  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.
