  Exciton polaritons are hybrid particles of excitons (bound electron-hole
pairs) and cavity photons, which are renowned for displaying Bose Einstein
condensation and other coherent phenomena at elevated temperatures. However,
their formation in semiconductor microcavities is often accompanied by the
appearance of an incoherent bath of optically dark excitonic states that can
interact with polaritons via their matter component. Here we show that the
presence of such a dark excitonic medium can "dress" polaritons with density
fluctuations to form coherent polaron-like quasiparticles, thus fundamentally
modifying their character. We employ a many-body Green's function approach that
naturally incorporates correlations beyond the standard mean-field theories
applied to this system. With increasing exciton density, we find a reduction in
the light-matter coupling that arises from the polaronic dressing cloud rather
than any saturation induced by the fermionic constituents of the exciton. In
particular, we observe the strongest effects when the spin of the polaritons is
opposite that of the excitonic medium. In this case, the coupling to light
generates an additional polaron quasiparticle - the biexciton polariton - which
emerges due to the dark-exciton counterpart of a polariton Feshbach resonance.
Our results can explain recent experiments on polariton interactions in
two-dimensional semiconductors and potentially provide a route to tailoring the
properties of exciton polaritons and their correlations.
