity, Stark shift, relative phase and intensity-dependent atoms-field coupling. Also, the coupling parameter is modulated to be time dependent. The exact solution of this model is given by using the Schrődinger equation when the atoms and the field are initially prepared in superposition states and coherent states, respectively. We employed the results to calculate some aspects such as linear entropy, total atomic inversion and cross-correlation function.