Searching for scalar dark matter with compact mechanical resonators

We explore the viability of laboratory-scale mechanical resonators as detectors for ultralight scalar dark matter. The signal we investigate is an atomic strain due to modulation of the fine structure constant and the lepton mass at the Compton frequency of dark matter particles. The resulting stress can drive an elastic body with acoustic breathing modes, producing displacements that are accessible with opto- or electromechanical readout techniques. To address the unknown mass of dark matter particles (which determines their Compton frequency), we consider various resonator designs operating at kHz to MHz frequencies, corresponding to $10^{-12}-10^{-5}$ eV particle mass. Current resonant-mass gravitational wave detectors that have been repurposed as dark matter detectors weigh $\sim \! 10^3$ kg. We find that a large unexplored parameter space can be accessed with ultra-high-$Q$, cryogenically-cooled, cm-scale mechanical resonators possessing $\sim \! 10^7$ times smaller mass.