Sensing directional forces in levitated optomechanics

Optomechanical devices are being actively harnessed as sensors for ultraweak forces, with a growing range of applications including inertial sensing or dark matter sensors. Dark matter searches aim to use directional detection to discriminate from interfering backgrounds. We present a calibration-free approach to measurements of directional stochastic forces by using the cross-correlation power spectra. We show that these provide a distinctive signature of the presence of a directional broad-spectrum force, as well as its orientation quadrant. Accurate measurement of the angle offers something akin to a force compass in the x-y plane and a promising tool for dark matter searches.