Quasiparticles in an interacting system of charge and monochromatic field

TL;DR

This paper analyzes the quasiparticle spectrum of a charged particle interacting with a quantized electromagnetic mode, revealing polarization-dependent dispersion relations and implications for plasma properties and Casimir-like forces.

Contribution

It provides an exact solution for the quasiparticle spectrum in a charge-field system with various polarizations, highlighting new dispersion features and physical effects.

Findings

Dispersion relations depend on polarization, showing bulk plasmon and singular behaviors.

Modified plasma frequencies and reflectivities are derived from the dispersion.

Zero-point energy induces a repulsive force between plates, absent when charge is zero.

Abstract

The spectrum of an exactly solvable non-relativistic system of a charged particle interacting with a quantized electromagnetic mode is studied with various polarizations. Quasiparticle dispersion relations can be derived from the diagonalized Hamiltonian which, in the case of a linearly polarized field, indicates a bulk plasmon excitation, whereas in the elliptically and circularly polarized cases the dispersions exhibit a global minimum and show a singular behavior as the wavenumber tends to zero. These new type of dispersion relations lead to modified plasma frequencies and reflectivities, as well as to negative group velocities. It is shown that the zero-point energy of the system implies a repulsive force between two parallel plates, which vanishes when the charge is set to zero.