We present a generalization of the input-output formalism that provides an analytic and systematic computation tool for few-photon scattering matrix in waveguide quantum electrodynamics (QED) systems. We also discuss the theoretical constraints on such scattering matrix from the cluster decomposition principle in quantum field theory.
Shanshan Xu and Shanhui Fan, "Theory of few-photon quantum scattering in nanophotonic structures," Proc. SPIE 10119, Slow Light, Fast Light, and Opto-Atomic Precision Metrology X, 101190S (Presented at SPIE OPTO: February 01, 2017; Published: 20 February 2017); https://doi.org/10.1117/12.2261178.
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