Quench from Mott insulator to superfluid

We study a linear ramp of the nearest-neighbor tunneling rate in the Bose-Hubbard model driving the system from the Mott insulator state into the superfluid phase. We employ the truncated Wigner approximation to simulate linear quenches of a uniform system in one, two, and three dimensions, and in a harmonic trap, in three dimensions. In all these setups, the excitation energy decays like one over third root of the quench time. The -1/3 scaling arises from an impulse-adiabatic approximation-a variant of the Kibble-Zurek mechanism-describing a crossover from nonadiabatic to adiabatic evolution when the system begins to keep pace with the increasing tunneling rate.