Scattering resonances and bound states for strongly interacting Rydberg polaritons

We provide a theoretical framework describing slow-light polaritons
interacting via atomic Rydberg states. We use a diagrammatic method to
analytically derive the scattering properties of two polaritons. We identify
parameter regimes where polariton-polariton interactions are repulsive.
Furthermore, in the regime of attractive interactions, we identify multiple
two-polariton bound states, calculate their dispersion, and study the resulting
scattering resonances. Finally, the two-particle scattering properties allow us
to derive the effective low-energy many-body Hamiltonian. This theoretical
platform is applicable to ongoing experiments.