Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Journal of Physics and Electronics

Order parameters in Dicke model

Sergiy F. Lyagushyn, Alexander I. Sokolovsky

Published Dec 30, 2022• 0 citations
Publisher

Abstract

Dicke model provides describing the superradiance effect when the spontaneous emission of a great number of excited two-level atoms is running in a correlated way due to their interaction via field. The process is identical to a giant dipole emission. Since the ordering takes place, it is interesting to study the possibility for using the terms of phase transition theory in such physical situation. Equilibrium properties of Dicke type models were studied for a long time because of their relevance for explaining some phenomena in matter-field interaction. The existence of an ordered phase in the emitter subsystem together with macroscopic photon mode filling is established, wherein the correct solution requires the Bogolyubov concept of quasiaverages to exclude the phase uncertainty of quasispin component structures <R+> and <R-> (for the concentrated model). In this paper, the behavior of similar order parameters for the non-equilibrium process description is analyzed and using the order parameter <R+R-> associated with the squared electric dipole moment of the emitter complex is substantiated. Such fact justifies <R3> application in the literature devoted to the superradiance theory. The situation with quasiaverages is compared with the problem of uniformity breaking in the numerical modeling.

DOI
10.15421/332213

Related papers

Correlations in superradiance of a two-dimensional system

Sergiy F. Lyagushyn

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.

Journal of Physics and Electronics•Dec 15, 2021•0 citations

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

Sergiy F. Lyagushyn

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.

IEEE International Conference on Electronics and Nanotechnology (ELNANO)•Apr 1, 2020•1 citation

Non-equilibrium dynamics of the Dicke model for mesoscopic aggregates: signatures of superradiance

Sebastian Fuchs, Joachim Ankerhold, M. P. Blencowe +1 more

Abstract The dynamics of the Dicke model, which describes the interaction of N two-level atoms with a resonant field mode, is studied in the presence of dissipation and in strong non-equilibrium for a moderate number of atoms. Starting from a highly excited state, it is investigated to what extent signatures of superradient phenomena known from the thermodynamic limit , namely, superradiant light emission and atom-field correlations characteristic for the superradiant phase, appear on transient time scales. Attention is also paid to subtleties of modeling dissipation in the weak coupling limit and to the dynamics in phase space. The latter allows phase space correlators to be defined as indicators for collective behavior on transient time scales. These findings may be of relevance for the realization of Dicke physics with superconducting circuits.

arXiv:1501.07841•Journal of Physics B Atomic Molecular and Optical Physics•Jan 8, 2016•9 citations

Ferromagnetism methods in the theory of superradiance

Alexander I. Sokolovsky, Sergiy F. Lyagushyn

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.

Low Temperature Physics•Mar 1, 2025•1 citation

Superradiance and solids: Reduced description method

Sergiy F. Lyagushyn, Alexander I. Sokolovsky

Spontaneous ordering in a system of excited emitters with a powerful short radiation pulse predicted by Dicke attracted the great attention of scientists for decades as a bright example of the nontrivial behavior of a nonequilibrium system. The Bogolyubov reduced description method has some advantages and provides new possibilities in the theoretical investigation of the Dicke process. The paper presents the authors’ results of modeling such processes concerning both optical ones in the presence of crystal lattice influence and acoustic superradiance, which is possible in solids. The right choice of reduced description parameters allows the account of atom motions (phonons), cavity influence, and excitations in the emitter system (excitons) in the electromagnetic radiation process. The mathematical analogy between the Dicke system and a spin system in a magnetic field opens the way to applying the reduced description technique to acoustic phenomena previously investigated with the boson variable elimination method. Such a new approach to superradiance in crystals with paramagnetic impurities and with competing mechanisms of relaxation (Wagner model) is outlined. Acoustic superradiance is discussed in connection with the problem of structural phase transitions.

