Measuring the Quantum Capacitance of a Differential Single Cooper-Pair Box

We present a simple method for measuring the quantum capacitance (QC) of a charge qubit based on a Differential Single Cooper-Pair Box using a Differential Radio-Frequency Single Electron Transistor. Measurement of the QC, which is proportional to the second derivative of the energy bands, can in principle be used for state readout at the degeneracy point, where decoherence due to charge fluctuations is at a minimum. The QC is measured by examining the response of the qubit to a small-amplitude AC excitation. Using this technique, we make an independent measurement of the qubit energy relaxation time. Although we have performed this experiment with a differential SCB and differential charge readout, the technique can easily be applied to a conventional SCB.