Cooling and squeezing a microwave cavity state with magnons using an optomechanical-type coupling

We propose two geometries to realize a significant optomechanical-type coupling (XZ coupling) between magnons and a two-dimensionl microwave cavity mode. In both setups the cavity is analogous to the mechanical oscillator in a conventional optomechanical setup. The backaction effects are calculated with realistic experimental parameters. The analytical results show that we can not only make the backaction damping (antidamping) rate larger than the bare microwave resonator damping rate, but that we can also achieve quantum squeezing of the resonator where the uncertainty in one quadruture (charge or current) is smaller than its zero-point fluctuation.