Optomechanical vector sensing of new forces at 6 micron separation

The search for new gravity-like interactions at the sub-millimeter scale is a compelling area of research, with important implications for the understanding of classical gravity and its connections with quantum physics. We report improved constraints on Yukawa-type interactions in the $10\,\mathrm{\mu m}$ regime using optically levitated dielectric microspheres as test masses. The search is performed, for the first time, sensing multiple spatial components of the force vector, and with sensitivity improved by a factor of $\sim 100$ with respect to previous measurements using the same technique. The resulting upper limit on the strength of a hypothetical new force is $10^7$ at a Yukawa range $\lambda\simeq 5\;\mu$m and close to $10^6$ for $\lambda \gtrsim 10\;\mu$m. This result also advances our efforts to measure gravitational effects using micrometer-size objects, with important implications for embryonic ideas to investigate the quantum nature of gravity.