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The optical lever is a precision displacement sensor with broad applications. In principle, it can track the motion of a mechanical oscillator with added noise at the standard quantum limit (SQL); however, demonstrating this performance requires an oscillator with exceptionally high torque sensitivity or, equivalently, zero-point angular displacement spectral density. Here, we describe optical lever measurements on nanoribbons possessing torsion modes with torque sensitivities of and zero-point displacement spectral densities of . By compensating for aberrations and leveraging immunity to classical intensity noise, we realize angular displacement measurements with imprecisions 20 dB below the SQL and demonstrate feedback cooling, using a position-modulated laser beam as a torque actuator, from room temperature to Si₃N₄phonons. Our study signals the potential for a new class of torsional quantum optomechanics. 

We derive a nonlinear equation of motion for a chip-scale pendulum comprising a thick plate suspended from a tensioned nanoribbon. Recently, we explored the use of such a device as a clock gravimeter, exploiting the parametric coupling of its frequency to the local acceleration of gravity and demonstrating micro-g resolution with a silicon nitride prototype. Here we consider the restoring torque arising from the mid-plane stretching of the nanoribbon, finding it is a hardening spring that can be used to counteract the softening of gravitational torques, reducing parametric frequency noise and extending the range of isochronous pendulation. Using the method of multiple scales, we predict that parametric frequency-amplitude coupling can be driven to zero by exploiting fabrication tolerances available using modern nanolithography. 

Membrane-based cavity optomechanical systems have been widely successful; however, their chip-scale integration remains a significant challenge. Here we present a solution based on metasurface design. Specifically, by non-periodic photonic crystal patterning of a Si₃N₄membrane, we realize a suspended metamirror with a finite focal length, enabling formation of a stable optical cavity with a plane end-mirror. We present simulation, fabrication, and characterization of the metamirror using both free-space and cavity-based measurements, demonstrating reflectivities as high as 99% and cavity finesse as high as 600. The mirror radius of curvature (∼30cm) is inferred from the cavity mode spectrum. In combination with phononic engineering, focusing membrane mirrors offer a route towards high-cooperativity, vertically integrated cavity optomechanical systems with applications ranging from precision force sensing to hybrid quantum transduction.