  We consider the ground state of a bilayer system of dipolar bosons, where
dipoles are oriented by an external field in the direction perpendicular to the
parallel planes. Quantum Monte Carlo methods are used to calculate the
ground-state energy, the one-body and two-body density matrix, and the
superfluid response as a function of the separation between layers. We find
that by decreasing the interlayer distance for fixed value of the strength of
the dipolar interaction, the system undergoes a quantum phase transition from a
single-particle to a pair superfluid. The single-particle superfluid is
characterized by a finite value of both the atomic condensate and the
super-counterfluid density. The pair superfluid phase is found to be stable
against formation of many-body cluster states and features a gap in the
spectrum of elementary excitations.
