  We have fabricated a Cooper-pair transistor (CPT) with parameters such that
for appropriate voltage biases, the sub-gap charge transport takes place via
slow tunneling of quasiparticles that link two Josephson-coupled charge
manifolds. In between the quasiparticle tunneling events, the CPT behaves
essentially like a single Cooper-pair box (SCB). The effective capacitance of a
SCB can be defined as the derivative of the induced charge with respect to gate
voltage. This capacitance has two parts, the geometric capacitance, C_geom, and
the quantum capacitance C_Q. The latter is due to the level anti-crossing
caused by the Josephson coupling. It depends parametrically on the gate voltage
and is dual to the Josephson inductance. Furthermore, it's magnitude may be
substantially larger than C_geom. We have been able to detect C_Q in our CPT,
by measuring the in-phase and quadrature rf-signal reflected from a resonant
circuit in which the CPT is embedded. C_Q can be used as the basis of a charge
qubit readout by placing a Cooper-pair box in such a resonant circuit.
