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

Optomechanical devices are being harnessed as sensors of ultraweak forces for applications ranging from inertial sensing to the search for the elusive dark matter. For the latter, there is a focus on detection of either higher energy single recoils or ultralight, narrowband sources; a directional signal is expected. However, the possibility of searching for a stochastic stream of weak impulses, or more generally a directional broadband signal, need not be excluded; with this and other applications in mind, we investigate the experimental signature of Gaussian white noise impulses with a well defined direction $\Psi$ on a levitated nanosphere, trapped and 3D cooled in an optical tweezer. We find that cross-correlation power spectra offer a calibration-free distinctive signature of the presence of a directional but stochastic microscopic force and its orientation quadrant, unlike normal power spectral densities (PSDs). We obtain excellent agreement between theoretical and experimental results. With calibration we are able to measure the angle $\Psi$, akin to a force compass in a plane. We discuss prospects for extending this technique into quantum regime and compare the expected behaviour of quantum baths and classical baths.