  We propose a novel quantum electrodynamics (QED) platform where quantum
emitters interact with a Hofstadter-ladder waveguide. We demonstrate several
intriguing phenomena stemming from the exotic dispersion relation and vacuum
mode properties led by the effective spin-orbit coupling, which have no analog
in other QED setups. First, by assuming emitter's frequency to be resonant with
the lower band, we find that the spontaneous emission is chiral with most
photonic field decaying unidirectionally. Both numerical and analytical results
indicate that the Hofstadter-ladder waveguide can be engineered as a
well-performed chiral quantum bus. Second, the dynamics of emitters of giant
atom form is explored by considering their frequencies below the lower band.
Due to quantum interference, we find that both the emitter-waveguide
interaction and the amplitudes of bound states are periodically modulated by
giant emitter's size. The periodical length depends on the positions of energy
minima points induced by the spin-orbit coupling. Last, we consider the
interaction between two giant emitters mediated by bound states, and find that
their dipole-dipole interaction vanishes (is enhanced) when maximum destructive
(constructive) interference happens.
