Magnon-microwave backaction noise evasion in cavity magnomechanics

In cavity magnomechanical systems, magnetic excitations couple simultaneously with mechanical
vibrations and microwaves, incorporating the tunability of magnetism and the long lifetimes of
mechanical modes. Applications of such systems, such as thermometry and sensing, require precise
measurement of the mechanical degree-of-freedom with as less added noise as possible, a feature not
proposed in the literature. In this paper, we propose a scheme for realizing backaction evading
measurements of the mechanical vibrations in cavity magnomechanics. Our proposal involves driving
the microwave cavity with two tones separated by twice the phonon frequency and with amplitudes
satisfying a balance relation. We show that the minimum added imprecision noise is obtained for drives
centered around the lower frequency magnon-microwave polaritons, which can beat the standard
quantum limit at modest drive amplitudes. Our scheme is a simple and flexible way of engineering
backaction evasion measurements that can be further generalized to other multimode systems.