  Oscillators based on levitated particles are promising for the development of
ultrasensitive force detectors. The theoretical performance of levitated
nanomechanical sensors is usually characterized by the so-called thermal noise
limit force detection sensitivity, which does not exhibit spectral specificity
in practical measurements. To characterize the actual detection performance, we
propose a method for the force detection sensitivity calibration of a levitated
nanomechanical sensor based on the harmonic Coulomb force. Utilizing the
measured transfer function, we obtained the force detection sensitivity
spectrum from the position spectrum. Although the thermal noise limit force
detection sensitivity of the system reached $\rm\left( {4.39 \pm 0.62} \right)
\times {10^{ - 20}} N/H{z^{1/2}}$ at $\rm{2.4\times10^{-6} mbar}$ with feedback
cooling, the measured sensitivity away from the resonance was of the order of
$\rm10^{-17} N/Hz^{1/2}$ based on the existing detection noise level. The
calibration method established in our study is applicable to the performance
evaluation of any optical levitation system for high-sensitivity force
measurements.
