Superior frequency stability and long-lived state-swapping in cubic-SiC mechanical mode pairs

The multimode cavity optomechanical system offers versatile applications, including state transduction, coherent interconnection, and many-body simulations. In this work, we establish a high-quality-factor 3C-SiC membrane resonator as a versatile platform for multimode cavity optomechanics, demonstrating its capabilities from precise stress characterization to coherent quantum operations. We first perform a collective fit of the measured frequencies of 57 mechanical modes to a theoretical expression that incorporates nonuniform in-plane stress. This analysis reveals a biaxial stress difference on the order of MPa and demonstrates the remarkable resolution of this method for stress analysis in thin films. Subsequently, the membrane is integrated with a rectangular superconducting cavity to form an electromechanical system, enabling the investigation of frequency stability in degeneracy-broken mechanical mode pairs. These modes exhibit exceptional quality factors up to 108 at 10 mK. Furthermore, Allan deviation indicates that these modes exhibit extremely stable frequencies compared with different types of optomechanical devices. Finally, we demonstrate a state-swapping between near-degenerate mode pairs, demonstrating the transfer efficiency exceeding 78%, attributed to their exceptionally long lifetimes. This study paves the way for the design of compact quantum phononic devices featuring high-quality-factor mechanical multimodes.