Cavity Quantum Hall Hydrodynamics

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.