  Optically trapped nanospheres in high-vaccum experience little friction and
hence are promising for ultra-sensitive force detection. Here we demonstrate
measurement times exceeding $10^5$ seconds and zeptonewton force sensitivity
with laser-cooled silica nanospheres trapped in an optical lattice. The
sensitivity achieved exceeds that of conventional room-temperature solid-state
force sensors, and enables a variety of applications including electric field
sensing, inertial sensing, and gravimetry. The optical potential allows the
particle to be confined in a number of possible trapping sites, with precise
localization at the anti-nodes of the optical standing wave. By studying the
motion of a particle which has been moved to an adjacent trapping site, the
known spacing of the lattice anti-nodes can be used to calibrate the
displacement spectrum of the particle. Finally, we study the dependence of the
trap stability and lifetime on the laser intensity and gas pressure, and
examine the heating rate of the particle in high vacuum in the absence of
optical feedback cooling.
