We follow up on a recent suggestion by C. Orzel et. al., Science, 291, 2386
(2001), whereby bosons in an optical lattice would be subjected to a sudden
parameter change from the Mott to the superfluid phase. We analyze the Bose
Hubbard model with a modified coherent states path integral which can escribe -
both - phases. The saddle point theory yields collective oscillations of the
uniform superfluid order parameter. These would be seen in time resolved
interference patterns made by the released gas. We calculate the collective
oscillation's damping rate by phason pair emission. In two dimensions the
overdamped region largely overlaps with the quantum critical region.
Measurements of critical dynamics on the Mott side are proposed.Comment: 4 pages 1 eps figures; Final version as appears in PRL. Added
discussion on spontaneous generation of vortice