Analysis of chaos and regularity in the open Dicke model

TL;DR

This paper investigates chaos and regularity in the open Dicke model with cavity losses, introducing a numerical criterion for complex spectrum analysis and confirming theoretical conjectures about spectral distributions in different regimes.

Contribution

It develops a method to analyze the complex spectrum of the open Dicke model and validates the GHS conjecture for dissipative quantum chaos.

Findings

Regular regimes follow 2D Poisson distribution

Chaotic regimes follow Ginibre unitary ensemble distribution

Method effectively distinguishes chaos from regularity in infinite-dimensional systems

Abstract

We present an analysis of chaos and regularity in the open Dicke model, when dissipation is due to cavity losses. Due to the infinite Liouville space of this model, we also introduce a criterion to numerically find a complex spectrum which approximately represents the system spectrum. The isolated Dicke model has a well-defined classical limit with two degrees of freedom. We select two case studies where the classical isolated system shows regularity and where chaos appears. To characterize the open system as regular or chaotic, we study regions of the complex spectrum taking windows over the absolute value of its eigenvalues. Our results for this infinite-dimensional system agree with the Grobe-Haake-Sommers (GHS) conjecture for Markovian dissipative open quantum systems, finding the expected 2D Poisson distribution for regular regimes, and the distribution of the Ginibre unitary ensemble (GinUE) for the chaotic ones, respectively.