  We show that photon number measurement can be used to detect superfluidity
for a two-band Bose-Hubbard model coupled to a cavity field. The atom-photon
coupling induces transitions between the two internal atomic levels and results
in entangled polaritonic states. In the presence of a cavity field, we find
different photon numbers in the Mott-insulating versus superfluid phases,
providing a method of distinguishing the atomic phases by photon counting.
Furthermore, we examine the dynamics of the photon field after a rapid quench
to zero atomic hopping by increasing the well depth. We find a robust
correlation between the field's quench dynamics and the initial superfluid
order parameter, thereby providing a novel and accurate method of determining
the order parameter.
