  We propose and demonstrate wide-band capacitance measurements on a
semiconductor double-quantum dot (DQD) to study tunneling dynamics. By applying
phase-tunable high-frequency signals independently to the DQD and a nearby
quantum-point-contact charge detector, we perform on-chip lock-in detection of
the capacitance associated with the single-electron motion over a wide
frequency range from hertz to a few ten gigahertz. Analyzing the phase and the
frequency dependence of the signal allows us to extract the characteristic
tunneling rates. We show that, by applying this technique to the interdot
tunnel coupling regime, quantum capacitance reflecting the strength of the
quantum-mechanical coupling can be measured.
