Squeezing and quantum control of the antiferromagnetic magnon pseudospin

Antiferromagnets have been shown to harbor strong magnon squeezing in equilibrium, making them a potential resource for quantum correlations and entanglement. Recent experiments have also found them to host coherently coupled magnonic excitations forming a magnon pseudospin, in analogy to electronic spin. Here, we delineate the quantum properties of the antiferromagnetic magnon pseudospin by accounting for spin nonconserving interactions and going beyond the rotating wave approximation. Employing concrete examples of nickel oxide and hematite, we find strong squeezing of the magnon pseudospin highlighting its important role in determining the eigenmode quantum properties. Via ground-state quantum fluctuations engineering, this pseudospin squeezing enables an enhancement and control of coupling between the magnonic modes and other excitations. Finally, we evaluate the quantum superpositions that comprise a squeezed pseudospin ground state and delineate a qubit spectroscopy protocol to detect them. Our results are applicable to any system of coupled bosons and thus introduce quantum fluctuations engineering of a general bosonic pseudospin.