Mass measurement of optically levitated microspheres using gravitational acceleration and electrostatic force

Optically levitated particles in a vacuum play a key role in the development of precision sensors and the exploration of new physics to our knowledge. However, the uncertainty in particle mass measurement significantly limits the accuracy of such sensors and restricts their practical applications. Here, we present a method for directly measuring the mass of a trapped silica microsphere in a weakly focused vertical levitation system under 10^-5<i>m</i><i>b</i><i>a</i><i>r</i>, without prior knowledge of the particle properties. With absolute gravitational acceleration and a known electric field force as references, this method enables traceable nanogram-level mass measurement of trapped microspheres with an uncertainty of 3.1% in vacuum. This method provides a traceable and low-uncertainty calibration protocol for microsphere mass measurement under vacuum conditions, paving the way for reliable sensing and metrology applications of levitated optomechanical systems.