We theoretically study a system composed of a waveguide and a quantum emitter moving in a one-dimensional potential along the waveguide axis. We focus on the single-excitation subspace and treat the emitter motional degrees of freedom fully quantum mechanically. We first characterize single-photon scattering off a single moving quantum emitter, showing both direction-dependent transmission and recoil-induced reduction of the quantum emitter motional energy. We then characterize the bound states within the band gap, which display a motion-induced asymmetric phase in real space. We also demonstrate how these bound states form a continuous band with exotic dispersion relations. Finally, we study the spontaneous emission of an initially excited quantum emitter with various initial momentum distributions, finding strong deviations with respect to the static emitter counterpart both in the occupation dynamics and in the spatial distribution of the emitted photons. Our work extends the waveguide-QED toolbox by including the quantum motional degrees of freedom of emitters, whose impact on the few-photon dynamics could be harnessed for quantum technologies.

• Received 20 March 2020
• Accepted 8 July 2020

DOI:https://doi.org/10.1103/PhysRevA.102.013726