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Modern Physics Letters B

SOLUTION OF THE GENERALIZED KINETIC EQUATION FOR INTERACTING TWO-LEVEL ATOM AND CAVITY FIELD SYSTEM

M. Yu. Rasulova, Ilhom Tishabaev

Published Jun 10, 2011• 1 citation
Publisher

Abstract

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.

DOI
10.1142/s0217984911026528

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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.
The dynamics of the much studied Jaynes–Cummings model, of a single two-level atom interacting with a single quantized field mode, is simple to solve for because the number of quanta in the system is strictly conserved. Including the effects of cavity damping makes the model significantly more difficult to treat. Here we present a simple derivation of the evolution of the atomic inversion in the presence of cavity damping. This will enable us to explain the physical meaning of the solution, first derived more than 20 years ago, and also to show that it is valid for much stronger damping than was appreciated at that time.