Strong coupling between moving atoms and slow-light Cherenkov photons

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 nonperturbative 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.