Cavity Quantum Hall Hydrodynamics

TL;DR

This paper explores how coupling quantum Hall systems to a cavity QED environment affects their electromagnetic response, revealing a second-order reactance effect and shifts in collective excitation modes, while preserving topological properties.

Contribution

It introduces a theoretical framework for understanding cavity-induced effects on quantum Hall hydrodynamics, including a universal approach applicable to various quantum Hall states.

Findings

Hall conductivity remains unchanged with cavity coupling.

Cavity induces a second-order quantum reactance effect.

Shift in the Kohn mode frequency due to cavity coupling.

Abstract

Motivated by recent experiments, we study the coupling of quantum Hall (QH) hydrodynamics to quantum electrodynamics (QED) within a resonance cavity. In agreement with experimental observations, we find that the Hall conductivity remains unchanged. However, the coupling to the cavity induces a second-order quantum reactance effect, contributing distinctly to the longitudinal AC conductivity. This effect arises from the exchange of energy between the QH fluid and cavity photons. Beyond the topological response, we show that the cavity couples to collective excitations, resulting in a shift of the Kohn mode frequency. Our methods are broadly applicable to both integral and fractional QH liquids, and our results offer a universal perspective on the protection of topological properties against long-range interactions induced by electromagnetic cavity modes.