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IEEE International Conference on Electronics and Nanotechnology (ELNANO)

Resonance and Non-Resonance Interaction in Superradiance Modeling with Correlation Functions

Sergiy F. Lyagushyn

Published Apr 1, 2020• 1 citation
Publisher

Abstract

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.

DOI
10.1109/elnano50318.2020.9088765

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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 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.
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 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.
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.
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.
Superradiance, both optical and acoustic, is one of the most important methods of generating the coherent pulses and obtaining the information about emitters via resonant phenomena. The process of ordering in a system of excited emitters, which results in a powerful short radiation pulse, is described with correlation functions of emitter and field parameters. Their behavior is problem of interest, especially in a spatial system. The known theoretical approaches to such questions are based on using some ways of correlator decoupling, at the same time the validity and exactness of applied operations remain without evaluation. The authors propose a way to solve this problem in the framework of the Bogolyubov reduced description method in the Peletminskii–Yatsenko formulation. Additionally to the usual small parameter of the method (the interaction constant), a new small parameter (the difference between correlation functions in the theory using it as an independent reduced description parameter and the process picture with one less parameter) is introduced. The method is developed for a concentrated Dicke model. The conventional application of quasispin operators for two-level objects allows to describe the system of emitters as a spin system and use the perfect methods of calculating the averages of spin operator combinations, which were developed in the ferromagnetism theory.