Cooper pair splitting in a nanoSQUID geometry at high transparency

TL;DR

This paper proposes a Josephson device with two quantum dots for detecting Cooper pair splitting via Aharonov-Bohm measurements, analyzing phase effects and efficiency across different transparencies.

Contribution

It introduces a novel high-transparency nanoSQUID geometry for probing Cooper pair splitting using a path integral approach and phase analysis.

Findings

Crossed Andreev reflection can be detected via DC Josephson current measurements.

Phase configurations can be optimized to enhance Cooper pair splitting efficiency.

The model applies to nanowire-based quantum dot systems.

Abstract

We describe a Josephson device composed of two superconductors separated by two interacting quantum dots in parallel, as a probe for Cooper pair splitting. In addition to sequential tunneling of electrons through each dot, an additional transport channel exists in this system: crossed Andreev reflection, where a Cooper pair from the source is split between the two dots and recombined in the drain superconductor. Unlike non-equilibrium scenarios for Cooper pair splitting which involves superconducting/normal metal "forks", our proposal relies on an Aharonov-Bohm measurement of the DC Josephson current when a flux is inserted between the two dots. We provide a path integral approach to treat arbitrary transparencies, and we explore all contributions for the individual phases ($0$ or $\pi$) of the quantum dots. We propose a definition of the Cooper pair splitting efficiency for arbitrary transparencies, which allows us to find the phase associations which favor the crossed Andreev process. Possible applications to experiments using nanowires as quantum dots are discussed.