# Adiabatic transition from superfluid to Mott insulator?

I have a question about the dynamical passage from superfluid to Mott insulator state in the Bose-Hubbard model. Is it possible to go from superfluid region to the Mott insulator by changing the lattice depth adiabatically? Adiabatically means that the rate of change is slow enough that the state adjust itself to the ground state. Although there is experiment by Greiner et al. and theoretical analysis by Kashurnikov et al. or Zakrzewski, it doesn't talk to me. I would imagine that due to different phases, rate of change would grow to infinity close to the transition point.

Moreover, if you look at the BHM phase diagram you can choose many paths in the Mott insulator state because mean number of particles is everywhere constant.

Note that this diagram is only formally true for the Grand Canonical ensemble, which is necessary to have a well-defined $\mu$. So the path that you take in a phase transition is uniquely set by what $\mu$ is, which is a physical parameter in your system. So there is no ambiguity about which path into the MI region the system takes.