  The crossover between low and high density regimes of exciton-polariton
condensates is examined using a BCS wavefunction approach. Our approach is an
extension of the BEC-BCS crossover theory for excitons, but includes a cavity
photon field. The approach can describe both the low density limit, where the
system can be described as a Bose-Einstein condensate (BEC) of
exciton-polaritons, and the high density limit, where the system enters a
photon dominated regime. In contrast to the exciton BEC-BCS crossover where the
system approaches an electron-hole plasma, the polariton high density limit has
strongly correlated electron-hole pairs. At intermediate densities, there is a
regime with BCS-like properties, with a peak at non-zero momentum of the
singlet pair function. We calculate the expected photoluminescence and give
several experimental signatures of the crossover.
