Light-Induced Hofstadter's Butterfly Spectrum of Ultracold Atoms on the Two-Dimensional Kagomé Lattice

We investigate the energy spectrum of ultracold atoms on the two-dimensional Kagomé optical lattice under an effective magnetic field, which can be realized with laser beams. We derive the generalized Harper's equations from the Schrödinger equation. The energy spectrum with a fractal band structure is obtained by numerically solving the generalized Harper's equations. We analyze the properties of the Hofstadter's butterfly spectrum and discuss its observability.