%0 Journal Article %J Physical Review Letters %D 2015 %T Coulomb bound states of strongly interacting photons %A Mohammad F. Maghrebi %A Michael Gullans %A P. Bienias %A S. Choi %A I. Martin %A O. Firstenberg %A M. D. Lukin %A H. P. Büchler %A Alexey V. Gorshkov %X We show that two photons coupled to Rydberg states via electromagnetically induced transparency can interact via an effective Coulomb potential. This interaction gives rise to a continuum of two-body bound states. Within the continuum, metastable bound states are distinguished in analogy with quasi-bound states tunneling through a potential barrier. We find multiple branches of metastable bound states whose energy spectrum is governed by the Coulomb potential, thus obtaining a photonic analogue of the hydrogen atom. Under certain conditions, the wavefunction resembles that of a diatomic molecule in which the two polaritons are separated by a finite "bond length." These states propagate with a negative group velocity in the medium, allowing for a simple preparation and detection scheme, before they slowly decay to pairs of bound Rydberg atoms. %B Physical Review Letters %V 115 %P 123601 %8 2015/09/16 %G eng %U http://arxiv.org/abs/1505.03859v1 %N 12 %! Phys. Rev. Lett. %R 10.1103/PhysRevLett.115.123601 %0 Journal Article %J Physical Review A %D 2014 %T Scattering resonances and bound states for strongly interacting Rydberg polaritons %A P. Bienias %A S. Choi %A O. Firstenberg %A Mohammad F. Maghrebi %A Michael Gullans %A M. D. Lukin %A Alexey V. Gorshkov %A H. P. Büchler %X 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. %B Physical Review A %V 90 %8 2014/11/3 %G eng %U http://arxiv.org/abs/1402.7333v1 %N 5 %! Phys. Rev. A %R 10.1103/PhysRevA.90.053804