  Optomechanical systems are rapidly becoming one of the most promising
platforms for observing quantum behaviour, especially at the macroscopic level.
Moreover, thanks to their state-of-the-art methods of fabrication, they may now
enter regimes of non-linear interactions between their constituent mechanical
and optical degrees of freedom. In this work, we show how this novel
opportunity may serve to construct a new generation of optomechanical sensors.
We consider the canonical optomechanical setup with the detection scheme being
based on time-resolved counting of photons leaking from the cavity. By
performing simulations and resorting to Bayesian inference, we demonstrate that
the non-classical correlations of the detected photons may crucially enhance
the sensor performance in real time. We believe that our work may stimulate a
new direction in the design of such devices, while our methods apply also to
other platforms exploiting non-linear light-matter interactions and photon
detection.
