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Domain of applicability of various approaches to description of electromagnetic field in medium

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

Published Jan 1, 2012• 1 citation
OpenAlex

Abstract

The problem of parameters, which are necessary for nonequilibrium electromagnetic field description, is investigated on the basis of the Bogolyubov reduced description method establishing the necessity of binary correlations in the minimal set of parameters taken into account in evolution equations. The corresponding theory can be built in terms of one-particle density matrices, Wigner distribution functions, simultaneous correlation functions of field operators, and generating functionals. The obtained results can be analyzed with the help of approaches elaborated in quantum optics. Various methods in theoretical and experimental research into field correlations are compared.

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The problem of parameters, which are necessary for nonequilibrium electromagnetic field description, is investigated on the basis of the Bogolyubov reduced description method establishing the necessity of binary correlations in the minimal set of parameters taken into account in evolution equations. The corresponding theory can be built in terms of one-particle density matrices, Wigner distribution functions, simultaneous correlation functions of field operators, and generating functionals. The obtained results can be analyzed with the help of approaches elaborated in quantum optics. Various methods in theoretical and experimental research into field correlations are compared.
In optical experiments electromagnetic field manifests itself as a quantum-statistical object. Its state should be described with a statistical operator or with correlation functions calculated with it. A rather full description of field is provided with field amplitudes and simultaneous binary functions. Incidentally Glauber functions serve as a tool for diagnostics of field properties. The correlation functions are regarded as averaged macroscopic values and can be calculated as electrodynamic parameters of medium. The paper presents a scheme of such calculations for a system of two-level emitters interacting via field (Dicke model). Evolution equations are built on the basis of Bogolyubov reduced description method. Solving them can be put in life with modern computational technologies such as GPU.
Modern electromagnetic theory based on quantum conceptions supposes turn to averages of operator dynamic variables for describing the field state and analyzing experimental results with computational methods. Theoretical analysis of such non-equilibrium phenomenon as Dicke superfluorescence leads to an algebra of variables which are necessary for building a set of evolution equations. Rather different correlation functions can be determined in measurements according to the coincidence scheme using Glauber's quantum detectors. A natural way of connecting various correlation functions is expressing them via the photon density matrix and Wigner function. The problem of comparing the theoretical and experimental approaches is analyzed in the present paper.
Kinetics of electromagnetic field in noneqilibrim medium of atoms is studied on the basis of the Dicke model. The field is described by average electric and magnetic fields and their binary correlations. The atoms are considered in two-level approximation and assumed to be fixed in the space. States of the medium are described by the energy density. Nonresonant atom-field interaction is accounted phenomenologically. The theory is built on the Bogolyubov idea of the functional hypothesis that is the basis of his method of the reduced description of nonequilibrium processes. The investigation of the system is carried out in the framework of the Peletminsky–Yatsenko model. Atom-field interaction is assumed to be small and is taken into account up to the second contributions in the interaction included. Average electric and magnetic fields satisfy the Maxwell equations. Material equations for them express average current and charge densities through the average field. Evolution equations for the binary correlation of the field are constructed. Material equations for these equations express correlations field-current trough correlations field-field. The time equation for energy density of the medium is obtained. Density evolution is governed by the average field and field correlations. All material coefficients of the system are found.
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.
The paper presents mathematical apparatus allowing to calculate the correlation properties of electromagnetic field generated by the Dicke system of two-level emitters. Evolution equations are constructed on the basis of Bogolyubov reduced description method for the system macrostate depicted with energy density of emitters and field amplitudes and binary correlation functions with using ideas of electrodynamics of continuous media. Modern computer calculation tools make it possible to simulate and analyze field states for various space arrangements of emitters; the corresponding mathematical problem is formulated. Glauber correlation functions should be used for diagnosing emission characteristics.