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arXiv · 1811.00963

The quantized Hall conductance of a single atomic wire: A proposal based on synthetic dimensions

G. Salerno·H. M. Price·M. Lebrat·S. Häusler·T. Esslinger·L. Corman·J. -P. Brantut·N. Goldman
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Abstract

We propose a method by which the quantization of the Hall conductance can be directly measured in the transport of a one-dimensional atomic gas. Our approach builds on two main ingredients: (1) a constriction optical potential, which generates a mesoscopic channel connected to two reservoirs, and (2) a time-periodic modulation of the channel, specifically designed to generate motion along an additional synthetic dimension. This fictitious dimension is spanned by the harmonic-oscillator modes associated with the tightly-confined channel, and hence, the corresponding "lattice sites" are intimately related to the energy of the system. We analyze the quantum transport properties of this hybrid two-dimensional system, highlighting the appealing features offered by the synthetic dimension. In particular, we demonstrate how the energetic nature of the synthetic dimension, combined with the quasi-energy spectrum of the periodically-driven channel, allows for the direct and unambiguous observation of the quantized Hall effect in a two-reservoir geometry. Our work illustrates how topological properties of matter can be accessed in a minimal one-dimensional setup, with direct and practical experimental consequences.,

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G. Salerno, H. M. Price, M. Lebrat, S. Häusler, T. Esslinger, L. Corman, J. -P. Brantut, N. Goldman. 2018-11-02. The quantized Hall conductance of a single atomic wire: A proposal based on synthetic dimensions. https://doi.org/10.1103/physrevx.9.041001

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