Emergent cavity-QED dynamics along the edge of a photonic lattice

We investigate qubits coupled to the boundary of a two-dimensional photonic lattice that supports dispersionless edge modes—unlike conventional edge modes that sustain propagating photons. As a case study, we consider a honeycomb lattice (photonic graphene) of coupled resonators with a zigzag edge, where the edge modes form a flat band defined only over a restricted region of momentum space. We show that light–matter interactions are effectively captured by a dissipative cavity-QED model, wherein the emitter coherently couples to a localized mode emerging as a superposition of edge modes. This mode has support on only one sublattice and displays an unconventional power-law localization around the qubit—yet remaining normalizable in the thermodynamic limit—with a spatial range that can be tuned by introducing lattice anisotropy. We predict the occurrence of vacuum Rabi oscillations and state transfer between distant emitters. An experimental demonstration using superconducting circuits is proposed.