Quantum-limited optical lever measurement of a torsion oscillator

Abstract: 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 an exceptionally high torque sensitivity, or, equivalently, zero-point angular displacement spectral density. Here, we describe optical lever measurements on Si$_3$N$_4$ nanoribbons possessing $Q>3\times 10^7$ torsion modes with torque sensitivities of $10^{-20}\,\text{N m}/\sqrt{\text{Hz}}$ and zero-point displacement spectral densities of $10^{-10}\,\text{rad}/\sqrt{\text{Hz}}$. Compensating 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 $\sim5000$ phonons. Our study signals the potential for a new class of torsional quantum optomechanics.