Measuring gravitational force from Femto-gram source masses

Gravity is the weakest of all known forces. Measuring the force of gravity from micro and nano-scale source masses is an essential first step toward low-energy quantum gravity tests. In addition, measuring gravitational forces where the center-of-mass inter-distance is at the sub-mm scale extends the experimentally achievable parameter space for tests of Yukawa-like corrections to Newtonian gravity and tests for higher dimensions proposed to resolve the hierarchy problem of fundamental forces. Here, we propose an experiment using two optically trapped particles in ultrahigh vacuum conditions where the center of mass inter-distance is on the order of $10^2 nm$. In the proposed experiment, the source mass is a rotating Janus nano-particle such that the test mass (sensor) experiences a periodic gravitational potential. Using realistic experimental parameters, a signal-to-noise ratio $\geq 1$ is obtained for a Janus particle with radius $\geq 10^2 nm$ and a mass $\geq \text{10 } fg$. The proposed experiment extends the search of Yukawa corrections to gravity at $\approx 10^{-5}$ times gravity regime at $10^{2}nm$ interaction range, opens the door to low energy tests for quantum gravity, and enables direct experimental tests of extra-dimensional solutions to the hierarchy problem.