Frequency-resolved photon correlations have proven to be a useful resource to unveil nonlinearities hidden in standard observables such as the spectrum or the standard (color-blind) photon correlations. In this manuscript, we analyze the frequency-resolved correlations of the photons being emitted from an optomechanical system where light is nonlinearly coupled to the quantized motion of a mechanical mode of a resonator, but where the quantum nonlinear response is typically hard to evidence. We present and unravel a rich landscape of frequency-resolved correlations, and discuss how the time-delayed correlations can reveal information about the dynamics of the system. We also study the dependence of correlations on relevant parameters such as the single-photon coupling strength, the filtering linewidth, or the thermal noise in the environment. This enriched understanding of the system can trigger new experiments to probe nonlinear phenomena in optomechanics, and provide insights into dynamics of generic nonlinear systems.

频率分辨光子相关性已被证明是揭示隐藏在标准可观察量（例如光谱或标准（色盲）光子相关性）中的非线性的有用资源。在这份手稿中，我们分析了从光机械发射的光子的频率分辨相关性光与谐振器机械模式的量化运动非线性耦合的系统，但量子非线性响应通常难以证明。我们呈现并解开丰富的频率分辨相关性图景，并讨论时滞相关性如何揭示有关系统动力学的信息。我们还研究了相关参数对相关参数的依赖性，例如单光子耦合强度、滤波线宽或环境中的热噪声。这种对系统的丰富理解可以触发新的实验来探测光力学中的非线性现象，并提供对通用非线性系统动力学的见解。