Towards directional force sensing in levitated optomechanics

TL;DR

This paper introduces a method using mechanical cross-correlation spectra in levitated optomechanics to detect the orientation of external stochastic forces, potentially advancing quantum-limited force sensing and applications like dark matter detection.

Contribution

It proposes a novel approach leveraging $S_{xy}()$ spectra to determine force directionality, addressing detector misalignments and quantum noise effects in levitated nanoparticle sensors.

Findings

Spectral shape of $S_{xy}()$ indicates force orientation.

Method suppresses misalignment and back-action effects.

Quantifies quantum shot noise imprecision near quantum regimes.

Abstract

Levitated nanoparticles are being intensively investigated from two different perspectives: as a potential realisation of macroscopic quantum coherence; and as ultra-sensitive sensors of force, down to the zeptoNewton level, with a range of various applications, including the search for Dark Matter. A future aim is to merge these two strands, enabling the development of quantum-limited sensors. Here we propose that mechanical cross-correlation spectra $S_{xy}(\omega)$ offer new possibilities: once detector misalignment errors are minimised, the spectral shape of $S_{xy}(\omega)$ directly points out the orientation of an external stochastic force, offering something akin to a compass in the $x-y$ plane. We analyse this for detection of microscopic gas currents, but any broad spectrum directed force will suffice, enabling straightforward investigation with laboratory test forces with or without cavities. For a cavity set-up, we analyse misalignment imprecisions between detectors and motional modes due to for example optical back-actions that mask the signature of the directed forces, and show how to suppress them. Near quantum regimes, we quantify the imprecision due to the $x-y$ correlating effect of quantum shot noise imprecision.