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Optomechanical devices are being harnessed as sensors of ultraweak forces forapplications ranging from inertial sensing to the search for the elusive darkmatter. For the latter, there is a focus on detection of either higher energysingle recoils or ultralight, narrowband sources; a directional signal isexpected. However, the possibility of searching for a stochastic stream of weakimpulses, or more generally a directional broadband signal, need not beexcluded; with this and other applications in mind, we investigate theexperimental signature of Gaussian white noise impulses with a well defineddirection $\Psi$ on a levitated nanosphere, trapped and 3D cooled in an opticaltweezer. We find that cross-correlation power spectra offer a calibration-freedistinctive signature of the presence of a directional but stochasticmicroscopic force and its orientation quadrant, unlike normal power spectraldensities (PSDs). We obtain excellent agreement between theoretical andexperimental results. With calibration we are able to measure the angle $\Psi$,akin to a force compass in a plane. We discuss prospects for extending thistechnique into quantum regime and compare the expected behaviour of quantumbaths and classical baths.

Sensing microscopic directional noise baths with an optically cooled and levitated nanoparticle