  We propose the Optomechanical Dark-matter INstrument (ODIN), based on a new
method for the direct detection of low-mass dark matter. We consider dark
matter interacting with superfluid helium in an optomechanical cavity. Using an
effective field theory, we calculate the rate at which dark matter scatters off
phonons in a highly populated, driven acoustic mode of the cavity. This
scattering process deposits a phonon into a second acoustic mode in its ground
state. The deposited phonon ($\mu$eV range) is then converted to a photon (eV
range) via an optomechanical interaction with a pump laser. This photon can be
efficiently detected, providing a means to sensitively probe keV scale dark
matter. We provide realistic estimates of the backgrounds and discuss the
technical challenges associated with such an experiment. We calculate projected
limits on dark matter-nucleon interactions for dark matter masses ranging from
0.5 to 300 keV and estimate that a future device could probe cross-sections as
low as $\mathcal{O}(10^{-32})$ cm$^2$.
