Correlated Phases in Bose-Hubbard Models with Simulated Magnetic Fields

Proposed methods for imprinting gauge fields (tunneling phases) in optical lattices open up the prospect of experimental studies of atomic Bose gases that are well described by the Bose-Hubbard model in an effective magnetic field. I shall discuss the nature of the groundstates of such systems. The relevant physics involves the interplay between the fractional quantum Hall effect for bosons and the ``Hofstadter butterfly'' spectrum. I shall explain how this interplay can lead to novel strongly correlated phases. [G. M{\" o}ller and N. R. Cooper, Phys. Rev. Lett. {\bf 103}, 105303 (2009).]