  Using the quantum collapse and revival phenomenon of a Bose--Einstein
condensate in three-dimensional optical lattices, the atom number statistics on
each lattice site are experimentally investigated. We observe an interaction
driven time evolution of on-site number fluctuations in a constant lattice
potential with the collapse and revival time ratio as the figure of merit.
Through a shortcut loading procedure, we prepare a three-dimensional array of
coherent states with Poissonian number fluctuations. The following dynamics
clearly show the interaction effect on the evolution of the number fluctuations
from Poissonian to sub-Poissonian. Our method can be used to create squeezed
states which are important in precision measurement.
