  Strong long-distance spin-spin coupling is desperately demanded for
solid-state quantum information processing, but it is still challenged. Here,
we propose a hybrid quantum system, consisting of a coplanar waveguide (CPW)
resonator weakly coupled to a single nitrogen-vacancy spin in diamond and a
yttrium-iron-garnet (YIG) nanosphere holding Kerr magnons, to realize strong
long-distance spin-spin coupling. With a strong driving field on magnons, the
Kerr effect can squeeze magnons, and thus exponentially enhance the coupling
between the CPW resonator and the squeezed magnons, which produces two
cavity-magnon polaritons, i.e., the high-frequency polariton (HP) and
low-frequency polariton (LP). When the enhanced cavity-magnon coupling
approaches to the critical value, the spin is fully decoupled from the HP,
while the coupling between the spin and the LP is significantly improved. In
the dispersive regime, a strong spin-spin coupling is achieved with accessible
parameters, and the coupling distance can be up to $\sim$cm. Our proposal
provides a promising way to manipulate remote solid spins and perform quantum
information processing in weakly coupled hybrid systems.
