Lehmann-Symanzik-Zimmermann Reduction Approach to Multi-Photon   Scattering in Coupled-Resonator Arrays
  We present a quantum field theoretical approach based on the Lehmann-Symanzik-Zimmermann reduction for the multi-photon scattering process in a nano-architecture consisting of the coupled resonator arrays (CRA), which are also coupled to some artificial atoms as the controlling quantum node. By making use of this approach, we find the bound states of single photon for an elementary unit, the T-type CRA, and explicitly obtain its multi-photon scattering S-matrix in various situations. We also use this method to calculate the multi-photon S-matrices for the more complex quantum network constructed with main T-type CRA's, such as a H-type CRA waveguide. 
T. Shi and C. P. Sun