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arXiv:2606.31151

Topological phase transition in chaotic optomechanical systems

Xiao-Jun Zhang

quant-phnlin.CDSubmitted Jun 30, 2026• Announced Jul 1, 2026
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Abstract

Hidden structures with well-defined predictability are uncovered in the evolution of a chaotic optomechanical system from the perspective of the $ε$-machine. Tuning the frequency of the driving laser can switch off this predictability, and such behaviour corresponds to a phase transition that is deeply related to topological changes in phase space. The transition probabilities between causal states allow us to define an entropy (uncertainty) that serves as an effective order parameter. This phase transition can be readily demonstrated in currently available experiments by monitoring the quadrature of the optical mode. We hope that this work could fundamentally broaden the regimes of cavity micromechanics and nonlinear optics.

Comments
5 pages, 6 figures

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Hidden structures with well-defined predictability are uncovered in the evolution of a chaotic optomechanical system from the perspective of the εεε-machine. Tuning the frequency of the driving laser can switch off this predictability, and such behaviour corresponds to a phase transition that is deeply related to topological changes in phase space. The transition probabilities between causal states allow us to define an entropy (uncertainty) that serves as an effective order parameter. This phase transition can be readily demonstrated in currently available experiments by monitoring the quadrature of the optical mode. We hope that this work could fundamentally broaden the regimes of cavity micromechanics and nonlinear optics.
The study of the quantum to classical transition is of fundamental as well as technological importance, and focuses on mesoscopic devices, with a size for which either classical physics or quantum physics can be brought to dominate. A particularly diverse selection of such devices is available in cavity quantum optomechanics. We show that these can be leveraged for the study of dynamical tunneling in a quantum chaotic system. This effect probes the quantum to classical transition deeply, since tunneling rates sensitively depend on the ability of the quantum system to resolve the underlying classical phase space. We show that the effective Planck's constant, which determines this phase space resolution, can be varied over orders of magnitude as a function of tunable parameters in an optomechanical experiment. Specifically, we consider a membrane-in-the-middle configuration of a mechanical oscillator within an optical cavity, where the intracavity field is modulated periodically by the external laser source. We demonstrate that a mixed regular and chaotic phase space can be engineered in one spatial dimension, through a significant quartic optomechanical interaction. For that case, we explore the expected dynamical tunneling rates using Floquet theory and map out values of the effective Planck's constant that should be within practical reach.
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We investigate nonequilibrium criticality and chaos in a two-photon-driven optomechanical system. The parametric drive preserves a discrete Z2\mathbb{Z}_2Z2​ symmetry of the optical field, while radiation-pressure coupling transfers the resulting nonlinear dynamics to a mechanical oscillator. Combining semiclassical stability analysis, exact Liouvillian spectra, and stochastic quantum trajectories, we show that this driven-dissipative optomechanical model supports both first- and second-order dissipative phase transitions. At negative detuning a second-order transition yields spontaneous breaking of the cavity-parity symmetry in the thermodynamic limit. At positive detuning the same symmetry breaking coexists with a first-order transition, signaled by metastability and by an additional symmetric Liouvillian mode. At stronger pump power the mean-field dynamics loses all stable fixed points and develops limit cycles and chaotic attractors with positive Lyapunov exponent. Quantum trajectories in this regime display chaotic-like motion, enhanced steady-state entropy, and delocalization over many entropic Liouvillian modes. These results establish two-photon-driven optomechanics as a platform where dissipative criticality, symmetry breaking, and quantum signatures of chaos emerge within the same experimentally accessible setting.
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