Relaxation time of a quantum RL circuit in the presence of Coulomb interactions

Abstract

We report on gigahertz admittance measurements indicative of intrinsic relaxation time for an interacting quantum resistance-inductance ($RL$) circuit formed by a gate-defined quantum point contact in the quantum Hall regime. The dependence of the admittance on intrinsic parameters of the circuit is mapped and found to be highly relevant to the driving frequency, the magnetic field, and the edge potential profile. Remarkably, measurements show that in the coherent limit the relaxation time is universal irrespective of resistance and inductance of the circuit, which is given by the electronic time of flight in the circuit. When the quantum $RL$ circuit is exposed to strong electron interactions, classical laws of electrodynamic response of the whole circuit are recovered, associated with observable variations of relaxation time with resistance. The observed transition of the relaxation time is explained in terms of the effect of Coulomb interaction which is tunable in a gate-defined quantum point contact. Our experiment demonstrates that deviations from the resistance-independent relaxation time are governed by the strength of Coulomb interactions, which provides valuable information to sufficiently determine the interaction parameter.