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A Cooper pair splitter consists of two quantum dots side-coupled to aconventional superconductor. Usually, the quantum dots are assumed to have alarge charging energy compared to the superconducting gap, in order to suppressprocesses other than the coherent splitting of Cooper pairs. In this work, incontrast, we investigate the limit in which the charging energy is smaller thanthe superconducting gap. This allows us, in particular, to study the effect ofa Zeeman field comparable to the charging energy. We find analytically that inthis parameter regime the superconductor mediates an inter-dot tunneling termwith a spin symmetry determined by the Zeeman field. Together withelectrostatically tunable quantum dots, we show that this makes it possible toengineer a spin triplet state shared between the quantum dots. Compared toprevious works, we thus extend the capabilities of the Cooper pair splitter tocreate entangled non local electron pairs.

Non local quantum state engineering with the Cooper pair splitter beyond the Coulomb blockade regime