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arXiv · 1312.3484

Quantum particle in a parabolic lattice in the presence of a gauge field

Andrey R. Kolovsky·Fabian Grusdt·Michael Fleischhauer
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Abstract

We analyze the eigenstates of a two-dimensional lattice with additional harmonic confinement in the presence of an artificial magnetic field. While the softness of the confinement makes a distinction between bulk and edge states difficult, the interplay of harmonic potential and lattice leads to a different classification of states in three energy regions: In the low-energy regime, where lattice effects are small, all states are transporting topologically non-trivial states. For large energies above a certain critical value, the periodic lattice causes localization of all states through a mechanism similar to Wannier-Stark localization. In the intermediate energy regime transporting, topologically non- trivial states coexist with topologically trivial counter-transporting chaotic states. The character of the eigenstates, in particular their transport properties are studied numerically and are explained using a semiclassical analysis.

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Andrey R. Kolovsky, Fabian Grusdt, Michael Fleischhauer. 2014-02-19. Quantum particle in a parabolic lattice in the presence of a gauge field. https://doi.org/10.1103/physreva.89.033607

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