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Seminar/Workshop on Direct and Inverse Problems of Electromagnetic and Acoustic Wave Theory

Computation scheme for collective spontaneous radiation in a medium of two-level emitters

Sergiy F. Lyagushyn, Alexander I. Sokolovsky

Published Sep 1, 2017• 0 citations
Publisher

Abstract

The process of self-organization in a system of excited emitters studied by Dicke can be the basis of coherent emission generation without stimulated emission phenomena. Conventional analytic investigations in this field were concentrated on emitter subsystem behavior for obtaining the parameters of electromagnetic pulse. We propose the research into field characteristics in the process of pulse formation on the basis of the Bogolyubov method of reduced description by including into its parameters electromagnetic field strengths and binary correlation functions. We mean the macroscopic picture in a finite quantity of points, which provide the possibility of numerical modeling. Now we discuss the structure of numerical equations and the availability of physical parameters for such simulations.

DOI
10.1109/diped.2017.8100616

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The process of self-organization in a system of excited emitters studied by Dicke can be the basis of coherent emission generation without stimulated emission phenomena. Conventional analytic investigations in this field were concentrated on emitter subsystem behavior for obtaining the parameters of electromagnetic pulse. We propose the research into field characteristics in the process of pulse formation on the basis of the Bogolyubov method of reduced description by including into its parameters electromagnetic field strengths and binary correlation functions. We mean the macroscopic picture in a finite quantity of points, which provide the possibility of numerical modeling. Now we discuss the structure of numerical equations and the availability of physical parameters for such simulations.
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.
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 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.
The reduced description method proceeds from Bogolyubov’s idea that at large times the non-equilibrium system evolution can be described with the limited number of parameters and principle of correlation weakening. The way to the right choice of such parameters and constructing the time evolution equations for them was opened by the works of Kharkiv school in statistical physics. A quarter of a century ago at Dnipropetrovsk National University the developed method was first applied to the Dicke system of two-level emitters interacting via electromagnetic field. The paper presents a short review of the results obtained. They include the analysis of Dicke Hamiltonian structure, the choice of reduced description parameters satisfying the Peletminskii – Yatsenko scheme conditions, the realization of this scheme for concentrated and prolonged Dicke systems resulting in the temporal equation for emitter subsystemstatistical operator. The reduced description method possibilities are illustrated with using the effective Hamiltonian concept, in particular taking into account emitter motion and higher correlations. Reformulating the theory in terms of electromagnetic field allowed to construct the electrodynamics of medium formed by two-level emitters with considering binary correlations of field variables and to put forward the problem of correlation development picture. A new method of investigating correlations in quasispin subsystem with using ferromagnetism theory approach was also proposed.
The self-organization process in a Dicke model is studied with taking into account electromagnetic field states. The interaction between two-level emitters provided by the field results in generating field waves of increasing amplitudes. The picture of superradiance development in a prolonged system can be described in terms of electromagnetic field in continuous medium formed by emitters. The generalized induction in the Dicke system is introduced on the basis of the material equation for charge current obtained using the Bogolyubov reduced description method. The dispersion equation for waves and its solutions are derived and analyzed. Non-singular expressions for material coefficients are proposed and used for calculating the wave characteristics.
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.