  The accurate measurement of the net charge on a nanoparticle is critical in
both the research and application of nanoparticles. Particularly, in the field
of precision sensing based on optically levitated nanoparticles, the precise
measurement of the net charge on a nanoparticle is prerequisite for stable
levitation before electric control process and for the detecting of quantities
such as the electric field. However, the accurate measurement of the net charge
on a levitated nanoparticle still faces challenges. Here, we proposes a method
to measure the net charge accurately through its thermally and harmonically
driven motional signals. With the numerical calculation of the dynamic
temperature of the optically-levitated nanoparticle, the long-term dynamic net
charge on the nanoparticle can be tracked. This method can achieve an accurate
measurement with the accuracy of better than 5% at thermal equilibrium
pressures of more than 10 mbar and accuracy of ~20% till 3 mbar, where the net
charge barely changes spontaneously, and nonlinearities in the levitated
oscillator is relatively small. As the net charge is integer discrete, the
method provides nearly completely accurate measurements of nanoparticles with
few charges. The result can be applied to improve the measurement accuracy for
mass and density through iteration and this method provides a way toward
non-contact characterization of aerology, space dust, etc.
