Delocalization and quantum chaos in atom-field systems

TL;DR

This paper investigates the transition between regular and chaotic behavior in the Dicke atom-field model using diagonalization, revealing correlations between classical chaos indicators and quantum state localization.

Contribution

It provides a detailed quantitative analysis of quantum chaos in the Dicke model, linking classical Lyapunov exponents with quantum participation ratios and their scaling behaviors.

Findings

Participation Ratio correlates with Lyapunov exponents

Linear scaling of Participation Ratio with atom number in chaos

Square root scaling in regular regions

Abstract

Employing efficient diagonalization techniques, we perform a detailed quantitative study of the regular and chaotic regions in phase space in the simplest non-integrable atom-field system, the Dicke model. A close correlation between the classical Lyapunov exponents and the quantum Participation Ratio of coherent states on the eigenenergy basis is exhibited for different points in the phase space. It is also shown that the Participation Ratio scales linearly with the number of atoms in chaotic regions, and with its square root in the regular ones.