Distinguishing models of surface response through the self-energy of an electron

Abstract

The self-energy of an electron confined between parallel surfaces with arbitrary dielectric properties is calculated. The mechanism for this effect is the surface-induced modification of the fluctuating quantised vacuum field to which the electron is coupled, thereby endowing it with a surface-dependent self-energy in broad analogy to the Casimir-Polder effect for an atom. We derive a general formula for this self-energy shift and find that its sign is different for two commonly-used models of surface response, namely the plasma model and the Drude model. We propose an experiment which could detect this difference in sign, shedding light on continuing uncertainty about the correct description of the interaction of low-frequency vacuum photons with media.