Localization on a synthetic Hall cylinder
arXiv:2012.02204 · doi:10.1103/PhysRevLett.126.193001
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.
arXiv comment6 pages, 5 figures
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Cited by in corpus (7)
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- Bose-Einstein Condensate on a Synthetic Topological Hall Cylinder
- 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
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- Quantum States and Spectra of Small Cylindrical and Toroidal Lattices