Constraints on Velocity and Spin Dependent Exotic Interaction at the Millimeter Scale with a Diamagnetic-Levitated Force Sensor.

Light bosons, beyond the standard model and as prominent candidates for dark matter, can mediate velocity and spin dependent exotic interaction between electron spins and nucleons. At short ranges, it remains an open challenge to test this exotic interaction with high precision. Here, we present a method based on a diamagnetic-levitated force sensor to detect the exotic interaction at the millimeter scale. Improved constraints for the coupling g_{A}^{e}g_{V}^{N} are established, within the force range spanning from 0.15 to 1.5 mm. The constraint |g_{A}^{e}g_{V}^{N}|≤4.39×10^{-26} at λ=0.5  mm at the 95% confidence level significantly surpasses previous results by more than 3 orders of magnitude. The diamagnetic levitation force measurement system developed here can also be repurposed to probe other exotic spin dependent interactions, such as the exotic spin-spin interaction. This system provides a platform for the exploration of dark matter.