Quantum dot admittance probed at microwave frequencies with an on-chip   resonator
  We present microwave frequency measurements of the dynamic admittance of a quantum dot tunnel coupled to a two-dimensional electron gas. The measurements are made via a high-quality 6.75 GHz on-chip resonator capacitively coupled to the dot. The resonator frequency is found to shift both down and up close to conductance resonance of the dot corresponding to a change of sign of the reactance of the system from capacitive to inductive. The observations are consistent with a scattering matrix model. The sign of the reactance depends on the detuning of the dot from conductance resonance and on the magnitude of the tunnel rate to the lead with respect to the resonator frequency. Inductive response is observed on a conductance resonance, when tunnel coupling and temperature are sufficiently small compared to the resonator frequency. 
T. Frey, P. J. Leek, M. Beck, J. Faist, A. Wallraff, K. Ensslin, T.   Ihn, and M. B\"uttiker
cond-mat.mes-hall