One of the most commonly investigated superconducting quits is the so called Cooper-pair box. The energy levels of such a Cooper-pair box have different curvature in the ground state and in the excited state. This curvature can be thought of as an effective capacitance of the Cooper-pair box consisting of two parts: the geometric capacitance and the quantum capacitance due to the avoided level crossing. This quantum capacitance can be observed directly by rf- reflectometry which allows us to measure the state of a Cooper-pair box qubit.
This read-out method is used to study dressed states of a Cooper-pair box qubit which is driven by a strong microwave field, we show that the level splitting of the dressed states follow Bessel function dependence with excellent agreement between experiment and theory. We can also extract the T1 of these dressed states, we find T1 of the order of a few µs.