Some statistical approach to two-level atom-cavity field system in nonlinear optics

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.