Measuring the complex admittance of a carbon nanotube double quantum dot

We investigate radio-frequency (rf) reflectometry in a tunable carbon nanotube double quantum dot coupled to a resonant circuit. By measuring the in-phase and quadrature components of the reflected rf signal, we are able to determine the complex admittance of the double quantum dot as a function of the energies of the single-electron states. The measurements are found to be in good agreement with a theoretical model of the device in the incoherent limit. Besides being of fundamental interest, our results present an important step forward towards non-invasive charge and spin state readout in carbon nanotube quantum dots.