Optical measurement and feedback control of a ferromagnetic mechanical resonator

The measurement and control of mechanical resonators are critical for cavity magnomechanics, which has emerged as an important frontier for hybrid quantum systems based on magnonics. Traditional microwave-based measurements require handling high-frequency signals and cannot achieve field distribution detection. Here, we demonstrate a method for optically measuring and manipulating a ferromagnetic mechanical resonator. This technique allows for direct observation of the response and field distribution of mechanical oscillations during magnomechanically induced transparency/absorption processes, confirming that the mechanical mode S1,2 is coupled with the magnon. The optical measurement not only serves to validate the magnomechanical coupling theory but also reduces the necessity for high-frequency measurements. Furthermore, we utilize the instantaneously measured results to implement feedback control of the self-oscillating mechanical resonator to overcome the dynamical back-action limit, achieving a threefold enhancement of phonon lasing amplitude. This feedback control lays the foundation for the study of quantum cavity magnomechanics, such as the feedback cooling of a magnomechanical resonator.