Weakened Topological Protection of the Quantum Hall Effect in a Cavity.

We study the quantum Hall effect in a two-dimensional homogeneous electron gas coupled to a quantum cavity field. As initially pointed out by Kohn, Galilean invariance for a homogeneous quantum Hall system implies that the electronic center of mass (c.m.) decouples from the electron-electron interaction, and the energy of the c.m. mode, also known as Kohn mode, is equal to the single particle cyclotron transition. In this work, we point out that strong light-matter hybridization between the Kohn mode and the cavity photons gives rise to collective hybrid modes between the Landau levels and the photons. We provide the exact solution for the collective Landau polaritons and we demonstrate the weakening of topological protection at zero temperature due to the existence of the lower polariton mode which is softer than the Kohn mode. This provides an intrinsic mechanism for the recently observed topological breakdown of the quantum Hall effect in a cavity [F. Appugliese et al., Breakdown of topological protection by cavity vacuum fields in the integer quantum Hall effect, Science 375, 1030 (2022).SCIEAS0036-807510.1126/science.abl5818]. Importantly, our theory predicts the cavity suppression of the thermal activation gap in the quantum Hall transport. Our work paves the way for future developments in cavity control of quantum materials.

Relevance of the Quadratic Diamagnetic and Self-Polarization Terms in Cavity Quantum Electrodynamics.

Experiments at the interface of quantum optics and chemistry have revealed that strong coupling between light and matter can substantially modify the chemical and physical properties of molecules and solids. While the theoretical description of such situations is usually based on nonrelativistic quantum electrodynamics, which contains quadratic light-matter coupling terms, it is commonplace to disregard these terms and restrict the treatment to purely bilinear couplings. In this work, we clarify the physical origin and the substantial impact of the most common quadratic terms, the diamagnetic and self-polarization terms, and highlight why neglecting them can lead to rather unphysical results. Specifically, we demonstrate their relevance by showing that neglecting these terms leads to the loss of gauge invariance, basis set dependence, disintegration (loss of bound states) of any system in the basis set limit, unphysical radiation of the ground state, and an artificial dependence on the static dipole. Besides providing important guidance for modeling of strongly coupled light-matter systems, the presented results also indicate conditions under which those effects might become accessible.

Quantum Electrodynamical Bloch Theory with Homogeneous Magnetic Fields.

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: 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 us 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.