Testing the Renormalization of the von Klitzing Constant by Cavity Vacuum Fields

The value of fundamental physical constants is affected by the coupling of matter to the electromagnetic vacuum state, as predicted and explained by quantum electrodynamics. In this work, we present a millikelvin magnetotransport experiment in the quantum Hall regime that assesses the possibility of the von Klitzing constant being modified by strong cavity vacuum fields. By employing a Wheatstone bridge, we measure the difference between the quantized Hall resistance of a cavity-embedded Hall bar and the resistance standard, achieving an accuracy down to one part in ${10}^5$ for the lowest Landau level. While our results do not suggest any deviation that could imply a modified Hall resistance, our work represents pioneering efforts in exploring the fundamental implications of vacuum fields in solid-state systems.