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International Conference on Mathematical Methods in Electromagnetic Theory

A way to taking into account fluctuations in superfluorescence in the Dicke model

Sergiy F. Lyagushyn, Yu.M. Salyuk, Alexander I. Sokolovsky

Published Apr 1, 2005• 0 citations
Publisher

Abstract

Kinetics of emitters interacting with equilibrium photon field has been studied with taking into account nonequilibrium fluctuations in the subsystem, of emitters. The consideration is based on the Bogolyubov reduced description method applied to the basic kinetic equation for the statistical operator of the emitters. The general stochastic approach is applied to construct kinetic equations for the system with nonequilibrium correlations.

DOI
10.1109/mmet.2004.1397109

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Kinetics of emitters interacting with equilibrium photon field has been studied with taking into account nonequilibrium fluctuations in the subsystem, of emitters. The consideration is based on the Bogolyubov reduced description method applied to the basic kinetic equation for the statistical operator of the emitters. The general stochastic approach is applied to construct kinetic equations for the system with nonequilibrium correlations.
A new step in research into the Dicke model kinetics is proposed on the basis of the Bogolyubov reduced description method. A more precise description of the emitter subsystem and electromagnetic field is considered. New reduced description parameters — emitter energy density and binary correlation functions of electric and magnetic field amplitudes — open the way to investigating non-uniform systems of two-level emitters and nonequilibrium electromagnetic field with its correlation properties. Kinetic equations for such systems have been obtained in terms of electrodynamics of continuous media consisting of two-level emitters. Material equations for corresponding media are analyzed.
The necessity of more thorough description of electromagnetic field is substantiated for the problems of quantum optics. An attempt to construct the correlation functions of emission generated by a superfluorescent system of Dicke type is done. Operator evolution equations for a system of two-level emitters interacting with electromagnetic field lead to quantum analogues of Maxwell equations. Reduced description method applied to the superfluorescent process allows to find parameters characterizing the field fluctuations and some generalizations of matter equations.
Our research into Dicke superradiance process is directed to building the connected picture of the behavior of emitter and field subsystems in order to elucidate the correlation properties of generated field. The interaction between subsystems has a resonant nature, so we can start from the fixed operation frequency of emitters. There are phenomenological methods for taking into account the frequency broadening of different natures. In our approach based on the Bogolyubov's functional hypothesis allowing the macrostate description with a limited number of parameters, some concepts of electrodynamics of continuous media are used and evolution equations of Maxwell type should be supplemented with material equations dependent on the operation frequency and field mode ones. Singularity in material coefficients disappears, if nonresonant interaction is considered. The manifestation of the role of nonresonant modes in field kinetics is a goal of this investigation.
The process of cooperative spontaneous emission in a system of two-level emitters interacting via electromagnetic field is analyzed using the Bogolyubov reduced description method, which provides the possibility of studying the state of the generated field. Field macrostates are described with electric and magnetic field amplitudes and binary correlation functions of their components. Since the previously obtained set of differential equations describing the Dicke system evolution with considering field correlations is very cumbersome, we must find some way of simplifying the model to make it accessible for numerical modeling. The general picture of correlation development can be elucidated with using one- and two-dimensional models. The paper presents the set of evolution equations for Dicke system with fixed orientation of dipole moments of emitters forming a two-dimensional structure. The material equations and equilibrium correlations are discussed. The transition to the Cauchy problem for ordinary differential equations is proposed.
Using the method of nonequilibrium statistical operator by Zubarev, an approach is proposed for the description of kinetics which takes into account the nonlinear hydrodynamic fluctuations for a quantum Bose system.Non-equilibrium statistical operator is presented which consistently describes both the kinetic and nonlinear hydrodynamic processes.Both a kinetic equation for the nonequilibrium one-particle distribution function and a generalized Fokker-Planck equation for nonequilibrium distribution function of hydrodynamic variables (densities of momentum, energy and particle number) are obtained.A structure function of hydrodynamic fluctuations in cumulant representation is calculated, which makes it possible to analyse the generalized Fokker-Planck equation in Gaussian and higher approximations of the dynamic correlations of hydrodynamic variables which is important in describing the quantum turbulent processes.