Frequency-resolved photon correlations in cavity optomechanics

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.MKS thanks Michael J Steel for stimulating discussions, and acknowledges funding from Australian Research Council (Discovery Project No. DP160101691) and the Macquarie University Research Fellowship Scheme. AGT acknowledges support from CSIC Research Platform on Quantum Technologies PTI-001 and from Spanish Project No. PGC2018-094792-B-100 (MCIU/AEI/FEDER, EU). RE and JA acknowledge project PID2019-107432GB-I00 from the Spanish Ministry of Science and Innovation, Project No. H2020- FET Open 'THOR' Nr. 829067 from the European Commission, and Grant No. IT1164-19 from the Basque Government for consolidated groups of the Basque University.Peer reviewe