Coherent few-photon quantum transport in one-dimensional systems

We give exact solutions for correlated two-photon transport in one-dimensional waveguide coupled to a two-level system, using, a Bethe-Ansatz-like approach. The S-matrix is explicitly constructed to account for the transport properties of the photons. We show that, the scattering eigenstates of this system include a two-photon bound state that passes through the two-level system as a composite single particle. Also, the two-level system can induce effective attractive or repulsive interactions in space for photons. This general procedure can be applied to the Anderson model as well.