  We consider the possible phases of microcavity polaritons tuned near a
bipolariton Feshbach resonance. We show that, as well as the regular polariton
superfluid phase, a "molecular" superfluid exists, with (quasi-)long-range
order only for pairs of polaritons. We describe the experimental signatures of
this state. Using variational approaches we find the phase diagram (critical
temperature, density and exciton-photon detuning). Unlike ultracold atoms, the
molecular superfluid is not inherently unstable, and our phase diagram suggests
it is attainable in current experiments.
