The Free Electron Gas in Cavity Quantum Electrodynamics

TL;DR

This paper provides an exact analytical solution for the free electron gas in cavity QED, revealing how cavity fields modify electronic properties, induce excitations, and affect forces, with implications for experimental observation.

Contribution

It offers the first exact solution of an extended electron system in a cavity, including the thermodynamic limit and many-body effects, filling a key gap in cavity QED theory.

Findings

Electron-photon ground state is a Fermi liquid with virtual photons.

Cavity field induces plasmon-polariton excitations.

Cavity modifies optical and DC conductivity, and introduces a Casimir force.

Abstract

Cavity modification of material properties and phenomena is a novel research field largely motivated by the advances in strong light-matter 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 finite-system 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 long-wavelength limit for an arbitrary number of non-interacting electrons, and we demonstrate that the electron-photon 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 plasmon-polariton 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 many-body renormalization of the electron mass, which modifies the fermionic quasiparticle excitations of the Fermi liquid and the Wigner-Seitz radius of the interacting electron gas. Lastly, we show how the matter-modified photon field leads to a repulsive Casimir force and how the continuum of modes introduces dissipation into the light-matter system. Several of the presented findings should be experimentally accessible.