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Gravity is the weakest of all known forces. Measuring the force of gravityfrom micro and nano-scale source masses is an essential first step towardlow-energy quantum gravity tests. In addition, measuring gravitational forceswhere the center-of-mass inter-distance is at the sub-mm scale extends theexperimentally achievable parameter space for tests of Yukawa-like correctionsto Newtonian gravity and tests for higher dimensions proposed to resolve thehierarchy problem of fundamental forces. Here, we propose an experiment usingtwo optically trapped particles in ultrahigh vacuum conditions where the centerof mass inter-distance is on the order of $10^2 nm$. In the proposedexperiment, the source mass is a rotating Janus nano-particle such that thetest mass (sensor) experiences a periodic gravitational potential. Usingrealistic experimental parameters, a signal-to-noise ratio $\geq 1$ is obtainedfor 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 togravity at $\approx 10^{-5}$ times gravity regime at $10^{2}nm $ interactionrange, opens the door to low energy tests for quantum gravity, and enablesdirect experimental tests of extra-dimensional solutions to the hierarchyproblem.

Measuring gravitational force from Femto-gram source masses