Searching for Vector Dark Matter with an Optomechanical Accelerometer

Several dark matter candidates are expected to interact with ordinary matter to produce a weak mechanical signal, such as a vector force/acceleration or scalar strain. Here we focus on acceleration signals due to vector dark matter in the 1 kHz - 10 MHz range (particle masses 10⁻¹¹ −10⁻⁷ eV/c² ). The acceleration signal can be enhanced on mechanical resonance, motivating the use of a high Q, cryogenically cooled mechanical resonator. As a concrete example, we describe a detector based on a silicon nitride membrane fixed to a beryllium mirror, forming an optical cavity. The use of different materials gives access to forces proportional to baryon (B) and lepton (L) charge, which are believed to be coupling channels for vector dark matter particles. The cavity meanwhile provides access to quantum-limited displacement measurements. For a centimeter-scale membrane pre-cooled to 10 mK, we argue that sensitivity to vector B-L dark matter can exceed that of the Eot-Wash experiment in integration times of minutes, over a fractional bandwidth of ∼ 0.1% near 10 kHz. Our analysis can be translated to alternative systems and suggests the possibility of a new generation of table-top experiments.