Superconducting proximity effect in interacting double-dot systems

We study subgap transport from a superconductor through a double quantum dot with large on-site Coulomb repulsion to two normal leads. Non-local superconducting correlations in the double dot are induced by the proximity to the superconducting lead, detectable in non-local Andreev transport that splits Cooper pairs in locally separated, spin-entangled electrons. We find that the $I$--$V$ characteristics are strongly asymmetric: for a large bias voltage of certain polarity, transport is blocked by populating the double dot with states whose spin symmetry is incompatible with the superconductor. Furthermore, by tuning gate voltages one has access to splitting of the Andreev excitation energies, which is visible in the differential conductance.