Lehmann-Symanzik-Zimmermann reduction approach to multiphoton scattering in coupled-resonator arrays

Abstract

We present a quantum field theoretical approach based on the Lehmann-Symanzik-Zimmermann reduction for the multiphoton scattering process in a nanoarchitecture consisting of the coupled-resonator arrays (CRA), which are also coupled to some artificial atoms as a controlling quantum node. By making use of this approach, we find the bound states of a single photon for an elementary unit, the $T$-type CRA, and explicitly obtain its multiphoton scattering $S$ matrix in various situations. We also use this method to calculate the multiphoton $S$ matrices for the more complex quantum network constructed with main $T$-type CRAs, such as a $H$-type CRA waveguide.