Weak-coupling bound states in semi-infinite topological waveguide QED

A striking feature of cavity QED is the existence of atom-photon bound states, which typically form when the coupling between the (excited) atom and its environment are strong enough that after emitting a photon, the atom can "grab" and re-absorb the photon again, resulting in a virtual photon cloud surrounding the atom. In this talk, we will instead demonstrate bound states that form only in the case of weak coupling. Specifically, we show that when a quantum emitter is weakly coupled to a structured reservoir exhibiting topologically-protected surface states, hybridizations between these states and the emitter can result in pairs of bound states. We illustrate this using a semi-infinite extension of the Su-Schrieffer-Heeger (SSH) model as our 1-D reservoir. First, we diagonalize the bare semi-infinite SSH chain and reveal a winding number that predicts only the edge state on the finite side of the chain survives the semi-infinite extension. Then, after coupling the quantum emitter to this end of the chain, we analyze the modified emitter spectrum and reveal the existence of bound states in three parameter regions. Two of these represent the usual strong-coupling bound states, while the third gives the weak-coupling bound states with eigenvalue appearing in the SSH band gap. These states exhibit partial sublattice localization and interesting dynamical properties.