Topological multimode waveguide QED

Topological insulators feature a number of topologically protected boundary modes linked to the value their bulk invariant. While in one-dimensional systems are zero dimensional and localized, two-dimensional topological chiral, propagating along edges system. Thus, photonic with large Chern numbers naturally display multimode waveguide at edges. Here, we show how take advantage these by interfacing them quantum emitters. In particular, using Harper-Hofstadter lattice, find situations which emitters quasiquantized decay rates due increasing edge modes, where spontaneous emission spatially separates different modes. We also single $\ensuremath{\pi}$ pulse combination such spatial separation interacting character leads formation single-photon time-bin entangled state no classical analog, characterize computing its entanglement entropy. Finally, can selectively interact channels nonlocal light-matter couplings as ones that be obtained giant atoms. Such capabilities pave way for generating gates among photons well more complex states light channels.