Coherent Plasma in a Lattice

Abstract

We present a fully second-quantized calculation showing the emergence of spontaneous coherent configurations of the electromagnetic field interacting with charged bosons in a regular lattice. The bosons tend to oscillate at their plasma frequency, and in addition are subjected to electrostatic forces which keep them confined close to the lattice sites while causing a frequency shift in the oscillation. Under certain conditions upon these frequencies, we find that a suitably defined set of coherent states (coherent both in the field and matter degrees of freedom) exhibit a negative energy gap with respect to the perturbative ground state. This is true in the RWA approximation and for position-independent fields to both the first and second order in the interaction Hamiltonian. We compare this result with other recent findings from cavity QED, and note that (1) consideration of full 3D wavefunctions and a careful definition of the coherent states are essential for obtaining the energy gap, and (2) although our calculation is made in reference to bosons, it may apply to protons bound in a crystal matrix as well if their density is very low compared to the density of available states.