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We consider an s-wave superconductor (SC) which is tunnel-coupled to twospatially separated Luttinger liquid (LL) leads. We demonstrate that such asetup acts as an entangler, i.e. it creates spin-singlets of two electronswhich are spatially separated, thereby providing a source of electronicEinstein-Podolsky-Rosen pairs. We show that in the presence of a bias voltage,which is smaller than the energy gap in the SC, a stationary current ofspin-entangled electrons can flow from the SC to the LL leads due to Andreevtunneling events. We discuss two competing transport channels for Cooper pairsto tunnel from the SC into the LL leads. On the one hand, the coherenttunneling of two electrons into the same LL lead is shown to be suppressed bystrong LL correlations compared to single-electron tunneling into a LL. On theother hand, the tunneling of two spin-entangled electrons into different leadsis suppressed by the initial spatial separation of the two electrons comingfrom the same Cooper pair. We show that the latter suppression dependscrucially on the effective dimensionality of the SC. We identify a regime ofexperimental interest in which the separation of two spin-entangled electronsis favored. We determine the decay of the singlet state of two electronsinjected into different leads caused by the LL correlations. Although theelectron is not a proper quasiparticle of the LL, the spin information canstill be transported via the spin density fluctuations produced by the injectedspin-entangled electrons.Comment: 15 pages, 2 figure

Superconductor coupled to two Luttinger liquids as an entangler for electron spins