  The propagation of light in strongly coupled atomic media takes place through
the formation of polaritons - hybrid quasi-particles resulting from a
superposition of an atomic and a photonic excitation. Here we consider the
propagation under the condition of electromagnetically-induced transparency and
show that a novel many-body phenomenon can appear due to strong, dissipative
interactions between the polaritons. Upon increasing the photon-pump strength,
we find a first-order transition between an opaque phase with strongly
broadened polaritons and a transparent phase where a long-lived polariton
branch with highly tunable occupation emerges. Across this non-equilibrium
phase transition, the transparency window is reconstructed via nonlinear
interference effects induced by the dissipative polariton interactions. Our
predictions are based on a systematic diagrammatic expansion of the
non-equilibrium Dyson equations which is quantitatively valid, even in the
non-perturbative regime of large single-atom cooperativities, provided the
polariton interactions are sufficiently long ranged. Such a regime can be
reached in photonic crystal waveguides thanks to the tunability of
interactions, allowing to observe the interaction-induced-transparency
transition even at low polariton densities.
