Realizing the Harper model with Ultracold Atoms in a Ring Lattice

Abstract

We demonstrate that all of the salient features of the Harper-Hofstadter model can be implemented with ultracold atoms trapped in a bichromatic ring-shaped lattice. Using realistic sinusoidal lattice potentials rather than assume the idealized tight-binding picture, we determine the optimal conditions necessary to realize the critical point where the spectrum becomes fractal, and identify the nature and cause of the departures from the discrete model predictions. We also show that even with a commensurate ring with a few lattice sites, the Aubry-André localization transition can be realized. Localized states that behave like edge states with energies that reside in the band gaps can be generated by introducing a surprisingly small local perturbation within the ring. Spectrum oscillation arising from complex coupling can be implemented by uniform rotation of the ring, but with certain significant differences that are explained

arXiv comment8 pages and 8 figures

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Cited by in corpus (9)

• Competition and interplay between topology and quasi-periodic disorder in Thouless pumping of ultracold atoms
• Topologically quantized current in quasiperiodic Thouless pumps
• Analytical solution of open crystalline linear 1D tight-binding models
• Effects of a rotating periodic lattice on coherent quantum states in a ring topology: The case of positive nonlinearity
• Generalized phase-space description of non-linear Hamiltonian systems and the Harper-like dynamics
• Coexistence of 1D and 2D topology and genesis of Dirac cones in the chiral Aubry-André model
• Rotation Sensitive Quench and Revival of Coherent Oscillations in a Ring Lattice
• Ring Rydberg Composites
• Instability and particle current control of a parametrically driven Bose-Einstein condensate in a ring-shaped lattice