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We propose a scheme for preparing magnon squeezed states in a hybridcavity-magnon-qubit system. The system consists of a microwave cavity thatsimultaneously couples to a magnon mode of a macroscopic yttrium-iron-garnet(YIG) sphere via the magnetic-dipole interaction and to a transmon-typesuperconducting qubit via the electric-dipole interaction. By far detuning fromthe magnon-qubit system, the microwave cavity is adiabatically eliminated. Themagnon mode and the qubit then get effectively coupled via the mediation ofvirtual photons of the microwave cavity. We show that by driving the qubit withtwo microwave fields and by appropriately choosing the drive frequencies andstrengths, magnonic parametric amplification can be realized, which leads tomagnon quadrature squeezing with the noise below vacuum fluctuation. We provideoptimal conditions for achieving magnon squeezing, and moderate squeezing canbe obtained using currently available parameters. The generated squeezed statesare of a magnon mode involving more than $10^{18}$ spins and thus macroscopicquantum states. The work may find promising applications in quantum informationprocessing and high-precision measurements based on magnons and in the study ofmacroscopic quantum states.

Magnon squeezing by two-tone driving of a qubit in cavity-magnon-qubit systems