  We present a numerical approach to study the coherent transport of Cooper
pairs through a Hubbard chain, and study the role of the contacts in achieving
perfect Andreev reflection. We calculate the pair transport using the Density
Matrix Renormalization Group by measuring the response of the system to quantum
pair fields with complex phases on the two ends of an open system. This
approach gives an effective superfluid weight which is in close agreement with
the Bethe Ansatz results for the superfluid weight for closed Hubbard rings.
