Energy relaxation in hot electron quantum optics via acoustic and optical phonon emission

We study theoretically the relaxation of hot quantum-Hall edge-channel electrons under the emission of both acoustic and optical phonons. Aiming to model recent experiments with single-electron sources, we describe simulations that provide the distribution of electron energies and arrival times at a detector a fixed distance from the source. From these simulations we extract an effective rate of emission of optical phonons that contains contributions from both a direct emission process as well as one involving inter-edge-channel transitions that are driven by the sequential emission of first an acoustic -- and then an optical -- phonon. Furthermore, we consider the mean energy loss due to acoustic phonon emission and resultant broadening of the electron energy distribution and derive an effective drift-diffusion model for this process.