Few-body quantum physics with strongly interacting Rydberg polaritons
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- Bienias, P. Eur. Phys. J. Spec. Top. (2016) 225: 2957. doi:10.1140/epjst/e2016-60004-x
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We present an extension of our recent paper [Bienias et al., Phys. Rev. A 90, 053804 (2014)] in which we demonstrated the scattering properties and bound-state structure of two Rydberg polaritons, as well as the derivation of the effective low-energy many-body Hamiltonian. Here, we derive a microscopic Hamiltonian describing the propagation of Rydberg slow light polaritons in one dimension. We describe possible decoherence processes within a Master equation approach, and derive equations of motion in a Schroedinger picture by using an effective non-Hermitian Hamiltonian. We illustrate diagrammatic methods on two examples: First, we show the solution for a single polariton in an external potential by exact summation of Feynman diagrams. Secondly, we solve the two body problem in a weakly interacting regime exactly.