The Free Electron Gas in Cavity Quantum Electrodynamics
Abstract
Cavity modification of material properties and phenomena is a novel research field largely motivated by the advances in strong lightmatter interactions. Despite this progress, exact solutions for extended systems strongly coupled to the photon field are not available, and both theory and experiments rely mainly on finitesystem models. Therefore a paradigmatic example of an exactly solvable extended system in a cavity becomes highly desireable. To fill this gap we revisit Sommerfeld's theory of the free electron gas in cavity quantum electrodynamics (QED). We solve this system analytically in the longwavelength limit for an arbitrary number of noninteracting electrons, and we demonstrate that the electronphoton ground state is a Fermi liquid which contains virtual photons. In contrast to models of finite systems, no ground state exists if the diamagentic $\textbf{A}^2$ term is omitted. Further, by performing linear response we show that the cavity field induces plasmonpolariton excitations and modifies the optical and the DC conductivity of the electron gas. Our exact solution allows us to consider the thermodynamic limit for both electrons and photons by constructing an effective quantum field theory. The continuum of modes leads to a manybody renormalization of the electron mass, which modifies the fermionic quasiparticle excitations of the Fermi liquid and the WignerSeitz radius of the interacting electron gas. Lastly, we show how the mattermodified photon field leads to a repulsive Casimir force and how the continuum of modes introduces dissipation into the lightmatter system. Several of the presented findings should be experimentally accessible.
 Publication:

arXiv eprints
 Pub Date:
 June 2020
 arXiv:
 arXiv:2006.09236
 Bibcode:
 2020arXiv200609236R
 Keywords:

 Quantum Physics;
 Condensed Matter  Mesoscale and Nanoscale Physics