Quantum scarring in a spin-boson system: fundamental families of periodic orbits

TL;DR

This paper investigates quantum scarring in the Dicke model, identifying fundamental periodic orbits that influence eigenstate localization and dynamics in both regular and chaotic regimes.

Contribution

It introduces a detailed analysis of periodic orbits in the Dicke model, linking classical orbits to quantum eigenstate structure and dynamics, including a new scar quantification measure.

Findings

Identification of two fundamental periodic orbit families in the Dicke model.

Quantization of energies associated with these periodic orbits.

A measure to quantify eigenstate scarring and its impact on dynamics.

Abstract

As the name indicates, a periodic orbit is a solution for a dynamical system that repeats itself in time. In the regular regime, periodic orbits are stable, while in the chaotic regime, they become unstable. The presence of unstable periodic orbits is directly associated with the phenomenon of quantum scarring, which restricts the degree of delocalization of the eigenstates and leads to revivals in the dynamics. Here, we study the Dicke model in the superradiant phase and identify two sets of fundamental periodic orbits. This experimentally realizable atom-photon model is regular at low energies and chaotic at high energies. We study the effects of the periodic orbits in the structure of the eigenstates in both regular and chaotic regimes and obtain their quantized energies. We also introduce a measure to quantify how much scarred an eigenstate gets by each family of periodic orbits and compare the dynamics of initial coherent states close and away from those orbits.