Quantum-limited optical lever measurement of a torsion oscillator

TL;DR

This paper demonstrates quantum-limited optical lever measurements on high-Q nanoribbons, achieving displacement sensitivities below the Standard Quantum Limit and enabling feedback cooling, advancing torsional quantum optomechanics.

Contribution

It reports the first optical lever measurements reaching below the SQL on high-Q torsional nanoribbons, showing potential for quantum torsional optomechanics.

Findings

Angular displacement measurement imprecisions 20 dB below SQL.

Achieved feedback cooling from room temperature to ~5000 phonons.

Demonstrated high torque sensitivity of 10^{-20} N·m/√Hz.

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.