Topological multi-mode waveguide QED

Two-dimensional topological insulators with quantized large Chern numbers feature a number of protected, chiral edge modes linked to the value of the invariant. When implemented in photonic setups, these systems then naturally display a topologically-protected multi-mode waveguide at their edges. Here, we show how to take advantage of these setups by interfacing them with quantum emitters. Using a Harper-Hofstadter lattice as a particular model, we find situations in which the emitters feature quasi-quantized decay rates due to the increasing number of edge modes in the different emergent band-gaps, and where their spontaneous emission spatially separates in different modes, enabling the generation of non-local time-bin entangled states already with a single π-pulse. Besides, we show how the emitters can selectively interact with the different channels using non-local light-matter couplings as the ones that can be obtained with giant atoms. Such capabilities pave the way for generating quantum gates among topologically-protected photons as well as generating more complex entangled states of light in topological channels.