Few-photon transport via a multimode nonlinear cavity: Theory and applications

Few-photon transport via waveguide-coupled local quantum systems has attracted extensive theoretical and experimental studies. Most of the study focused on atomic or atomic-like due to their strong light-matter interaction useful for applications. Here, we few-photon a multimode optical cavity with second-order bulk nonlinearity. We develop Feynman diagram approach compute scattering matrix one- two-photon transport. Based calculated matrix, show highly nonclassical photonic effects, including photon blockade $\pi-$conditional phase shift, are achievable in system interference linear response engineering. Our results might lead significant applications circuits all-optical information processing network protocols.