  We investigate theoretically magnon-mediated superconductivity in a
heterostructure consisting of a normal metal and a two-sublattice
antiferromagnetic insulator. The attractive electron-electron pairing
interaction is caused by an interfacial exchange coupling with magnons residing
in the antiferromagnet, resulting in p-wave, spin-triplet superconductivity in
the normal metal. Our main finding is that one may significantly enhance the
superconducting critical temperature by coupling the normal metal to only one
of the two antiferromagnetic sublattices employing, for example, an
uncompensated interface. Employing realistic material parameters, the critical
temperature increases from vanishingly small values to values significantly
larger than 1 K as the interfacial coupling becomes strongly
sublattice-asymmetric. We provide a general physical picture of this
enhancement mechanism based on the notion of squeezed bosonic eigenmodes.
