Abstract
A quantum approach is developed for describing the behavior of Cherenkov radiation (CR). Then we propose a scheme of terahertz CR operating in a quantum regime for which the discreteness of momentum exchange in the free electrons-light interaction is significant. In this quantum regime, the spectrum of the emitted radiation appears as discrete spectral lines with a significantly narrow linewidth. The resonant wavelength, wavelength spacing, and linewidth of the emission lines can be tuned by adjusting the parameters of electron beam and waveguide. It is verified that the criteria and constraints of the requirements for essential experimental parameters are practically feasible. This work has implications for future studies of the quantum interaction of free electrons with light as well as visualization of quantum light applications in sensing, imaging, and spectroscopy. (C) 2022 Optica Publishing Group