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International Conference on Mathematical Methods in Electromagnetic Theory

Superradiance in Dicke systems: A picture with field correlation functions

Sergiy F. Lyagushyn, Alexander I. Sokolovsky

Published Jul 1, 2016• 2 citations
Publisher

Abstract

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.

DOI
10.1109/mmet.2016.7544123

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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.
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.
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.
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 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.
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 discusses some approaches to elucidating the picture of electromagnetic field correlations emerging and developing in the Dicke system of two-level atoms interacting via field. Based on the reduced description method, a set of differential equations for the reduced description parameters including field correlation functions is constructed using different quantum evolution pictures and regarding field-matter interaction as a small parameter. Calculations are based on the electrodynamics of continuous media. Meaningful results are obtained in the second-order in interaction. The material equations are found in the class of generalized functions and the material coefficients are estimated in the dependence of coordinates for applying to the spatial description of correlations. Initial and border conditions are discussed. A simplified form of the set of equations is proposed for the initial stage of the process with the supposition about the fixed orientation of emitters acceptable for a one-dimensional system.