Cusp-singularity-enhanced Coriolis effect for sensitive chip-scale gyroscopes | Nature

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Subjects

- Design, synthesis and processing

- Electronic and spintronic devices

- Mechanical engineering

Abstract

Gyroscopes, as fundamental inertial sensors, are crucial for rotation measurements in the consumer electronics, automotive and aerospace industries, with the most widely used kind relying on the Coriolis effect1,2,3,4,5,6. The chip-scale Coriolis vibratory gyroscopes (CVGs) show reduced size, weight and cost1,2 but have far lower performance than traditional macroscale CVGs3,4,5,6, as the weak intrinsic Coriolis factor sets a fundamental limit on scaling the sensitivity against the inherently louder Brownian noise in microchips compared with the macroscale ones. Here, to overcome this physical limit, we propose and experimentally demonstrate the use of third-order singularities lying within cusp catastrophes in the phase-tracked oscillations of an on-chip CVG to facilitate a cubic-root scaling of the Coriolis-effect-induced frequency modulation. Using this effect, we achieve a three-orders-of-magnitude enhancement in the Coriolis factor, yielding a 253-fold improvement in the signal-to-noise ratio and a 297-fold increase in precision. Moreover, the cusp singularity enables a previously unattainable ultrasensitive phase-modulated sublinear measurement, achieving record signal-to-noise ratio performance for silicon-chip gyroscopes. These findings not only provide revolutionary advancements in gyroscope technologies, by filling the gap in observing and controlling the singularity-enhanced Coriolis effect, but also shed new light on other ultrasensitive sensing applications.

Main

Gyroscopes, essential sensors for measuring rotations in free space without the need for external references, play a key role in navigation and stabilization of all kinds of platforms. The most widely used type of gyroscopes operates on the same principle that governs the flight control of certain biological organisms7,8—the Coriolis effect, which refers to the perceived deflection of a moving object in a rotating reference frame. Known as CVGs, they sense angular rotation through Coriolis-force-induced interactions between mechanical (phononic) vibratory modes. Traditional CVGs, such as the hemispherical resonator gyroscopes (HRGs), offer high performance and reliability for applications such as oil drilling, maritime navigation and spacecraft pointing3,4,5,6. However, their high cost limits their widespread use.

Recently, chip-scale CVGs have been developed for much broader uses, including movement monitoring and stabilization control of consumer electronics, automobiles and more1,2, owing to their reduced size, weight and cost compared with traditional CVGs. Despite these advantages, chip-scale CVGs still lag behind HRGs in performance, making them suitable only for medium-end or low-end applications. Enhancing chip-scale CVG performance to match the level of the current HRGs, while preserving their miniaturization and affordability, is highly desirable to enable revolutionary technologies such as GPS-denied personal navigation, advanced robotics and microsatellites. Yet, this goal remains elusive owing to substantial challenges in microfabrication errors and, more fundamentally, the Brownian noise that increases as sensor dimensions shrink, which in turn degrades the signal-to-noise ratio (SNR).

At the heart of this challenge is the limited efficiency of the Coriolis interaction, quantified by the Coriolis factor κ0 that measures the proportion of modal mass contributing to the Coriolis effect. This factor is intrinsically determined by vibratory-mode geometry and always constrained to κ0 ≤ 1 (Supplementary Note 1). Consequently, for small rotation rates Ω, the strength of the Coriolis coupling, 2κ0Ω, is weak. The resulting physical modulations (for example, amplitude or frequency changes) are easily blurred by the inherently stronger Brownian noise of microscale resonators in chip-scale CVGs relative to macroscale HRGs. Whether and how the Coriolis effect itself can be enhanced beyond this sensitivity limit imposed by the Coriolis factor, κ0 ≤ 1, remains an unresolved challenge. Resolving this barrier could enable HRG-level performance in chip-scale CVGs and unlock transformative applications.

Relating to this challenge, recent advances in singularity physics9,10,11,12,13 provide new possibilities for breaking the limit of classical sensing theory, in which sensing responses are proportional to a perturbation ϵ. Instead, Nth-order singularities can provide a sublinear response14,15,16,17,18,19, ∝ϵ1/N, outperforming classical sensors under small perturbations (|ϵ| < 1). For example, up to 20-fold sensitivity enhancements have been reported in the operation of optical gyroscopes near exceptional-point singularities20,21, surpassing the intrinsic limits of the Sagnac effect22. Some singularities were also demonstrated to boost SNR in sensing11,23,24,25,26,27. However, given the inherent complexity