Method for measuring surface potential of the test mass with an optically levitated charged microsphere

To investigate the surface potential distribution of the test mass in a gravitational experiment, what we believe to be a novel measurement scheme utilizing a levitated charged microsphere is proposed. The sensitivity of potential measurement is influenced by several key factors, including the diameter of the microsphere, the separation distance, the net charge of the microsphere, and the spring constant. An SiO₂ microsphere with a diameter of 2 µm is optically trapped using collinear laser beams. Through ionization of residual gas molecules in the chamber, the microsphere acquires charge via ion adsorption. The amount of charge on the microsphere is adjusted through a high-voltage power supply. The harmonic motion of the microsphere is monitored by laser interferometry, with corresponding parameter measurements and error analysis provided. The expected force noise is about 4.5×10^-22N/Hz^1/2 at the natural frequency, and the measurement sensitivity of the potential difference reaches 0.15mV/Hz^1/2. This method offers a promising approach for mapping surface potential distribution with higher precision, thereby supporting advancements in precision gravitational experiments.