Control of nanoparticles with arbitrary two-dimensional force fields.

An anti-Brownian electrophoretic trap is used to create arbitrary two-dimensional force fields for individual nanoscale objects in solution. The trap couples fluorescence microscopy with digital particle tracking and real-time feedback to generate a position-dependent electrophoretic force on a single nanoparticle. The force may vary over nanometer distances and millisecond times and need not be the gradient of a potential. As illustrations of this technique, I study Brownian motion in harmonic, power-law, and double-well potentials.