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 desirable. To fill this gap we revisit Sommerfeld's theory of the free electron gas in cavity quantum electrodynamics. We solve this system analytically in the long-wavelength limit for an arbitrary number of noninteracting 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 ${\mathbf{A}}^{2}$ 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. Last, 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.
Highlights
The free electron gas introduced by Sommerfeld in 1928 [1] is a paradigmatic model for solid state and condensed matter physics
The free electron gas with the inclusion of the electron-electron interactions was transformed into the homogeneous electron gas [2,3], known as the jellium model, and with the advent of density functional theory (DFT) and the local density approximation (LDA) [4] has become one of the most useful computational tools and methods in physics, chemistry and materials science [5]
In standard quantum mechanics and solid state physics usually one applies to the system an external field, force or potential and focuses on how the electrons respond to the perturbation by computing matter-matter response functions, like the current-current response function χ
Summary
The free electron gas introduced by Sommerfeld in 1928 [1] is a paradigmatic model for solid state and condensed matter physics It was originally developed for the description of thermal and conduction properties of metals and has served since as one of the fundamental models for understanding and describing materials. In most cases simplifications of QED are employed for the practical use of the theory (due to its complexity) in which matter is described by a few states This leads to the well-known models of quantum optics, like the Rabi, JaynesCummings or Dicke models [25,26,27]. We are able to describe consistently and from first principles dissipation and absorption processes without the need of any artificial damping parameter [3,93]
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