Emergence of a Landau level structure in dark optical lattices

An optical flux lattice is a set of light beams that couple different internal states of an atom, thereby producing topological energy bands. Here we present a configuration in which the atoms exhibit a dark state, i.e. an internal state that is not coupled to the light. At large light intensity, the low-energy dynamics is restricted to the dark state, leading to an effective continuum model with a Landau-level-like structure. This structure is dramatically different from that of usual topological optical lattices, which lead to discrete models in the tight-binding limit. For well-chosen atomic species, the proposed system is essentially immune to heating due to photon scattering, making it a highly promising way to emulate the integer or fractional quantum Hall effect.