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.

Figure 1

Dispersion relations of the quasimode $\mathrm{\Omega }$ for various polarizations (13). The frequency and the wave number are rescaled by ${\omega }_p$ and $k_p$, respectively. The black dots represent the minimum of the functions. The dispersion of the free photon is shown for reference.

Figure 2

The (a) real and (b) imaginary parts of the wave number $k$ for various polarizations. In both panels the $k^{+}$ and $k^{-}$ branches are shown from Eq. (15). The black dots indicate the value where the wave number develops an imaginary part (at $\mathrm{\Omega }={\mathrm{\Omega }}^{*}$). The black triangles show where the real part of the wave number vanishes and hence $k$ becomes purely imaginary (at $\mathrm{\Omega }=\tilde{\mathrm{\Omega }}$).

Figure 3

Reflectivity of EM waves in plasma. The well-known curve is obtained for the LP case. For all the other polarizations the complete reflection is at $\tilde{\mathrm{\Omega }}$ and the curves bifurcate at ${\mathrm{\Omega }}^{*}$, likewise in Fig. 2.

Figure 4

The phase and group velocities above and below light speed (solid black line), respectively. The EP cases are in the shaded area, and likewise for the gray line for which $\xi =0.2$, bounded by the CP and LP velocities.

Figure 5

The energy spectrum of (a) the CP and (b) the LP case in a $(p,\omega )$ plot, with the oscillator excitation number set to $n_{a\left(b\right)}=0$. The momentum is chosen so that in Eq. (20) (a) $p_z=0$ in $E_c$ and (b) $\mathbf{p}$ is parallel to $\mathbf{\epsilon }$ and hence $\varphi =0$ in $E_l$. The most apparent difference between the two plot is in the $\omega \to 0$ limit: (a) exhibiting a singular behavior and (b) having a finite value $E_l=\hslash {\omega }_p/2$. The axes have been rescaled appropriately for clarity.