Quantized hall conductance of a single atomic wire: a proposal based on synthetic dimensions

Research output: Contribution to journalArticlepeer-review

Authors

  • G. Salerno
  • M. Lebrat
  • S. Haüsler
  • T. Esslinger
  • L. Corman
  • J. P. Brantut
  • N. Goldman

Colleges, School and Institutes

External organisations

  • Université Libre de Bruxelles
  • ETH Zurich
  • Laboratory of Photonics and Interfaces, Department de Chimie, Ecole Polytechnique Federale de Lausanne, CH-1015 Lausanne, Switzerland. ahmad@mpip-mainz.mpg.de

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 quasienergy 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.

Details

Original languageEnglish
Article number041001
Number of pages21
JournalPhysical Review X
Volume9
Issue number4
Publication statusPublished - 1 Oct 2019

ASJC Scopus subject areas