  The discovery of topological materials has challenged our understanding of
condensed matter physics and led to novel and unusual phenomena. This has
motivated recent developments to export topological concepts into photonics to
make light behave in exotic ways. Here, we predict several unconventional
quantum optical phenomena that occur when quantum emitters interact with a
topological waveguide QED bath, namely, the photonic analogue of the
Su-Schrieffer-Hegger model. When the emitters frequency lies within the
topological band-gap, a chiral bound state emerges, which is located at just
one side (right or left) of the emitter. In the presence of several emitters,
it mediates topological, long-range tunable interactions between them, that can
give rise to exotic phases such as double N\'eel ordered states. On the
contrary, when the emitters' optical transition is resonant with the bands, we
find unconventional scattering properties and different super/subradiant states
depending on the band topology. We also investigate the case of a bath with
open boundary conditions to understand the role of topological edge states.
Finally, we propose several implementations where these phenomena can be
observed with state-of-the-art technology.
