Conventional and unconventional Dicke models: Multistabilities and nonequilibrium dynamics

TL;DR

This paper explores a modified Dicke model with two spin ensembles interacting with a common radiation field, revealing multistability and complex nonequilibrium dynamics, including coexisting superradiant states and non-stationary behaviors.

Contribution

It introduces a variant of the Dicke model with opposite coupling strengths, uncovering multistabilities and analyzing their stability and dynamics through semiclassical and quantum approaches.

Findings

Identification of two coexisting superradiant states with different spin orderings.

Prediction of non-stationary behaviors due to multistabilities.

Quantum calculations confirm semiclassical predictions.

Abstract

The Dicke model describes the collective behavior of a sub-wavelength--size ensemble of two-level atoms (i.e., spin-1/2) interacting identically with a single quantized radiation field of a cavity. Across a critical coupling strength it exhibits a zero-temperature phase transition from the normal state to the superradiant phase where the field is populated and the collective spin acquires a nonzero $x$-component, which can be imagined as ferromagnetic ordering of the atomic spins along $x$. Here we introduce a variant of this model where two sub-wavelength--size ensembles of spins interact with a single quantized radiation field with different strengths. Subsequently, we restrict ourselves to a special case where the coupling strengths are opposite (which is unitarily equivalent to equal-coupling strengths). Due to the conservation of the total spin in each ensemble individually, the system supports two distinct superradiant states with $x$-ferromagnetic and $x$-ferrimagnetic spin ordering, coexisting with each other in a large parameter regime. The stability and dynamics of the system in the thermodynamic limit are examined using a semiclassical approach, which predicts non-stationary behaviors due to the multistabilities. At the end, we also perform small-scale full quantum-mechanical calculations, with results consistent with the semiclassical ones.