Kullback-Leibler quantum divergence as an indicator of quantum chaos

TL;DR

This paper explores the use of Kullback-Leibler quantum divergence as a novel tool for detecting quantum chaos in a nonlinear oscillator system, demonstrating its effectiveness over traditional fidelity measures.

Contribution

It introduces linear and nonlinear quantum divergences and shows their superiority in identifying quantum chaotic behavior, especially in short time series.

Findings

Nonlinear divergence is more sensitive to chaotic regions.

Quantum divergences outperform fidelity in chaos detection.

Power spectra of divergences reveal chaotic dynamics.

Abstract

We discuss a system of a nonlinear Kerr-like oscillator externally pumped by ultra-short, external, coherent pulses. For such a system, we analyse the application of the Kullback-Leibler quantum divergence $K[\rho||\sigma]$ to the detection of quantum chaotic behaviour. Defining linear and nonlinear quantum divergences, and calculating their power spectra, we show that these parameters are more suitable indicators of quantum chaos than the fidelity commonly discussed in the literature, and are useful for dealing with short time series. Moreover, the nonlinear divergence is more sensitive to chaotic bands and to boundaries of chaotic regions, compared to its linear counterpart.