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. 
P. Bienias, S. Choi, O. Firstenberg, M. F. Maghrebi, M. Gullans, M. D.   Lukin, A.V. Gorshkov, H. P. B\"uchler
quant-ph physics.atom-ph