Classical and Quantum Chaos in Chirally-Driven, Dissipative Bose-Hubbard Systems

TL;DR

This paper investigates chaotic dynamics in a driven-dissipative Bose-Hubbard system, revealing classical and quantum chaos features, including chaotic attractors and positive quantum Lyapunov exponents, through mean-field and quantum simulations.

Contribution

It demonstrates the emergence of chaos in a chiral-driven Bose-Hubbard model and links classical chaos with quantum signatures like the Wigner function and out-of-time-ordered correlators.

Findings

Chaotic attractors appear at high drive strengths.

Quantum Wigner functions reflect classical chaos.

Positive quantum Lyapunov exponents indicate quantum chaos.

Abstract

We study the dissipative Bose-Hubbard model on a small ring of sites in the presence of a chiral drive and explore its long-time dynamical structure using the mean field equations and by simulating the quantum master equation. Remarkably, for large enough drivings, we find that the system admits, in a wide range of parameters, a chaotic attractor at the mean-field level, which manifests as a complex Wigner function on the quantum level. The latter is shown to have the largest weight around the approximate region of phase space occupied by the chaotic attractor. We demonstrate that this behavior could be revealed via measurement of various bosonic correlation functions. In particular, we employ open system methods to calculate the out-of-time-ordered correlator, whose exponential growth signifies a positive quantum Lyapunov exponent in our system. This can open a pathway to the study of chaotic dynamics in interacting systems of photons.