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Anomalous transport in the Aubry-André-Harper model in isolated and open systems

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      Energy levels and wave functions of Bloch electrons in rational and irrational magnetic fields

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        Anderson localization of a non-interacting Bose-Einstein condensate

        One of the most intriguing phenomena in physics is the localization of waves in disordered media. This phenomenon was originally predicted by Anderson, fifty years ago, in the context of transport of electrons in crystals. Anderson localization is actually a much more general phenomenon, and it has been observed in a large variety of systems, including light waves. However, it has never been observed directly for matter waves. Ultracold atoms open a new scenario for the study of disorder-induced localization, due to high degree of control of most of the system parameters, including interaction. Here we employ for the first time a noninteracting Bose-Einstein condensate to study Anderson localization. The experiment is performed with a onedimensional quasi-periodic lattice, a system which features a crossover between extended and exponentially localized states as in the case of purely random disorder in higher dimensions. Localization is clearly demonstrated by investigating transport properties, spatial and momentum distributions. We characterize the crossover, finding that the critical disorder strength scales with the tunnelling energy of the atoms in the lattice. Since the interaction in the condensate can be controlled at will, this system might be employed to solve open questions on the interplay of disorder and interaction and to explore exotic quantum phases.
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          Observation of many-body localization of interacting fermions in a quasi-random optical lattice

          We experimentally observe many-body localization of interacting fermions in a one-dimensional quasi-random optical lattice. We identify the many-body localization transition through the relaxation dynamics of an initially-prepared charge density wave. For sufficiently weak disorder the time evolution appears ergodic and thermalizing, erasing all remnants of the initial order. In contrast, above a critical disorder strength a significant portion of the initial ordering persists, thereby serving as an effective order parameter for localization. The stationary density wave order and the critical disorder value show a distinctive dependence on the interaction strength, in agreement with numerical simulations. We connect this dependence to the ubiquitous logarithmic growth of entanglement entropy characterizing the generic many-body localized phase.
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            Author and article information

            Journal
            PRBMDO
            Physical Review B
            Phys. Rev. B
            American Physical Society (APS)
            2469-9950
            2469-9969
            May 2018
            May 24 2018
            : 97
            : 17
            10.1103/PhysRevB.97.174206
            © 2018

            https://link.aps.org/licenses/aps-default-license

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