Generating magnon Bell states via parity measurement

We propose a scheme to entangle two magnon modes based on parity measurement. In particular, we consider a system that two yttrium-iron-garnet spheres are coupled to a $V$-type superconducting qutrit through the indirect interactions mediated by cavity modes. An effective parity-measurement operator that can project the two macroscopic spin systems to the desired subspace emerges when the ancillary qutrit is projected to the ground state. Consequently, conventional and multi-excitation magnon Bell states can be generated from any separable states with a nonvanishing population in the desired subspace. The target state can be distilled with a near-to-unit fidelity only by several rounds of measurements and can be stabilized in the presence of the measurement imperfection and environmental decoherence. In addition, a single-shot version of our scheme is obtained by shaping the detuning in the time domain. Our scheme that does not rely on any nonlinear Hamiltonian brings insight to the entangled-state generation in massive ferrimagnetic materials via quantum measurement.