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arXiv:2607.12044

Dissipative phase transitions and chaos in two-photon driven quantum optomechanics

Giovanni Bragadin, Filippo Ferrari, Lorenzo Fioroni, Matteo Seclì, Vincenzo Macrì, Vincenzo Savona, Alberto Mercurio

quant-phSubmitted Jul 13, 2026• Announced Jul 15, 2026
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Abstract

We investigate nonequilibrium criticality and chaos in a two-photon-driven optomechanical system. The parametric drive preserves a discrete $\mathbb{Z}_2$ 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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Nonequilibrium phase transitions exist in damped-driven open quantum systems when the continuous tuning of an external parameter leads to a transition between two robust steady states.In second-order transitions this change is abrupt at a critical point, whereas in first-order transitions the two phases can coexist in a critical hysteresis domain.Here, we report the observation of a first-order dissipative quantum phase transition in a driven circuit quantum electrodynamics system.It takes place when the photon blockade of the driven cavity-atom system is broken by increasing the drive power.The observed experimental signature is a bimodal phase space distribution with varying weights controlled by the drive strength.Our measurements show an improved stabilization of the classical attractors up to the millisecond range when the size of the quantum system is increased from one to three artificial atoms.The formation of such robust pointer states could be used for new quantum measurement schemes or to investigate multiphoton phases of finite-size, nonlinear, open quantum systems.