  The only coupling dark matter is guaranteed to have with the standard model
is through gravity. Here we propose a concept for direct dark matter detection
using only this gravitational coupling. We suggest that an array of
quantum-limited mechanical impulse sensors may be capable of detecting the
correlated gravitational force created by a passing dark matter particle. We
consider the effects of irreducible noise from couplings of the sensors to the
environment and noise due to the quantum measurement process. We show that the
signal from Planck-scale dark matter is in principle detectable using a large
number of gram-scale sensors in a meter-scale array with sufficiently low
quantum noise, and discuss some experimental challenges en route to achieving
this target.
