  The center-of-mass motion of optically trapped dielectric nanoparticles in
vacuum is extremely well-decoupled from its environment, making a powerful tool
for measurements of feeble sub-attonewton forces. We demonstrate a method to
trap and manuever nanoparticles in an optical standing wave potential formed by
retro-reflecting a laser beam from a metallic mirror surface. We can reliably
position a $\sim 170$ nm diameter silica nanoparticle at distances of a few
hundred nanometers to tens of microns from the surface of a gold-coated silicon
mirror by transferring it from a single-beam tweezer trap into the standing
wave potential. We can further scan the two dimensional space parallel to the
mirror surface by using a piezo-driven mirror. This method enables
three-dimensional scanning force sensing near surfaces using optically trapped
nanoparticles, promising for high-sensitivity scanning force microscopy, tests
of the Casimir effect, and tests of the gravitational inverse square law at
micron scales.
