  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.
