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

Abstract

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 ${Q}_{P}\ensuremath{\sim}2e,$ 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 ${\ensuremath{\varphi}}_{0}$ between the electrodes; $1\ensuremath{-}{Q}_{P}/(2e)\ensuremath{\sim}{(E}_{J}{/E}_{C})\mathrm{cos}{\ensuremath{\varphi}}_{0}.$ 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.