Motivated by recent interest in quantum control of magnons in magnetic
insulators, we propose a scheme for engineering momentum-space entanglement
of fragmented magnon condensates. We consider easy plane frustrated
antiferromagnets where magnon dispersions have degenerate minima that
represent ``umbrella" chiral spin textures. We show that with an applied
sinusoidal magnetic field, the ground state can be tuned near a quantum
critical point that exhibits macroscopic quantum coherence. The size of the
macroscopic superposition as determined by the Fisher quantum information is
shown to be measureable through the magnetic structure factor obtained by
neutron scattering. We also show that the quantum phase transition is
signaled by a singularity in the momentum-space entanglement entropy. Our
model is representative of equilibrium magnon condensates in frustrated
antiferromagnets such as CsCuCl_3, and can also be simulated in spin-orbit
coupled Mott insulators in atomic optical lattices and circuit quantum
electrodynamics.