  Electromagnetically induced transparency (EIT) in a ladder system involving a
Rydberg level is known to yield giant optical nonlinearities for the probe
field, even in the few-photon regime. This enhancement is due to the strong
dipole-dipole interactions between Rydberg atoms and the resulting excitation
blockade phenomenon. In order to study such highly correlated media, ad hoc
models or low-excitation assumptions are generally used to tackle their
dynamical response to optical fields. Here, we study the behaviour of a cavity
Rydberg-EIT setup in the non-equilibrium quantum field formalism, and we obtain
analytic expressions for elastic and inelastic components of the cavity
transmission spectrum, valid up to higher excitation numbers than previously
achieved. This allows us to identify and interpret a polaritonic resonance
structure, to our knowledge unreported so far.
