AI 中文总结
研究双光子驱动光机械系统中的非平衡临界性和混沌，结合多种分析方法表明其支持一、二阶耗散相变，强泵浦下有混沌等现象，确立该系统为可出现多种特性的实验平台。
AI 中文摘要
我们研究了双光子驱动光机械系统中的非平衡临界性和混沌。参数驱动保持光场的离散\(\mathbb{Z}_2\)对称性，而辐射压力耦合将由此产生的非线性动力学传递给机械振荡器。结合半经典稳定性分析、精确的刘维尔谱和随机量子轨迹，我们表明这个驱动耗散光机械模型支持一阶和二阶耗散相变。在负失谐时，二阶相变在热力学极限下导致腔宇称对称性的自发破缺。在正失谐时，相同的对称性破缺与一阶相变共存，由亚稳性和一个额外的对称刘维尔模式表示。在更强的泵浦功率下，平均场动力学失去所有稳定不动点，并发展出具有正李雅普诺夫指数的极限环和混沌吸引子。该区域的量子轨迹显示出类似混沌的运动、增强的稳态熵以及在许多熵刘维尔模式上的离域。这些结果确立了双光子驱动光力学作为一个平台，在同一实验可及设置中出现耗散临界性、对称性破缺和混沌的量子特征。
英文摘要
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.
