Quantum Electrodynamical Bloch Theory with Homogeneous Magnetic Fields

TL;DR

This paper develops a quantum electrodynamical Bloch theory that incorporates photon field fluctuations, revealing modifications to Landau physics and the emergence of Landau polaritons, bridging condensed matter and quantum optics.

Contribution

It introduces a first-principles QED-Bloch theory for electrons in magnetic fields, capturing photon-electron interactions and novel phenomena beyond standard solid-state models.

Findings

Recovers standard Hofstadter spectrum in the classical limit

Shows modifications to Landau levels due to photon field

Predicts emergence of Landau polaritons

Abstract

We propose a solution to the problem of Bloch electrons in a homogeneous magnetic field by including the quantum fluctuations of the photon field. A generalized quantum electrodynamical (QED) Bloch theory from first principles is presented. In the limit of vanishing quantum fluctuations we recover the standard results of solid-state physics, for instance, the fractal spectrum of the Hofstadter butterfly. As a further application we show how the well known Landau physics is modified by the photon field and that Landau polaritons emerge. This shows that our QED-Bloch theory does not only allow to capture the physics of solid-state systems in homogeneous magnetic fields, but also novel features that appear at the interface of condensed matter physics and quantum optics.