Linked and knotted synthetic magnetic fields

Callum W. Duncan, Calum Ross, Niclas Westerberg, Manuel Valiente, Bernd J. Schroers, and Patrik Öhberg
Phys. Rev. A 99, 063613 – Published 17 June 2019
PDFHTMLExport Citation

Abstract

We show that the realization of synthetic magnetic fields via light-matter coupling in the Λ scheme implements a natural geometrical construction of magnetic fields, namely, as the pullback of the area element of the sphere to Euclidean space via certain maps. For suitable maps, this construction generates linked and knotted magnetic fields, and the synthetic realization amounts to the identification of the map with the ratio of two Rabi frequencies which represent the coupling of the internal energy levels of an ultracold atom. We consider examples of maps which can be physically realized in terms of Rabi frequencies and which lead to linked and knotted synthetic magnetic fields acting on the neutral atomic gas. We also show that the ground state of the Bose-Einstein condensate may inherit the topological properties of the synthetic gauge field, with linked and knotted vortex lines appearing in some cases.

  • Figure
  • Figure
  • Figure
  • Figure
  • Received 31 August 2018

DOI:https://doi.org/10.1103/PhysRevA.99.063613

©2019 American Physical Society

Physics Subject Headings (PhySH)

Atomic, Molecular & OpticalCondensed Matter, Materials & Applied Physics

Authors & Affiliations

Callum W. Duncan1,*, Calum Ross2, Niclas Westerberg1, Manuel Valiente3,1, Bernd J. Schroers2, and Patrik Öhberg1

  • 1SUPA, Institute of Photonics and Quantum Sciences, Heriot-Watt University, Edinburgh EH14 4AS, United Kingdom
  • 2Maxwell Institute for Mathematical Sciences and Department of Mathematics, Heriot-Watt University, Edinburgh EH14 4AS, United Kingdom
  • 3Institute for Advanced Study, Tsinghua University, Beijing 100084, China

  • *cd130@hw.ac.uk

Article Text (Subscription Required)

Click to Expand

Supplemental Material (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand
Issue

Vol. 99, Iss. 6 — June 2019

Reuse & Permissions
Access Options
Author publication services for translation and copyediting assistance advertisement

Authorization Required


×
×

Images

×

Sign up to receive regular email alerts from Physical Review A

Log In

Cancel
×

Search


Article Lookup

Paste a citation or DOI

Enter a citation
×