  We present an experimental study demonstrating the manipulation of
atom-number distributions of spinor gases after nonequilibrium quantum quenches
across superfluid to Mott-insulator phase transitions in cubic optical
lattices. Our data indicate that atom distributions in individual Mott lobes
can be tuned by properly designing quantum quench sequences, which suggests
methods of maximizing the fraction of atoms in Mott lobes of even occupation
numbers and has applications in attaining different quantum magnetic phases
including massively entangled states. Spatial distributions of gases in
three-dimensional lattices are derived from the observed number distributions,
which reveal complex spatial dynamics during the quantum quenches. Qualitative
agreements are also found between our experimental data and numerical
simulations based on time-dependent Gutzwiller approximations in
two-dimensional systems.
