"Bound luminosity" state in the extended Dicke model

TL;DR

This paper derives quasiclassical equations for the extended Dicke model, revealing a 'bound luminosity' state characterized by periodic energy exchange between the electromagnetic field and two-level systems, including analytical solutions and chaos analysis.

Contribution

It generalizes the 'bound luminosity' state from the ordinary to the extended Dicke model and provides analytical solutions using Jacobi elliptic functions.

Findings

Identification of a 'bound luminosity' state with periodic energy exchange.

Analytical solutions for specific initial conditions and parameters.

Numerical investigation of chaotic behavior in the model.

Abstract

The extended Dicke model describes interaction of the single--mode electromagnetic resonator with an ensemble of interacting two--level systems. In this paper we obtain quasiclassical equations of motion of the extended Dicke model. For certain initial conditions and range of parameters the equations of motion can be solved analytically via Jacobi elliptic functions. The solution is a "bound luminosity" state, which was described by the authors previously for ordinary Dicke model and now is generalized for the case of the extended Dicke model. In this state the periodic beatings of the electromagnetic field occur in the microwave cavity filled with the ensemble of two--level systems. At the beginning of the time period the energy is stored in the electromagnetic field in the cavity, then it is absorbed by the ensemble of two--level systems, being afterwards released back to the cavity in the end of the period. Also the chaotic properties of the semiclassical model are investigated numerically.