Cavity-optomechanical probe of gravity between massive mechanical oscillators

Exploring gravitational interactions between objects with small masses has become increasingly timely. Concurrently, oscillators with masses ranging between milligrams and grams in cavity optomechanical systems sparked interest for probing gravity and even investigating gravity-induced decoherence within massive mechanical systems. Here we present a measurement scheme for probing gravity in a microwave optomechanical setup that incorporates periodic gravitational modulation between the test mass and the driven source mass at the milligram scale. Optomechanically induced transparency (OMIT) can be utilized to sense the gravitational interactions between test masses and source masses. Specifically, the relative variation in the height of the OMIT peak, expressed as $|1+r{e}^{i\ensuremath{\phi}}{|}^{2}\ensuremath{-}1$, where $r$ represents the ratio of the amplitude of the gravitational driving force to the radiation pressure force of the probe tone and $\ensuremath{\phi}$ denotes their phase difference, can reach up to 2.3% under plausible experimental conditions. This work may facilitate cavity-optomechanical probing of gravitational coupling between milligram-scale mechanical oscillators, a mass regime where modifications to gravity, evidence for extra dimensions, or gravity-induced entanglement may emerge.