  In the field of ultracold atoms in optical lattices a plethora of phenomena
governed by the hopping energy $J$ and the interaction energy $U$ have been
studied in recent years. However, the trapping potential typically present in
these systems sets another energy scale and the effects of the corresponding
time scale on the quantum dynamics have rarely been considered. Here we study
the quantum collapse and revival of a lattice Bose-Einstein condensate (BEC) in
an arbitrary spatial potential, focusing on the special case of harmonic
confinement. Analyzing the time evolution of the single-particle density
matrix, we show that the physics arising at the (temporally) recurrent quantum
phase revivals is essentially captured by an effective single particle theory.
This opens the possibility to prepare exotic non-equilibrium condensate states
with a large degree of freedom by engineering the underlying spatial lattice
potential.
