Lasing and counter-lasing phase transitions in a cavity QED system

TL;DR

This paper investigates phase transitions in a cavity QED system, revealing how spontaneous emission and incoherent pumping induce counter-lasing and complex dynamical behaviors, including chaos, in the unbalanced Dicke model.

Contribution

It provides a comprehensive analysis of counter-lasing phenomena in the unbalanced Dicke model, connecting bifurcation theory with quantum optical phase transitions.

Findings

Counter-lasing appears via Hopf bifurcation at low co-rotating coupling.

Resurgent superradiant pulses occur with small spontaneous emission rates.

A chaotic attractor emerges during the transition between superradiant and counter-lasing phases.

Abstract

We study the effect of spontaneous emission and incoherent atomic pumping on the nonlinear semiclassical dynamics of the unbalanced Dicke model -- a generalization of the Dicke model that features independent coupling strengths for the co- and counter-rotating interaction terms. As well as the ubiquitous superradiant behavior the Dicke model is well-known for, the addition of spontaneous emission combined with the presence of strong counter-rotating terms creates laser-like behavior termed counter-lasing. These states appear in the semiclassical model as stable periodic orbits. We perform a comprehensive dynamical analysis of the appearance of counter-lasing in the unbalanced Dicke model subject to strong cavity dissipation, such that the cavity field can be adiabatically eliminated to yield an effective Lipkin-Meshkov-Glick (LMG) model. If the coupling strength of the co-rotating interactions is small, then the counter-lasing phase appears via a Hopf bifurcation of the de-excited state. We find that if the rate of spontaneous emission is small, this can lead to resurgent superradiant pulses. However, if the co-rotating coupling is larger, then the counter-lasing phase must emerge via the steady-state superradiant phase. Such a transition is the result of the competition of the coherent and incoherent processes that drive superradiance and counter-lasing, respectively. We observe a surprisingly complex transition between the two, associated with the formation of a chaotic attractor over a thin transitional parameter region.