Microscale torsion resonators for short-range gravity experiments

Measuring gravitational interactions on $\mathrm{sub}\text{\ensuremath{-}}100\text{\ensuremath{-}}\mathrm{\ensuremath{\mu}}\mathrm{m}$ length scales offers a window into physics beyond the Standard Model. However, short-range gravity experiments are limited by the ability to position sufficiently massive objects to within small separation distances. Here we propose mass-loaded silicon nitride ribbons as a platform for testing the gravitational inverse square law at separations currently inaccessible with traditional torsion balances. These microscale torsion resonators benefit from low thermal noise due to strain-induced dissipation dilution while maintaining compact size ($<100\text{ }\text{ }\mathrm{\ensuremath{\mu}}\mathrm{g}$) to allow close approach. Considering an experiment combining a $40\text{ }\text{ }\mathrm{\ensuremath{\mu}}\mathrm{g}$ torsion resonator with a source mass of comparable size ($130\text{ }\text{ }\mathrm{\ensuremath{\mu}}\mathrm{g}$) at separations down to $25\text{ }\text{ }\mathrm{\ensuremath{\mu}}\mathrm{m}$, and including limits from thermomechanical noise and systematic uncertainty, we predict these devices can set novel constraints on Yukawa interactions within the $1--100\text{ }\text{ }\mathrm{\ensuremath{\mu}}\mathrm{m}$ range.