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

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.

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