Measurement of coherent charge transfer in an adiabatic Cooper-pair pump

We study adiabatic charge transfer in a superconducting Cooper-pair pump, focusing on the influence of current measurement on coherence. We investigate the limit where the Josephson coupling energy EJ between the various parts of the system is small compared to the Coulomb charging energy EC. In this case, the charge transferred in a pumping cycle QP∼2e, the charge of one Cooper pair: The main contribution is due to incoherent Cooper-pair tunneling. We are particularly interested in the quantum correction to QP, which is due to coherent tunneling of pairs across the pump and which depends on the superconducting phase difference φ0 between the electrodes; 1−QP/(2e)∼(EJ/EC)cosφ0. A measurement of QP tends to destroy the phase coherence. We first study an arbitrary measuring circuit and then specific examples and show that coherent Cooper-pair transfer can, in principle, be detected using an inductively shunted ammeter.