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arXiv:2601.10147

Fluctuation-induced quenching of chaos in quantum optics

Mei-Qi Gao, Song-hai Li, Xun Li, Xingli Li, Jiong Cheng, Wenlin Li

quant-phSubmitted Jan 15, 2026• Announced Jan 16, 2026• 0 citations
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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.

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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 10510^5105 to 10710^7107 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.
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 105-107 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.
The effect of a large environment on a finite-size quantum mechanical system is two-fold: It brings dissipation, but also fluctuations of thermal and quantum origin. While dissipation tends to stabilize the dynamics, we question if and how environmental quantum fluctuations can generate chaos in an otherwise classically non-chaotic system. We work out a paradigmatic model of quantum optics: the dissipative Dicke model, where a large spin interacts with a dissipative harmonic mode. We dial in the classical/quantum correspondence by working in the semiclassical regime at large but finite spin. We demonstrate that, starting from a classically regular phase space in the superradiant regime, quantum noise can generate a strange attractor with fractal dimension and a positive Lyapunov exponent. We unveil the deep connection with shear-induced chaos that was recently developed in the mathematical community.
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.
We study nonlinear phenomena of bistability and chaos at a level of few quanta. For this purpose, we consider a single-mode dissipative oscillator with strong Kerr nonlinearity with respect to the dissipation rate driven by a monochromatic force as well as by a train of Gaussian pulses. The quantum effects and decoherence in the oscillatory mode are investigated in the framework of the purity of states and the Wigner functions calculated from the master equation. We demonstrate the quantum chaotic regime by means of a comparison between the contour plots of the Wigner functions and the strange attractors on the classical Poincaré section. Considering bistability at a low limit of quanta, we analyze the minimal level of excitation numbers at which the bistable regime of the system is displayed. We also discuss the formation of an oscillatory chaotic regime by varying oscillatory excitation numbers at ranges of a few quanta. We demonstrate quantum-interference phenomena that are assisted hysteresis-cycle behavior and quantum chaos for the oscillator driven by a train of Gaussian pulses. We establish the border of quantum-classical correspondence for chaotic regimes in the case of strong nonlinearities.
Nonlinearity in Quantum Mechanics may have extrinsic or intrinsic origins and is a liable route to a chaotic behaviour that can be of difficult observations. In this paper, we propose two forms of nonlinear Hamiltonian, which explicitly depend upon the phase of the wave function and produce chaotic behaviour. To speed up the slow manifestation of chaotic effects, a resonant laser field assisting the time evolution of the systems causes cumulative effects that might be revealed, at least in principle. The nonlinear Schrödinger equation is solved within the two-state approximation; the solution displays features with characteristics similar to those found in chaotic Classical Mechanics: sensitivity on the initial state, dense power spectrum, irregular filling of the Poincaré map and exponential separation of the trajectories of the Bloch vector σ in the Bloch sphere.
How classical chaos emerges from quantum mechanics remains a central open question, as the unitary evolution of isolated quantum systems forbids exponential sensitivity to initial conditions. A key insight is that this quantum-classical link is provided by measurement processes. In this work, we identify gain competition in a chaotic photon gas as an operational quantum measurement that selects single motional modes from an initial superposition through stochastic, nonlinear amplification. We show that this mechanism naturally gives rise to classical chaotic behavior, most notably sensitivity to initial conditions. Our results provide a concrete physical mechanism for the quantum-classical transition in a chaotic system and demonstrate that essential aspects of quantum measurement-state projection, Born-rule-like selection, and irreversibility-can naturally emerge from intrinsic gain dynamics.