Circuit influence on Cooper-pair current in solid-state entanglers

We study the effects of the circuit impedance on tunneling of Cooper pairs from a superconductor into two normal-metal leads. We derive the expressions for the crossed and direct Andreev current and consider the limits of ballistic and diffusive electron motion in the electrodes. The derived analytic expressions show that voltage cross correlations, induced by the capacitive coupling of normal-metal leads, narrow the region where the crossed Andreev current dominates over the direct Andreev current, thereby reducing the efficiency of the entangler.