  Levitated optomechanics is showing potential for precise force measurements.
Here, we report a case study, to show experimentally the capacity of such a
force sensor. Using an electric field as a tool to detect a Coulomb force
applied onto a levitated nanosphere. We experimentally observe the spatial
displacement of up to 6.6 nm of the levitated nanosphere by imposing a DC
field. We further apply an AC field and demonstrate resonant enhancement of
force sensing when a driving frequency, $\omega_{AC}$, and the frequency of the
levitated mechanical oscillator, $\omega_0$, converge. We directly measure a
force of $3.0 \pm 1.5 \times 10^{-20}$ N with 10 second integration time, at a
centre of mass temperature of 3 K and at a pressure of $1.6 \times 10^{-5}$
mbar.
