Input-Output Formalism for Few-Photon Transport: A Systematic Treatment Beyond Two Photons

Abstract

We provide a systematic treatment of $N$-photon transport in a waveguide coupled to a local system, using the input-output formalism. The main result of the paper is a general connection between the $N$-photon S matrix and the Green functions of the local system. We also show that the computation can be significantly simplified, by exploiting the connectedness structure of both the S matrix and the Green function, and by computing the Green function using an effective Hamiltonian that involves only the degrees of freedom of the local system. We illustrate our formalism by computing $N$-photon transport through a cavity containing a medium with Kerr nonlinearity, with $N$ up to 3.

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• Dynamical theory of single photon transport in a one-dimensional waveguide coupled to identical and non-identical emitters
• One- and Two-Photon Scattering by Two Atoms in a Waveguide
• Diagrammatic approach for analytical non-Markovian time-evolution: Fermi's two atom problem and causality in waveguide quantum electrodynamics
• Few-photon transport via a multimode nonlinear cavity: theory and applications