  We propose to optimally control the harmonic potential of a levitated
nanoparticle to quantum delocalize its center-of-mass motional state to a
length scale orders of magnitude larger than the quantum zero-point motion.
Using a bang-bang control of the harmonic potential, including the possibility
to invert it, the initial ground-state-cooled levitated nanoparticle coherently
expands to large scales and then contracts to the initial state in a
time-optimal way. We show that this fast loop protocol can be used to enhance
force sensing as well as to dramatically boost the entangling rate of two
weakly interacting nanoparticles. We parameterize the performance of the
protocol, and therefore the macroscopic quantum regime that could be explored,
as a function of displacement and frequency noise in the nanoparticle's
center-of-mass motion. This noise analysis accounts for the sources of
decoherence relevant to current experiments.
