  We consider phase coherence collapse and revival in deep optical lattices,
and calculate within the Bose-Hubbard model the revival amplitude damping
incurred by a finite tunneling coupling of the lattice wells (after sweeping
from the superfluid to the Mott phase). Deriving scaling laws for the
corresponding decay of first-order coherence revival in terms of filling
factor, final lattice depth, and number of tunneling coupling partners, we
estimate whether revival-damping related to tunneling between sites can be or
even has already been observed in experiment.
