We consider a new kind of superconducting proximity effect created by the tunneling of "spin split" Cooper pairs between two conventional superconductors connected by a normal conductor containing a quantum dot. The difference compared to the usual superconducting proximity effect is that the spin states of the tunneling Cooper pairs are split into singlet and triplet components by the electron spin-orbit coupling, which is assumed to be active in the normal conductor only. We demonstrate that the supercurrent carried by the spin-split Cooper pairs can be manipulated both mechanically and electrically for strengths of the spin-orbit coupling that can realistically be achieved by electrostatic gates.

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