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, physical observables strongly depend on the axial magnetic flux, providing us a sensitive means to probe either the transition or the axial flux using one another. In the irrational limit, physical observables are no longer affected by the axial flux, signifying a scheme to suppress decoherence induced by fluctuations of the axial flux.

中文翻译：

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合成霍尔圆柱体上的本地化

通过工程激光-原子相互作用，最近在实验室中合成了霍尔带和霍尔圆柱体，将其作为凝聚态物理的基本理论工具。在这里，我们表明将合成霍尔带变成合成霍尔圆柱体自然会导致定位。与霍尔带不同，霍尔圆柱体具有本征晶格，该晶格是由于方位角方向上的周期性边界条件以及额外激光施加的外部周期性电势而产生的。当这两个晶格不相等时，可能会在合成霍尔圆柱体上发生定位。在定位-离域转换附近，物理观测值在很大程度上取决于轴向磁通量，从而为我们提供了一种敏感的手段来相互探测转换或轴向磁通。在不合理的范围内，