  Chiral quantum optics has become a burgeoning field due to its potential
applications in quantum networks or quantum simulation of many-body physics.
Current implementations are based on the interplay between local polarization
and propagation direction of light in nanophotonic structures. In this
manuscript, we propose an alternative platform based on coupling quantum
emitters to a photonic \emph{sawtooth} lattice, a one-dimensional model with an
effective flux per plaquette introduced by complex tunnelings. We study the
dynamics emerging from such structured photonic bath and find the conditions to
obtain quasi-perfect directional emission when the emitters are resonant with
the band. In addition, we find that the photons in this bath can also mediate
complex emitter-emitter interactions tunable in range and phase when the
emitters transition frequencies lie within a band-gap. Since these effects do
not rely on polarization they can be observed in platforms beyond nanophotonics
such as matter-waves or circuit QED ones, of which we discuss a possible
implementation.
