Sweeping from the superfluid to Mott phase in the Bose-Hubbard model

We study the sweep through the quantum phase transition from the superfluid to the Mott state for the Bose-Hubbard model with a time-dependent tunneling rate $J(t)$. In the experimentally relevant case of exponential decay, $J(t)\propto e^{-\gamma t}$, an adapted mean-field expansion for large fillings $n$ yields a scaling solution for the fluctuations. This enables us to analytically calculate the evolution of the number and phase variations (on-site) and correlations (off-site) for slow ($\gamma\ll\mu$), intermediate, and fast (non-adiabatic $\gamma\gg\mu$) sweeps, where $\mu$ is the chemical potential. Finally, we derive the dynamical decay of the off-diagonal long-range order as well as the temporal shrinkage of the superfluid fraction in a persistent ring-current setup.