Classical and quantum chaos in chirally-driven, dissipative Bose-Hubbard systems

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.

Bloch theorem dictated wave chaos in microcavity crystals

“…Understanding the chaotic signatures in this transitional regime promotes future technological applications [10][11][12][13] emerging at the interface between classical and quantum mechanics realms or, equivalently, ray and wave realms in optical microcavities 1,2,[14][15][16] . Yet, in a more general sense, the level statistics of the microcavity mirror universal behaviors observed in various chaotic physical systems, such as Rydberg atoms [17][18][19] , ultra-cold atoms [20][21][22] , quantum dots [23][24][25] , and many-body systems [26][27][28][29] .…”