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