Plasmon-polaritons on a single electron

TL;DR

This paper derives the photon polarization operator for a single electron, describing its dielectric response and plasmon-polariton modes, revealing how an electron can exhibit a dynamical dipole moment in different wavelength regimes.

Contribution

It provides an explicit expression for the photon polarization operator of a single electron and analyzes plasmon-polariton modes in various wavelength limits.

Findings

Eight plasmon-polariton modes for short wavelengths

Electron exhibits a dynamical dipole moment at long wavelengths

Describes dielectric properties of a single electron wave packet

Abstract

The explicit expression for the photon polarization operator in the presence of a single electron is found in the $in$-$in$ formalism in the one-loop approximation out of the photon mass-shell. This polarization operator describes the dielectric permittivity of a single electron wave packet in coherent scattering processes. The plasmons and plasmon-polaritons supported by a single electron wave packet are described. The two limiting cases are considered: the wavelength of the external electromagnetic field is much smaller than the typical scale of variations of the electron wave packet and the wavelength of the external electromagnetic field is much larger than the size of the electron wave packet. In the former case, there are eight independent plasmon-polariton modes. In the latter case, the plasmons boil down to the dynamical dipole moment attached to a point electron. Thus, in the infrared limit, the electron possesses a dynamical electric dipole moment manifesting itself in coherent scattering processes.