  We study the preparation and manipulation of states involving a small number
of interacting particles. By controlling the splitting and fusing of potential
wells, we show how to interconvert Mott-insulator-like and trapped BEC-like
states. We also discuss the generation of "Schr\"odinger cat" states by
splitting a microtrap and taking into practical consideration the asymmetry
between the resulting wells. These schemes can be used to perform multiparticle
interferometry with neutral atoms, where interference effects can be observed
only when all the participating particles are measured.
