Surface Excitations, Energy Loss, and Decoherence in Electron Interferometry

We develop a mode-resolved description of decoherence in split-beam electron interferometry near dielectric surfaces, and show how it connects to models from electron energy-loss spectroscopy (EELS). The central result is that the decoherence rate is a weighted integral over the differential EELS spectrum, with a factor 1-cos\(k_x d\) encoding the path distinguishability of the two electron trajectories. Incorporating retardation and thermal occupation reproduces the macroscopic QED model of Scheel and Buhmann. We compare non-retarded vs. retarded and non-thermal vs. thermally weighted variants of the model against published results from Kerker et al., finding that both retardation and finite temperature are required for reasonable quantitative agreement. The thermal weighting suggests an application: fringe visibility as a near-field thermometric probe of the substrate, sensitive to the evanescent regime inaccessible to far-field methods.