Generalized Aubry-Andre-Harper Models in Optical Superlattices

Abstract

Ultracold atoms trapped in optical superlattices provide a simple platform for realizing the seminal Aubry-André-Harper (AAH) model. However, the periodic modulations on the nearest-neighbour hoppings have been ignored in this model. In this paper, we find that optical superlattice system actually can be approximately described by a generalized AAH model in the case of $V_1\gg V_2$, with periodic modulations on both on-site energies and nearest-neighbour hoppings, supporting much richer topological properties that are absent in the standard AAH model. Specifically, by calculating Chern numbers and topological edge states, we show that the generalized AAH model possesses multifarious topological phases and topological phase transitions, as compared to the standard AAH model only supporting a single topological phase. Our findings can open up more opportunities for using optical superlattices to study topological and localization physics.

References in corpus (14)

• Topological Quantum Matter with Ultracold Gases in Optical Lattices
• Exploring 4D Quantum Hall Physics with a 2D Topological Charge Pump
• Nearest neighbor tight binding models with an exact mobility edge in one dimension
• Synthetic dimensions and spin-orbit coupling with an optical clock transition
• Spin-orbit coupled fermions in an optical lattice clock
• Localization in one dimensional lattices with non-nearest-neighbor hopping: Generalized Anderson and Aubry-André models
• Direct imaging of topological edge states in cold-atom systems
• Localization in one-dimensional incommensurate lattices beyond the Aubry-André model
• Detecting Chiral Edge States in the Hofstadter Optical Lattice
• Superradiance Lattice
• Topological insulator and particle pumping in a one-dimensional shaken optical lattice
• Dynamical Anderson transition in one-dimensional periodically kicked incommensurate lattices
• Fate of topological states in incommensurate generalized Aubry-André models
• Anomalous charge pumping in a one-dimensional optical superlattice