One of the most important techniques in the ultracold atom toolbox is the
optical lattice: a periodic scalar potential formed from standing waves of
light. Optical lattices are central to the use of atomic gases as quantum
simulators, and allow the exploration of strong-correlation phenomena
related to condensed matter systems. In this talk, I shall describe how
simple laser configurations can give rise to a new kind of optical lattice
-- a so-called "optical flux lattice" -- in which optically dressed atoms
experience a periodic effective magnetic flux with high mean density.
Optical flux lattices have narrow energy bands with nonzero Chern numbers,
analogous to the Landau levels of a charged particle in a uniform magnetic
field. These lattices will greatly facilitate the achievement of the
quantum Hall regime for ultracold atomic gases.