Localization on a synthetic Hall cylinder

Abstract

By engineering laser-atom interactions, both Hall ribbons and Hall cylinders as fundamental theoretical tools in condensed matter physics have recently been synthesized in laboratories. Here, we show that turning a synthetic Hall ribbon into a synthetic Hall cylinder could naturally lead to localization. Unlike a Hall ribbon, a Hall cylinder hosts an intrinsic lattice, which arises due to the periodic boundary condition in the azimuthal direction, in addition to the external periodic potential imposed by extra lasers. When these two lattices are incommensurate, localization may occur on a synthetic Hall cylinder. Near the localization-delocalization transitions, the dependence of physical observables on the axial magnetic flux allows us to tackle a fundamental question of determining the accuracy of rational approximation of irrational numbers. In the irrational limit, physical observables are no longer affected by fluctuations of the axial flux.

6 pages, 5 figures

References in corpus (13)

• Spin-Injection Spectroscopy of a Spin-Orbit Coupled Fermi Gas
• Degenerate Quantum Gases with Spin-Orbit Coupling
• Photonic topological pumping through the edges of a dynamical four-dimensional quantum Hall system
• Exploring 4D Quantum Hall Physics with a 2D Topological Charge Pump
• Topological quantum matter in synthetic dimensions
• Synthetic dimensions and spin-orbit coupling with an optical clock transition
• Spin-orbit coupled fermions in an optical lattice clock
• Localization in one-dimensional incommensurate lattices beyond the Aubry-André model
• Spin-orbit coupled two-electron Fermi gases of ytterbium atoms
• Semi-synthetic zigzag optical lattice for ultracold bosons
• Quantum simulation of non-trivial topology
• Coherence and decoherence in the Harper-Hofstadter model
• Tunable Flux through a Synthetic Hall Tube of Neutral Fermions

Cited by in corpus (5)

• A comprehensive review on developments of synthetic dimensions
• Experimental realization of a fermionic spin-momentum lattice
• Synthetic Hall ladder with tunable magnetic flux
• Many-body phases from effective geometrical frustration and long-range interactions in a subwavelength lattice
• Duality breaking, mobility edges, and the connection between topological Aubry-André and quantum Hall insulators in atomic wires with fermions