Chaos in a deformed Dicke model

TL;DR

This paper investigates how a new constant of motion influences the development of chaos in a modified Dicke model, revealing energy-dependent chaos and coexistence of regularity and chaos due to symmetry breaking.

Contribution

It introduces a study of chaos in a deformed Dicke model with broken parity symmetry, highlighting the role of a conserved quantity in the classical and quantum chaos transition.

Findings

Chaos depends on initial energy and well structure in the classical model.

Quantum conserved number influences the emergence of chaos.

Chaos and regularity can coexist at the same energy due to conservation law.

Abstract

The critical behavior in an important class of excited state quantum phase transitions is signaled by the presence of a new constant of motion only at one side of the critical energy. We study the impact of this phenomenon in the development of chaos in a modified version of the paradigmatic Dicke model of quantum optics, in which a perturbation is added that breaks the parity symmetry. Two asymmetric energy wells appear in the semiclassical limit of the model, whose consequences are studied both in the classical and in the quantum cases. Classically, Poincar\'{e} sections reveal that the degree of chaos not only depends on the energy of the initial condition chosen, but also on the particular energy well structure of the model. In the quantum case, Peres lattices of physical observables show that the appearance of chaos critically depends on the quantum conserved number provided by this constant of motion. The conservation law defined by this constant is shown to allow for the coexistence between chaos and regularity at the same energy. We further analyze the onset of chaos in relation with an additional conserved quantity that the model can exhibit.