Femtonewton force sensing with optically trapped nanotubes.

We extract the distribution of both center-of-mass and angular fluctuations from three-dimensional tracking of optically trapped nanotubes. We measure the optical force and torque constants from autocorrelation and cross-correlation of the tracking signals. This allows us to isolate the angular Brownian motion. We demonstrate that nanotubes enable nanometer spatial and femtonewton force resolution in photonic force microscopy, the smallest to date. This has wide implications in nanotechnology, biotechnology, nanofluidics, and material science.