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

Jing-Min Hou, Qing-Qing Lu

Jing-Min Hou, Wen‐Xing Yang

Jennie Guzman, Claire Thomas, Pavan Hosur +4 more

Jing-Min Hou

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.

Jing-Min Hou

We propose a scheme to create an effective magnetic field, which can be perceived by cold neutral atoms in a two-dimensional optical lattice, with a laser field with a space-dependent phase and a conventional laser field acting on Λ-type three-level atoms. When the dimensionless parameter α, being the ratio of flux through a lattice cell to one flux quantum, is rational, the energy spectrum shows a fractal band structure, which is so-called Hofstadter's butterfly.

Immanuel Bloch