TY - JOUR T1 - Scattering resonances and bound states for strongly interacting Rydberg polaritons JF - Physical Review A Y1 - 2014 A1 - P. Bienias A1 - S. Choi A1 - O. Firstenberg A1 - Mohammad F. Maghrebi A1 - Michael Gullans A1 - M. D. Lukin A1 - Alexey V. Gorshkov A1 - H. P. Büchler AB - 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. VL - 90 UR - http://arxiv.org/abs/1402.7333v1 CP - 5 J1 - Phys. Rev. A U5 - 10.1103/PhysRevA.90.053804 ER -