Static force characterization with Fano anti-resonance in levitated optomechanics

We demonstrate a classical analogy to the Fano anti-resonance in levitated optomechanics by applying a DC electric field. Specifically, we experimentally tune the Fano parameter by applying a DC voltage from 0~kV to 10~kV on a nearby charged needle tip. We find consistent results across negative and positive needle voltages, with the Fano line-shape feature able to exist at both higher and lower frequencies than the fundamental oscillator frequency. We can use the Fano parameter to characterize our system to be sensitive to static interactions which are ever-present. Currently, we can distinguish a static Coulomb force of $2.7 \pm 0.5 \times 10^{-15}$~N with the Fano parameter, which is measured with one second of integration time. Furthermore, we are able to extract the charge to mass ratio of the trapped nanoparticle.