  A scheme is presented for engineering momentum-space entanglement of
fragmented magnon condensates. We consider easy plane frustrated
antiferromagnets in which the magnon dispersion has degenerate minima that
represent umbrella chiral spin textures. With an applied magnetic field, we
tune the Hamiltonian near a quantum critical point that is is signaled by a
singularity in the entanglement entropy. The ground state develops
momentum-space entanglement of the chiral spin textures. The size of the
entangled superposition is accessible experimentally through the magnetic
structure factor. Our model is motivated by equilibrium magnon condensates in
frustrated antiferromagnets such as CsCuCl3, and it can also be simulated in
spin-orbit coupled Mott insulators in atomic optical lattices and circuit
quantum electrodynamics.
