Fluctuation-induced quenching of chaos in quantum optics

TL;DR

This paper investigates how quantum fluctuations at room temperature can suppress chaotic behavior in quantum optical systems, challenging mean-field approximations and revealing the role of nonlinearity and noise in quantum chaos.

Contribution

It demonstrates that thermal fluctuations can quench chaos in quantum optics at realistic frequencies, highlighting the importance of quantum noise and nonlinearity in chaotic dynamics.

Findings

Thermal fluctuations suppress chaos at room temperature for frequencies $10^5$ to $10^7$ Hz.

Nonlinearity causes deviations from Gaussian phase-space distributions, indicating attractor-like features.

Increasing nonlinearity lowers the noise threshold for chaos suppression, approaching vacuum fluctuations.

Abstract

Recent studies have extensively explored chaotic dynamics in quantum optical systems through the mean-field approximation, which corresponds to an ideal, fluctuation-free scenario. However, the inherent sensitivity of chaos to initial conditions implies that even minute fluctuations can be amplified, thereby questioning the applicability of this approximation. Here, we analyze these chaotic effects using stochastic Langevin equations or the Lindblad master equation. For systems operating at frequencies of $10^5$ to $10^7$ Hz, we demonstrate that room-temperature thermal fluctuations are sufficient to suppress chaos at the level of expectation values, even under weak nonlinearity. Furthermore, nonlinearity induces deviations from Gaussian phase-space distributions of the quantum state, revealing attractor-like features in the Wigner function. With increasing nonlinearity, the noise threshold for chaos suppression decreases, approaching the scale of vacuum fluctuations. These results provide a bidirectional validation of the quantum mechanical suppression of chaos.