Synthetic magnetic fluxes on the honeycomb lattice

We devise experimental schemes that are able to mimic uniform and staggered magnetic fluxes acting on ultracold two-electron atoms, such as ytterbium atoms, propagating in a honeycomb lattice. The atoms are first trapped into two independent state-selective triangular lattices and then further exposed to a suitable configuration of resonant Raman laser beams. These beams induce hops between the two triangular lattices and make atoms move in a honeycomb lattice. Atoms traveling around each unit cell of this honeycomb lattice pick up a nonzero phase. In the uniform case, the artificial magnetic flux sustained by each cell can reach about two flux quanta, thereby realizing a cold-atom analog of the Harper model with its notorious Hofstadter's butterfly structure. Different condensed-matter phenomena such as the relativistic integer and fractional quantum Hall effects, as observed in graphene samples, could be targeted with this scheme.