Strongly Interacting Photons in 2D Waveguide QED

One-dimensional confinement in waveguide quantum electrodynamics (QED) plays a crucial role to enhance light -matter interactions and to induce a strong quantum nonlinear optical response. In two or higher -dimensional settings, this response is reduced since photons can be emitted within a larger phase space, opening the question whether strong photon -photon interaction can be still achieved. In this study, we positively answer this question for the case of a 2D square array of atoms coupled to the light confined into a two-dimensional waveguide. More specifically, we demonstrate the occurrence of long-lived twophoton repulsive and bound states with genuine 2D features. Furthermore, we observe signatures of these effects also in free -space atomic arrays in the form of weakly subradiant in -band scattering resonances. Our findings provide a paradigmatic signature of the presence of strong photon -photon interactions in 2D waveguide QED.