  We apply the theory of inhomogeneous Kibble-Zurek mechanism to understand
quench dynamics from the Mott insulator to the superfluid in a cold Bose gases
confined in both a two-dimensional optical lattice and a harmonic trap. The
local quench time and the freeze-out region associated with the nonadiabatic
transition take a nontrivial positional dependence due to the Mott-lobe
structure of the ground state phase diagram of the Bose-Hubbard model. We
demonstrate that the quench dynamics through the time-dependent Gutzwiller
simulations, revealing inhomogeneous properties of the growth of the superfluid
order parameter. The inhomogeneous Kibble-Zurek theory is applicable for the
shallow harmonic trap.
