Gravimetry through non-linear optomechanics

We propose a new method for measurements of gravitational acceleration using a quantum optomechanical system. As a proof-of-concept, we investigate the fundamental sensitivity for a cavity optomechanical system for gravitational accelerometry with a light-matter interaction of the canonical `trilinear' radiation pressure form. The phase of the optical output of the cavity encodes the gravitational acceleration $g$ and is the only component which needs to be measured to perform the gravimetry. We analytically show that homodyne detection is the optimal readout in our scheme, based on the cyclical decoupling of light and matter, and predict a fundamental sensitivity of $\Delta g = 10^{-15}$ ms$^{-2}$ for currently achievable optomechanical systems which could, in principle, surpass the best atomic interferometers even for low optical intensities. Our scheme is strikingly robust to the initial thermal state of the mechanical oscillator as the accumulated gravitational phase only depends on relative position separation between components of the entangled optomechanical state arising during the evolution.