Improvement for Testing the Gravitational Inverse-Square Law at the Submillimeter Range

We improve the test of the gravitational inverse-square law at the submillimeter range by suppressing the vibration of the electrostatic shielding membrane to reduce the disturbance coupled from the residual surface potential. The result shows that, at a 95% confidence level, the gravitational inverse-square law holds ($|\ensuremath{\alpha}|\ensuremath{\le}1$) down to a length scale $\ensuremath{\lambda}=48\text{ }\text{ }\ensuremath{\mu}\mathrm{m}$. This work establishes the strongest bound on the magnitude $\ensuremath{\alpha}$ of the Yukawa violation in the range of $40--350\text{ }\text{ }\ensuremath{\mu}\mathrm{m}$, and improves the previous bounds by up to a factor of 3 at the length scale $\ensuremath{\lambda}\ensuremath{\approx}70\text{ }\text{ }\ensuremath{\mu}\mathrm{m}$. Furthermore, the constraints on the power-law potentials are improved by about a factor of 2 for $k=4$ and 5.