Quasiparticles in an interacting system of charge and monochromatic field

The spectrum of an exactly solvable nonrelativistic 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 wave number tends to zero. These types 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.