Interaction between a single photon and a weak coherent state mediated by a quantum emitter

Abstract

Photon-photon interaction, an essential ingredient for optical quantum technologies, is indirect actually, i.e., often mediated via a nonlinear medium. In this work, we consider a single photon interacting with a weak coherent state in a one-dimensional waveguide coupled to a two-level quantum emitter. We present a general input-output framework that applies to an arbitrary input Fock state and various types of quantum emitters. We then use this to compute the relevant scattering processes between the single photon and the weak coherent state. We analyse in detail the characteristics of the output state taking into account the continuous-mode nature of the input and output states which are treated as appropriate photon wavepackets.