  Cavity-mediated magnon-magnon coupling can lead to a transfer of spin-wave
excitations between two spatially separated magnetic samples. We enunciate how
the application of a two-photon parametric drive to the cavity can lead to
stark amplification in this transfer efficiency. The recurrent multiphoton
absorption by the cavity opens up an infinite ladder of accessible energy
levels, which can induce higher-order transitions within the magnon Fock space.
This is reflected in a heightened spin-current response from one of the
magnetic samples when the neighboring sample is coherently pumped. The
enhancement induced by the parametric drive can be considerably high within the
stable dynamical region. Specifically, near the periphery of the stability
boundary, the spin current is amplified by several orders of magnitude. Such
striking enhancement factors are attributed to the emergence of parametrically
induced strong coherences precipitated by a long-lived mode. While
contextualized in magnonics, the generality of the principle would allow
applications to energy transfer between systems contained in parametric
cavities.
