Cooper pair splitting and recombination in a nanoSQUID geometry at high transparency

Abstract

We describe a Josephson device composed of two superconductors separated by two interacting quantum dots in parallel, where clear manifestations of Cooper pair splitting and subsequent recombination occur. Indeed, 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 nonequilibrium scenarios for Cooper pair splitting which involve 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 π) of the quantum dots. We propose a definition of the Cooper pair splitting efficiency (the fraction of the electron transfer processes which involve the splitting of a Cooper pair) 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.

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