  We study theoretically spin pumping in bilayers consisting of superconductors
and antiferromagnetic insulators. We consider both compensated and
uncompensated interfaces and include both the regular scattering channel and
the Umklapp scattering channel. We find that at temperatures close to the
critical temperatures and precession frequencies much lower than the gap, the
spin-current is enhanced in superconductors as compared to normal metals.
Otherwise, the spin-current is suppressed. The relevant precession frequencies
where the spin-current in SC/AFI is enhanced compared to NM/AFI is much lower
than the typical resonance frequencies of antiferromagnets, which makes the
detection of this effect experimentally challenging. A possible solution lies
in the shifting of the resonance frequency by a static magnetic field.
