Localization on a Synthetic Hall Cylinder

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.

Automated summary

Hall ribbons and Hall cylinders, fundamental theoretical tools in condensed matter physics, have been successfully synthesized in laboratories through engineering laser-atom interactions. Converting a synthetic Hall ribbon into a synthetic Hall cylinder can naturally lead to localization, with physical observables strongly dependent on the axial magnetic flux near localization-delocalization transitions. In the irrational limit, physical observables are no longer affected by the axial flux, providing a scheme to suppress decoherence induced by fluctuations of the axial flux.