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We show that photon number measurement can be used to detect superfluidityfor a two-band Bose-Hubbard model coupled to a cavity field. The atom-photoncoupling induces transitions between the two internal atomic levels and resultsin entangled polaritonic states. In the presence of a cavity field, we finddifferent 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 quenchto zero atomic hopping by increasing the well depth. We find a robustcorrelation between the field's quench dynamics and the initial superfluidorder parameter, thereby providing a novel and accurate method of determiningthe order parameter.

Photon Counting as a Probe of Superfluidity in a Two-Band Bose Hubbard System Coupled to a Cavity Field