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We study adiabatic charge transfer in a superconducting Cooper pair pump,focusing on the influence of current measurement on coherence. We investigatethe limit where the Josephson coupling energy $E_J$ between the various partsof the system is small compared to the Coulomb charging energy $E_C$. In thiscase the charge transferred in a pumping cycle $Q_P \sim 2e$, the charge of oneCooper pair: the main contribution is due to incoherent Cooper pair tunneling.We are particularly interested in the quantum correction to $Q_P$, which is dueto coherent tunneling of pairs across the pump and which depends on thesuperconducting phase difference $\phi_0$ between the electrodes: $1-Q_P/(2e)\sim (E_J/E_C) \cos \phi_0$. A measurement of $Q_P$ tends to destroy the phasecoherence. We first study an arbitrary measuring circuit and then specificexamples and show that coherent Cooper pair transfer can in principle bedetected using an inductively shunted ammeter

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