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Using the quantum collapse and revival phenomenon of a Bose--Einsteincondensate in three-dimensional optical lattices, the atom number statistics oneach lattice site are experimentally investigated. We observe an interactiondriven time evolution of on-site number fluctuations in a constant latticepotential with the collapse and revival time ratio as the figure of merit.Through a shortcut loading procedure, we prepare a three-dimensional array ofcoherent states with Poissonian number fluctuations. The following dynamicsclearly show the interaction effect on the evolution of the number fluctuationsfrom Poissonian to sub-Poissonian. Our method can be used to create squeezedstates which are important in precision measurement.

Observation of atom-number fluctuations in optical lattices via quantum collapse and revival dynamics