Few-photon optical diode in a chiral waveguide

We study the coherent transport of one or two photons in a 1D waveguide chirally coupled to a nonlinear resonator. Analytic solutions of the one-photon and two-photon scattering is derived. Although the resonator acts as a non-reciprocal phase shifter, light transmission is reciprocal at one-photon level. However, the forward and reverse transmitted probabilities for two photons incident from either the left side or the right side of the nonlinear resonator are nonreciprocal due to the energy redistribution of the two-photon bound state. Hence, the nonlinear resonator acts as an optical diode at two-photon level.