An Optomechanical Accelerometer Search for Ultralight Dark Matter

Abstract: We use a cavity optomechanical accelerometer to perform a resonant search for ultralight dark matter at acoustic frequencies near 39 kHz (a particle mass of $0.16$ neV/$c^2$). The accelerometer is based on a Si$_3$N$_4$ membrane, cryogenically cooled to 4 K, with photothermal heating employed to scan the resonance frequency by $10^2$ detector linewidths. Leveraging shot-noise-limited displacement readout and radiation pressure feedback cooling, we realize an acceleration resolution of $\sim 10\;\text{n}g_0/\sqrt{\text{Hz}}$ over a bandwidth of $30$ Hz near the fundamental test mass resonance. We find no evidence of a dark matter signal and infer an upper bound on the coupling to normal matter that is several orders of magnitude above the stringent bounds set by equivalence principle experiments. We outline a path toward novel dark matter constraints in future experiments by exploiting arrays of mass-loaded optomechanical sensors at lower temperature probed with distributed squeezed light.