  We describe the coupling of moving atoms to a one dimensional photonic
waveguide in the regime where the atomic velocities are comparable to the
effective speed of light. Such conditions could be achieved, for example, in
photonic crystals or coupled resonator arrays, where the maximal photonic group
velocity is significantly reduced compared to free space. In this case the
interplay between a velocity-induced directionality and the emergence of new
divergencies in the photonic density of states gives rise to a range of novel
phenomena and non-perturbative effects in the emission of photons and the
resulting photon-mediated interactions between moving atoms. We show that apart
from potential implementations with optical waveguides, Rydberg atoms flying
above a coupled array of superconducting microwave resonators provide a
versatile platform for exploring this new regime of atom-light interactions
under experimentally accessible conditions.
