  Measuring the quantum dynamics of a mechanical system, when few phonons are
involved, remains a challenge. We show that a superconducting microwave
resonator linearly coupled to the mechanical mode constitutes a very powerful
probe for this scope. This new coupling can be much stronger than the usual
radiation pressure interaction by adjusting a gate voltage. We focus on the
detection of phonon blockade, showing that it can be observed by measuring the
statistics of the light in the cavity. The underlying reason is the formation
of an entangled state between the two resonators. Our scheme realizes a
phonotonic Josephson junction, giving rise to coherent oscillations between
phonons and photons as well as a self-trapping regime for a coupling smaller
than a critical value. The transition from the self-trapping to the oscillating
regime is also induced dynamically by dissipation.
