Single-Photon Momentum Displacement in Resonator Array with Optomechanics

We present the single-photon scattering in a resonator array system with optomechanical by solving the Lippmann-Schwinger equation iteratively. Up to the first order of the radiation pressure interaction, the single-photon transport is formulated as a three-channel scattering process. We calculate the scattering currents in different channels and obtain the transmission spectrum which shows a momentum displacement effect.