Nonlinear self-sustaining dynamics in cavity magnomechanics

A recent experiment [R. C. Shen et al., Phys. Rev. Lett. 129, 123601 (2022)] has demonstrated the occurrence of nonlinearity-induced asymptotic bistability in cavity magnomechanics. As an extension, we explore the theoretical ground of diverse potential self-sustaining effects in cavity magnomechanics by analyzing its nonlinear dynamics. The attractors which suggest dynamical multistability for the limit cycles are mapped out to the parameter space by deriving the corresponding slow amplitude dynamics. Our quantitative analysis also includes the fluctuation-dissipation process, which quantitatively predicts non-Gaussian phase spreading, amplitude squeezing, and the mixture of multiple limit cycle states. We finally explore the quantum self-sustaining dynamics by solving the full quantum master equation. The paper lays the foundation for various applications, e.g., high-precision measurements, squeezed-state and non-Gaussian-state preparation, and nonlinearly induced quantum phase transitions, based on cavity magnomechanics.