Attonewton-meter torque sensing with a macroscopic optomechanical torsion pendulum

Abstract

Precise measurements of the displacement of, and force acting on, a mechanical oscillator can be performed by coupling the oscillator to an optical cavity. Brownian thermal forces represent a fundamental limit to measurement sensitivity which impedes the ability to use precise force measurements as a tool of fundamental enquiry, particularly in the context of macroscopic quantum measurements and tabletop gravitational experiments. A torsion pendulum with a low mechanical resonant frequency can be limited by very small thermal forces—from its suspensions—at frequencies above resonance. Here, we report torque sensing of a 10-mg torsion pendulum formed by a bar mirror, using two optical cavities on either edge. The rotational mode was measured by subtracting the two signals from the cavities, while intracavity radiation pressure forces were used to trap the torsional mode with a 1 kHz optical spring. The resulting torque sensitivity of 20 aN m/sqrt[Hz] is a record for a milligram-scale torsional oscillator. This allows us to test spontaneous wave-function collapse in a parameter regime that falls in between that tested by space-based experiments, and high-frequency cryogenic cantilevers.