A zigzag optical cavity for sensing and controlling torsional motion

Abstract: Precision sensing and manipulation of milligram-scale mechanical oscillators has attracted growing interest in the fields of table-top explorations of gravity and tests of quantum mechanics at macroscopic scales. Torsional oscillators present an opportunity in this regard due to their remarked isolation from environmental noise. For torsional motion, an effective employment of optical cavities to enhance optomechanical interactions -- as already established for linear oscillators -- so far faced certain challenges. Here, we propose a novel concept for sensing and manipulating torsional motion, where exclusively the torsional rotations of a pendulum are mapped onto the path length of a single two-mirror optical cavity. The concept inherently alleviates many limitations of previous approaches. A proof-of-principle experiment is conducted with a rigidly controlled pendulum to explore the sensing aspects of the concept and to identify practical limitations in a potential state-of-the art setup. Based on this work, we anticipate development of precision torque sensors with sensitivities below $10^{-19}~\mathrm{N\cdot m/\sqrt{Hz}}$ and with the motion of the pendulums dominated by quantum radiation pressure noise at sub-microwatts of incoming laser power. This work, therefore, paves the way to new horizons for experiments at the interface of quantum mechanics and gravity.