  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.
