  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.
