  Weyl photons appear when two three-dimensional photonic bands with linear
dispersion are degenerate at a single momentum point, labeled as Weyl point.
These points have remarkable properties such as being robust topological
monopoles of Berry curvature as well as an associated vanishing density of
states. In this work, we report on a systematic theoretical study of the
quantum optical consequences of such Weyl photons. First, we analyze the
dynamics of a single quantum emitter coupled to a Weyl photonic bath as a
function of its detuning with respect to the Weyl point and study the
corrresponding emission patterns, using both perturbative and exact treatments.
Our calculations show an asymmetric dynamical behavior when the emitter is
detuned away from the Weyl frequency, as well as different regimes of highly
collimated emission, which ultimately translate in a variety of directional
collective decays. Besides, we find that the incorporation of staggered mass
and hopping terms in the bath Hamiltonian both enriches the observed
phenomenology and increases the tunability of the interaction. Finally, we
analyze the competition between the coherent and dissipative components of the
dynamics for the case of two emitters and derive the conditions under which an
effective interacting spin model description is valid.
