Micro- and nanomechanical resonators, due to their small mass and strong coupling with light and matter, are valuable for precision metrology (mass and force sensing) and exploring macroscopic quantum physics. Reducing mechanical dissipation is crucial for enhancing performance by increasing coherence time. Traditional methods focus on separating eigenmodes from lossy modes using deep energy potentials or periodic structures. However, for non-periodic resonators, minimizing supporting structures is necessary, increasing fabrication difficulty and limiting application scenarios (e.g., fluid-based applications). Bound states in the continuum (BICs), eigenstates with infinite lifetime overlapping with lossy states, offer a solution. While BICs have been demonstrated in optical, acoustic, and mechanical domains, mostly using periodic structures with specific symmetry, this study aims to experimentally demonstrate BICs in an individual, non-periodic mechanical resonator, offering advantages in miniaturization and applications in precision metrology and quantum physics. Previous work demonstrated BICs in individual optical and acoustic resonators, but not in individual mechanical resonators.

The concept of BICs, initially from quantum mechanics, has been extended to various fields. Numerous studies have explored BICs in optical systems, demonstrating applications in low-threshold lasing, ultrasensitive sensing, and vortex beam generation. Similarly, research on acoustic and mechanical BICs has shown promise. However, most experimental demonstrations relied on periodic structures with specific symmetries, limiting their applications due to large footprints and modal volumes. This research builds upon previous work on BICs in individual optical and acoustic resonators, extending the concept to the micromechanical domain to address the challenges of dissipation in individual mechanical resonators.

The researchers experimentally demonstrated mechanical BICs in an optomechanical microresonator by breaking the azimuthal symmetry of a ring-shaped resonator. This was achieved by modifying the inner boundary to an ellipse, introducing coupling between a radial-contour mode and a wine-glass mode. This coupling, described by a Hamiltonian considering resonant frequencies, dissipation rates, and a coupling coefficient, leads to an anticrossing of modes. The Friedrich-Wintgen condition, where κ(γ₁γ₂) = √γ₁γ₂(ω₁ − ω₂), was used to identify the BIC, resulting in a hybrid mode with zero dissipation. A wheel-shaped resonator with two supporting rods was designed and simulated to investigate the effect of supporting structures on modal coupling and BIC formation. Simulations varied the supporting rods' width (*d*) and the semi-major axis (*r_x*) of the ellipse to determine the conditions for achieving high-Q BICs. The fabricated wheel-shaped optomechanical microresonator, with dimensions defined by parameters like inner and outer radius, semi-major and semi-minor axes of the inner ellipse, rod width and center disk radius, utilized optomechanical transduction to detect thermomechanical vibrations. Optical whispering-gallery modes circulating around the outer periphery were used to measure the mechanical Q factors. Experiments involved measuring the mechanical Q factors of the resonators under varying ambient pressures to analyze the contribution of different loss mechanisms (clamping loss, air damping, material loss).

The study successfully demonstrated mechanical BICs in a fabricated optomechanical microresonator. Simulations showed an anticrossing of modal frequencies and a drastic variation in the mechanical Q factor of one mode (mode A') near *r_x* = 20.8 µm, regardless of the supporting rod width (*d*), indicating the formation of a Friedrich-Wintgen quasi-BIC. The simulated mechanical Q factor remained above 10⁸ for a wide range of *d* (0.5 to 8 µm), highlighting robustness against variations in the dissipation channel. Experimental measurements confirmed the existence of the two modes (A' and B') and their frequencies, showing good agreement with simulations. Mode A' achieved a maximum measured mechanical Q factor of 9453 at *r_x* = 20.8 µm, confirming the experimental realization of the mechanical BIC. Measurements under various ambient pressures revealed that air damping was the primary loss mechanism at higher pressures, while clamping loss was effectively eliminated at the BIC point.

The successful observation of mechanical BICs in an individual, non-periodic microresonator represents a significant advancement. This method offers a new paradigm for constructing high-Q micromechanical resonators by leveraging symmetry breaking and modal coupling, unlike conventional methods relying on minimized supporting structures or surrounding phononic bandgap structures. The robust nature of the BIC, maintained across a wide range of supporting rod widths, simplifies fabrication and enhances the practicality of the devices. The lower-than-simulated experimental Q factor at the BIC point is attributed to loss mechanisms such as air damping and material loss that were not fully accounted for in the simulations. This work opens possibilities for developing high-performance micromechanical resonators for various applications.

This research successfully demonstrated the experimental observation of mechanical bound states in the continuum (BICs) in an optomechanical microresonator. The achievement of high-Q factors, even with relatively large and robust supporting structures, offers a new path towards creating high-performance micromechanical devices. Future research could focus on further reducing residual losses (air damping and material loss) to reach even higher Q factors and exploring applications in sensitive sensing and quantum information processing.

The achieved experimental Q factor (9453) was lower than the simulated value, primarily due to air damping and material loss, which were not fully suppressed. Future studies should focus on minimizing these losses to further improve the Q factor. The study primarily focused on the clamping loss reduction, neglecting other loss mechanisms which might impact device performance in real-world applications.