Quantum Hall effect with small numbers of vortices in Bose-Einstein condensates

Tim Byrnes and Jonathan P. Dowling
Phys. Rev. A 92, 023629 – Published 20 August 2015

Abstract

When vortices are displaced in Bose-Einstein condensates (BECs), the Magnus force gives the system a momentum transverse in the direction to the displacement. We show that BECs in long channels with vortices exhibit a quantization of the current response with respect to the spatial vortex distribution. The quantization originates from the well-known topological property of the phase around a vortex; it is an integer multiple of 2π. In a way similar to that of the integer quantum Hall effect, the current along the channel is related to this topological phase and can be extracted from two experimentally measurable quantities: the total momentum of the BEC and the spatial distribution. The quantization is in units of m/2h, where m is the mass of the atoms and h is Planck's constant. We derive an exact vortex momentum-displacement relation for BECs in long channels under general circumstances. Our results present the possibility that the configuration described here can be used as a novel way of measuring the mass of the atoms in the BEC using a topological invariant of the system. If an accurate determination of the plateaus are experimentally possible, this gives the possibility of a topological quantum mass standard and precise determination of the fine structure constant.

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  • Received 25 February 2015

DOI:https://doi.org/10.1103/PhysRevA.92.023629

©2015 American Physical Society

Authors & Affiliations

Tim Byrnes1,2,3 and Jonathan P. Dowling4

  • 1New York University, 1555 Century Avenue, Pudong, Shanghai 200122, China
  • 2NYU-ECNU Institute of Physics at NYU Shanghai, 3663 Zhongshan Road North, Shanghai 200062, China
  • 3National Institute of Informatics, 2-1-2 Hitotsubashi, Chiyoda-ku, Tokyo 101-8430, Japan
  • 4Hearne Institute for Theoretical Physics, Department of Physics and Astronomy, Louisiana State University, Baton Rouge, Louisiana 70803-4001, USA

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Issue

Vol. 92, Iss. 2 — August 2015

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