Bienias, P.Choi, S.Firstenberg, O.Maghrebi, M. F.Gullans, M.Lukin, MikhailGorshkov, AlexeyBüchler, H. P.2015-07-022014Bienias, P., S. Choi, O. Firstenberg, M. F. Maghrebi, M. Gullans, M. D. Lukin, A. V. Gorshkov, and H. P. Büchler. 2014. “Scattering Resonances and Bound States for Strongly Interacting Rydberg Polaritons.” Phys. Rev. A 90 (5) (November). doi:10.1103/physreva.90.053804.1050-2947http://nrs.harvard.edu/urn-3:HUL.InstRepos:16953006We provide a theoretical framework describing slow-light polaritons interacting via atomic Rydberg states. The method allows us 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.en-USJournal Article2015-07-0210.1103/PhysRevA.90.053804