Measurement of coherent charge transfer in an adiabatic Cooper pair pump

TL;DR

This paper investigates how current measurement affects quantum coherence in a superconducting Cooper pair pump, demonstrating that coherent pair transfer can be detected with an inductively shunted ammeter.

Contribution

It provides a detailed analysis of the quantum correction to charge transfer in an adiabatic Cooper pair pump and proposes a measurement scheme to detect coherence effects.

Findings

Charge transferred per cycle is approximately 2e due to incoherent tunneling.

Quantum correction depends on the phase difference and ratio E_J/E_C.

Coherent tunneling can be observed with an inductively shunted ammeter.

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 $Q_P \sim 2e$, 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.