Enhancing entanglement by spin manipulation in Cooper pair splitters

We study a Cooper pair splitter device consisting of two single level quantum dots fabricated in a strong spin-orbit coupling material (such as InAs or InSb) and coupled to a superconductor. The combined presence of spin-orbit coupling and Zeeman field gives rise to a finite probability of Cooper pair tunneling accompanied by spin flip, thereby involving the spin-triplet states of the doubly occupied dots. We show that the population of triplet states leads to the spin blockade of Cooper pair tunneling. The blockade is advantageous for entanglement production if Cooper pair tunneling is resonant, when the blockaded electrons are in a fully entangled spin state. The entangled state is a superposition of singlet and triplet Bell states. We propose two detection schemes, the first based on conventional transport spectroscopy and a second, based on charge detectors, suitable for future devices capable of producing on-demand spin-entangled pairs.