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

Understand

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.