Bragg resonances and Zener tunneling in quasiperiodic two-dimensional optical lattices and photonic crystals

Nonresonant Zener tunneling in decagonal quasiperiodic structures in two spatial dimensions is defined by its relation to Bragg resonance and is studied by direct numerical simulations and an analytical approach. It is shown that, in the shallow lattice limit, the tunneling dynamics about the Bragg resonances is described by the multilevel Landau-Zener-Majorana models, which capture the essential peaks of the complicated Fourier spectrum. The results have applications to dynamics of cold atoms and Bose-Einstein condensates in quasiperiodic optical lattices, light propagation in quasiperiodic photonic crystals, and ultrasonic experiments with quasiperiodic structures.