  A Cooper pair splitter consists of two quantum dots side-coupled to a
conventional superconductor. Usually, the quantum dots are assumed to have a
large charging energy compared to the superconducting gap, in order to suppress
processes other than the coherent splitting of Cooper pairs. In this work, in
contrast, we investigate the limit in which the charging energy is smaller than
the superconducting gap. This allows us, in particular, to study the effect of
a Zeeman field comparable to the charging energy. We find analytically that in
this parameter regime the superconductor mediates an inter-dot tunneling term
with a spin symmetry determined by the Zeeman field. Together with
electrostatically tunable quantum dots, we show that this makes it possible to
engineer a spin triplet state shared between the quantum dots. Compared to
previous works, we thus extend the capabilities of the Cooper pair splitter to
create entangled non local electron pairs.
