  The controllable positioning of a vacuum-levitated object near a material
surface is of importance for studying short-range forces, such as Casimir
forces, interfacial friction forces, or gravity in yet unexplored parameter
regimes. Here we optically levitate a nanoparticle in a laser beam strongly
focused on a dielectric membrane. By investigating the motion of the trapped
particle in vacuum, we map the position-dependent optical potential of the
particle. We interferometrically measure the distance between the particle and
the surface and demonstrate stable trapping in sub-wavelength proximity of the
dielectric surface. Our work is important for the development of on-chip
levitated optomechanics and for measuring short-range forces at sub-wavelength
distances.
