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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Fokker-Planck equations method in the theory of multilevel atom relaxation

Alexander V. Gorokhov, V. A. Mikhailov

Published Sep 26, 1997• 1 citation
Publisher

Abstract

This work is devoted to the description of the interaction between n-level atom and a large dissipative system (heat bath). SU(n)-group coherent states as useful and convenient basis are employed. Fokker-Planck-like equations for (rho) - symbol of reduced density matrix taking into account possible squeezed fluctuations of heat bath are derived. New formulas for correlators of the transition operators between levels of system are obtained and influence of squeezing on the shape of radiation lines is discussed.

DOI
10.1117/12.287688

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This work is devoted to the description of the interaction between n-level atom and a large dissipative system (heat bath). SU(n)-group coherent states as useful and convenient basis are employed. Fokker-Planck-like equations for (rho) - symbol of reduced density matrix taking into account possible squeezed fluctuations of heat bath are derived. New formulas for correlators of the transition operators between levels of system are obtained and influence of squeezing on the shape of radiation lines is discussed.
Relaxation of a motionless three-level atom with a non-equidistant spectrum in a photon heat bath and an external stochastic field is investigated. In the Markovian approximation of the relaxation processes a master equation for the reduced density matrix is derived by making use of the averaging over realizations of the stochastic field. The master equation is solved exactly. The correlation functions, the shapes of the radiation lines, the intensity correlation and photon number spectrums are calculated for the V, Ξ and Λ atoms and realizations of the stochastic field by a delta-correlated and a Kubo-Anderson processes.
Relaxation of a three-level atom with non-equidistant spectrum interacting with a thermostat and an external stochastic field is studied. The master equation for the reduced density matrix and its solution in the first order of the perturbation theory are obtained. Using quantum regression theorem, explicit formulas for two-time correlation functions and shapes of radiation lines are derived for all types of three-level atoms and the following stochastic processes: a delta-correlated process and a Kubo-Anderson process. The influence of stochastic perturbations of atom’s energy levels and damping constants of adjacent transitions on width of radiation lines is shown.
A new method of elimination of squeezed field operators in nonlinear interaction with atomic subsystem is proposed. This method can be used for the opposite laser situation, in which the operators of an external coherent atomic source are eliminated from the density matrix equation. New types of master equations, belonging to su(1, 1) and su(2) symmetries are obtained. The solution of this equation is obtained using the generalized non-diagonal P and Q representations for su(1, 1) and su(2) symmetries. These master equations and their solutions can be used for further studies on the behavior of atomic polarization or quantum properties of the cavity field.