Dynamics of the Bose-Hubbard model: Transition from a Mott insulator to a superfluid

We study the dynamics of phase transitions in the one-dimensional Bose-Hubbard model. To drive the system from a Mott insulator to a superfluid phase, we change the tunneling frequency at a finite rate. We investigate the buildup of correlations during fast and slow transitions using variational wave functions, dynamical Bogoliubov theory, Kibble-Zurek mechanism, and numerical simulations. We show that time-dependent correlations satisfy characteristic scaling relations that can be measured in optical lattices filled with cold atoms.