  We develop a theory for light propagating in an atomic Bose-Einstein
condensate in the presence of strong interactions. The resulting many-body
correlations are shown to have profound effects on the optical properties of
this interacting medium. For weak atom-light coupling, there is a well-defined
quasiparticle, the polaron-polariton, supporting light propagation with
spectral features differing significantly from the noninteracting case. The
damping of the polaron-polariton depends nonmonotonically on the light-matter
coupling strength, initially increasing and then decreasing. This gives rise to
an interesting crossover between two quasiparticles: a bare polariton and a
polaron-polariton, separated by a complex and lossy mixture of light and
matter.
