  In spite or the large astronomical evidence for its existence, the nature of
dark matter remains enigmatic. Particles that interact only, or almost only,
gravitationally, in particular with masses around the Planck mass -- the
fundamental scale in quantum gravity, are intriguing candidates. Here we show
that there is a theoretical possibility to directly detect such particles using
highly sensitive gravity-mediated quantum phase shifts. In particular, we
consider a protocol utilizing Josephson junctions.
