Flat-band-mediated photon-photon interactions in two-dimensional waveguide QED networks

We investigate a Lieb lattice of quantum emitters coupled to a two-dimensional waveguide network and demonstrate that this system supports an energetically isolated flat band, enabling localization despite the presence of long-range photon-mediated couplings. We then explore the two-excitation dynamics in both the soft-core and hard-core interaction regimes, which arise from the nonlinearity of the emitters. In the soft-core regime, we observe interaction-induced photon transport within the flat band, mediated by the formation of bound photon pairs. In the hard-core regime, corresponding to the two-level atom limit, we instead find the emergence of metastable exciton-like dressed states involving both flat and dispersive bands. Our findings highlight how the interplay between the collective behavior of emitters and effective photon-photon interactions can provide a platform for studying highly correlated photonic states in flat-band systems.