  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 $E_J$ between the various parts
of the system is small compared to the Coulomb charging energy $E_C$. In this
case the charge transferred in a pumping cycle $Q_P \sim 2e$, 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 $Q_P$, which is due
to coherent tunneling of pairs across the pump and which depends on the
superconducting 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 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.
