Correlated Two-Photon Scattering in a 1D Waveguide Coupled to an N-Type Four-Level Emitter

Correlated two-photon scattering in a waveguide quantum electrodynamics system consisting of a four-level N$\text{N}$-type emitter (4LE) sidely coupled to a one-dimensional (1D) waveguide is studied. In the two-photon regime, scattering eigenstates of the system are constructed by imposing an open boundary condition and defining the incident state as a free plane wave, which includes a photon-photon bound state that passes through the 4LE as a composite single particle. In the multilevel system, the bound state can be tuned by the interference to generate controllable types of interactions (attractive or repulsive) and interaction strengths. Photon-induced tunneling (bunching) in transmission and photon blockade (antibunching) in reflection are found in the system. In addition, the scattering photon pair off the system is strongly entangled in momentum space.