Abstract
We present a general formalism describing the propagation of an arbitrary multi-particle wave packet in a one-dimensional multimode chiral channel coupled to an ensemble of emitters which are distributed at arbitrary positions. The formalism is based on a direct and exact resummation of a diagrammatic series for the multi-particle scattering matrix. It is complementary to the Bethe Ansatz approach and to approaches based on equations of motion, and it reveals a simple and transparent structure of scattering states. In particular, we demonstrate how this formalism works on various examples, including the scattering of one- and two-photon states off two- and three-level emitters, off an array of emitters, as well as the scattering of coherent light. We argue that this formalism can be used constructively for the study of the scattering of an arbitrary initial photonic state off emitters with an arbitrary degree of complexity.
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