Abstract
Following our study of the superfluidity of homogeneous Bose gases, this lecture examines the behavior of fluids in the presence of a periodic lattice. In particular, this study led us to the quantum phase transition between the superfluid state and the "Mott insulator" state, a transition demonstrated on cold atoms in 2002.
Our starting point was the superfluid state, described by a Gross-Pitaevskii approach similar to that used in Lecture 3. We described some experiments which showed that the presence of a periodic potential can destabilize a permanent current and break superfluidity. This led us to the superfluid-insulator phase transition, initially studied in a condensed matter context, but transposed to cold atoms in 1998. It has now become emblematic of the possibility of reaching strongly correlated states with dilute gases. We have tackled this superfluid-insulator transition using several approaches, including a simple theoretical treatment based on the Gutzwilleransatz.
