Aharonov–Bohm effect with an effective complex-valued vector potential

Ismael Lucas Paiva*, Yakir Aharonov, Jeff Tollaksen, Mordecai Waegell

*Corresponding author for this work

Research output: Contribution to journalArticle (Academic Journal)peer-review

1 Citation (Scopus)
29 Downloads (Pure)

Abstract

The interaction between a quantum charge and a dynamic source of a magnetic field is considered
in the Aharonov–Bohm (AB) scenario. It is shown that, in weak interactions with a post-selection
of the source, the effective vector potential is, generally, complex-valued. This leads to new
experimental protocols to detect the AB phase before the source is fully encircled. While this does
not necessarily change the nonlocal status of the AB effect, it brings new insights into it. Moreover,
we discuss how these results might have consequences for the correspondence principle, making
complex vector potentials relevant to the study of classical systems.
Original languageEnglish
Article number053017
Pages (from-to)1-11
Number of pages11
JournalNew Journal of Physics
Volume25
Issue number5
DOIs
Publication statusPublished - 22 May 2023

Bibliographical note

Funding Information:
The authors would like to thank Eliahu Cohen and Lev Vaidman for their comments on a previous version of this manuscript. I L P acknowledges financial support from the Science without Borders Program (CNPq/Brazil, Fund No. 234347/2014-7) and the ERC Advanced Grant FLQuant. Y A thanks the Federico and Elvia Faggin Foundation for support. This research was supported by the Fetzer-Franklin Fund of the John E Fetzer Memorial Trust and by Grant No. FQXi-RFP-CPW-2006 from the Foundational Questions Institute and Fetzer Franklin Fund, a donor-advised fund of Silicon Valley Community Foundation.

Publisher Copyright:
© 2023 The Author(s). Published by IOP Publishing Ltd on behalf of the Institute of Physics and Deutsche Physikalische Gesellschaft.

Keywords

  • Aharonov-Bohm effect
  • pre- and post-selected systems
  • weak values

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