  We show theoretically that feedback-cooling of two levitated, interacting
nanoparticles enables differential sensing of forces and the observation of
stationary entanglement. The feedback drives the two particles into a
stationary, non-thermal state which is susceptible to inhomogeneous force
fields and which exhibits entanglement for sufficiently strong inter-particle
couplings. We predict that force-gradient sensing at the zepto-Newton per
micron range is feasible and that entanglement due to the Coulomb interaction
between charged particles can be realistically observed in state-of-the-art
setups.