Low Temperature Physics•Jan 1, 2024•2 citations

Light-matter interaction and Bose-Einstein condensation of light

Vivek M. Vyas, Prasanta Kumar Panigrahi, Venkatraman Srinivasan

The atom - electromagnetic field interaction is studied in the Dicke model, wherein a single field mode is interacting with a collection of two level atoms at thermal equilibrium. It is found that in the superradiant phase of the system, wherein the Bose-Einstein condensation of photons takes place, the notion of photon as an elementary electromagnetic excitation ceases to exist. The phase and intensity excitations of the condensate are found to be the true excitations of electromagnetic field. It is found that in this phase, the atom interacts with these excitations in a distinct coherent transition process, apart from the known stimulated emission/absorption and spontaneous emission processes. In the coherent transition it is found that while the atomic state changes in course of the transition process, the state of electromagnetic field remains unaffected. It is found that the transition probability of such coherent transition process is macroscopically large compared to other stimulated emission/absorption and spontaneous emission processes.

arXiv:1602.08280•Feb 26, 2016•0 citations
Dicke model provides describing the superradiance effect when the spontaneous emission of a great number of excited two-level atoms is running in a correlated way due to their interaction via field. The process is identical to a giant dipole emission. Since the ordering takes place, it is interesting to study the possibility for using the terms of phase transition theory in such physical situation. Equilibrium properties of Dicke type models were studied for a long time because of their relevance for explaining some phenomena in matter-field interaction. The existence of an ordered phase in the emitter subsystem together with macroscopic photon mode filling is established, wherein the correct solution requires the Bogolyubov concept of quasiaverages to exclude the phase uncertainty of quasispin component structures <R+> and <R-> (for the concentrated model). In this paper, the behavior of similar order parameters for the non-equilibrium process description is analyzed and using the order parameter <R+R-> associated with the squared electric dipole moment of the emitter complex is substantiated. Such fact justifies <R3> application in the literature devoted to the superradiance theory. The situation with quasiaverages is compared with the problem of uniformity breaking in the numerical modeling.
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.
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.
Abstract The dynamics of the Dicke model, which describes the interaction of N two-level atoms with a resonant field mode, is studied in the presence of dissipation and in strong non-equilibrium for a moderate number of atoms. Starting from a highly excited state, it is investigated to what extent signatures of superradient phenomena known from the thermodynamic limit , namely, superradiant light emission and atom-field correlations characteristic for the superradiant phase, appear on transient time scales. Attention is also paid to subtleties of modeling dissipation in the weak coupling limit and to the dynamics in phase space. The latter allows phase space correlators to be defined as indicators for collective behavior on transient time scales. These findings may be of relevance for the realization of Dicke physics with superconducting circuits.
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.
Spontaneous ordering in a system of excited emitters with a powerful short radiation pulse predicted by Dicke attracted the great attention of scientists for decades as a bright example of the nontrivial behavior of a nonequilibrium system. The Bogolyubov reduced description method has some advantages and provides new possibilities in the theoretical investigation of the Dicke process. The paper presents the authors’ results of modeling such processes concerning both optical ones in the presence of crystal lattice influence and acoustic superradiance, which is possible in solids. The right choice of reduced description parameters allows the account of atom motions (phonons), cavity influence, and excitations in the emitter system (excitons) in the electromagnetic radiation process. The mathematical analogy between the Dicke system and a spin system in a magnetic field opens the way to applying the reduced description technique to acoustic phenomena previously investigated with the boson variable elimination method. Such a new approach to superradiance in crystals with paramagnetic impurities and with competing mechanisms of relaxation (Wagner model) is outlined. Acoustic superradiance is discussed in connection with the problem of structural phase transitions.
The atom - electromagnetic field interaction is studied in the Dicke model, wherein a single field mode is interacting with a collection of two level atoms at thermal equilibrium. It is found that in the superradiant phase of the system, wherein the Bose-Einstein condensation of photons takes place, the notion of photon as an elementary electromagnetic excitation ceases to exist. The phase and intensity excitations of the condensate are found to be the true excitations of electromagnetic field. It is found that in this phase, the atom interacts with these excitations in a distinct coherent transition process, apart from the known stimulated emission/absorption and spontaneous emission processes. In the coherent transition it is found that while the atomic state changes in course of the transition process, the state of electromagnetic field remains unaffected. It is found that the transition probability of such coherent transition process is macroscopically large compared to other stimulated emission/absorption and spontaneous emission processes.