Novel quantum phases become accessible when the molecules are able to tunnel in the lattice. The zero-temperature phase diagram as a function of tunnelling rate J and chemical potential (both scaled to the DDI strength V ) exhibits a devil’s staircase (DS) with chequerboard, stripe and star Mott lobes (shown right), as well as superfluid (SF) and supersolid (SS) phases. Other situations show topological phases. Panels adapted with permission from ref. 89 , APS
