腔中的随机光：标量势中的布朗粒子？
Stochastic light in a cavity: A Brownian particle in a scalar potential?
摘要：
随机光在相干驱动的非线性腔中的非平衡动力学类似于布朗粒子在标量势中的平衡动力学。这种相似性已经知道了几十年，但这两个系统之间的对应关系从未得到适当的评估。在这里，我们证明了这种对应关系可以是精确的，近似的，或打破，这取决于腔的非线性响应和驱动频率。对于弱共振驱动，非线性消失，对应是准确的：腔耗散和驱动振幅定义一个标量势，噪声方差定义一个有效温度，腔内场满足玻尔兹曼统计。对于中等强度的非共振驱动，对应关系是近似的：我们引入了一个潜在的近似捕获腔内场的非线性动力学，我们通过玻尔兹曼统计偏差量化这种近似的准确性。对于非常强的非共振驱动，对应关系被打破：腔内场动力学由非保守力控制，这排除了仅基于标量势的描述。我们还表明，这种击穿是伴随着一个相变的腔内场的波动，让人想起一个非厄米相变。我们的工作建立了明确的光学和随机热力学系统之间的联系，并建议过阻尼朗之万振荡器的许多基本结果可用于理解和改善谐振光学技术。
英文摘要：
The non-equilibrium dynamics of stochastic light in a coherently-driven nonlinear cavity resembles the equilibrium dynamics of a Brownian particle in a scalar potential. This resemblance has been known for decades, but the correspondence between the two systems has never been properly assessed. Here we demonstrate that this correspondence can be exact, approximate, or break down, depending on the cavity nonlinear response and driving frequency. For weak on-resonance driving, the nonlinearity vanishes and the correspondence is exact: The cavity dissipation and driving amplitude define a scalar potential, the noise variance defines an effective temperature, and the intra-cavity field satisfies Boltzmann statistics. For moderately strong non-resonant driving, the correspondence is approximate: We introduce a potential that approximately captures the nonlinear dynamics of the intra-cavity field, and we quantify the accuracy of this approximation via deviations from Boltzmann statistics. For very strong non-resonant driving, the correspondence breaks down: The intra-cavity field dynamics is governed by non-conservative forces which preclude a description based on a scalar potential only. We furthermore show that this breakdown is accompanied by a phase transition for the intra-cavity field fluctuations, reminiscent of a non-Hermitian phase transition. Our work establishes clear connections between optical and stochastic thermodynamic systems, and suggests that many fundamental results for overdamped Langevin oscillators may be used to understand and improve resonant optical technologies.
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