Phase transition in an Aubry-André system with a rapidly oscillating magnetic field

Abstract

We investigate a variant of the Aubry-André-Harper (AAH) model corresponding to a bosonic optical lattice of ultracold atoms under an effective oscillatory magnetic field. In the limit of high-frequency oscillation, the system maybe approximated by an effective time-independent Hamiltonian. We have studied localization-delocalization transition exhibited by the effective Hamiltonian. The effective Hamiltonian is found to retain the tight-binding tridiagonal form in position space. In a striking contrast to the usual AAH model, this non-dual system shows an energy-dependent mobility edge—a feature which is usually reminiscent of Hamiltonians with beyond-nearest-neighbor hoppings in real space. Finally, we discuss possibilities of experimentally realizing this system in optical lattices.