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Spin resonance without a spin: A microwave analog

Tobias Hofmann, Finn Schmidt, and Hans-Jürgen Stöckmann*

Ulrich Kuhl†

  • *Contact author: stoeckmann@physik.uni-marburg.de
  • †Contact author: ulrich.kuhl@univ-cotedazur.fr
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Phys. Rev. E 112, 054313 – Published 13 November, 2025

DOI: https://doi.org/10.1103/vbmy-23h4

Abstract

An analog of nuclear magnetic resonance is realized in a microwave network with symplectic symmetry. The network consists of two identical subgraphs coupled by a pair of bonds with a length difference corresponding to a phase difference of π for the waves traveling through the bonds. As a consequence, all eigenvalues appear as Kramers doublets. Detuning the length difference from the π condition Kramers degeneracy is lifted, which may be interpreted as a Zeeman splitting of a spin 12 in a magnetic field. The lengths of another pair of bonds are modulated periodically with frequencies of some 10 MHz by means of diodes, thus emulating a magnetic radio-frequency field. This setup enables the realization of well-known NMR phenomena, such as the transformation from the laboratory to the rotating frame and the observation of Lorentzian-shaped resonance lines.

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Phys. Rev. E 112, 054313– Published 13 November, 2025
  • Received 23 September 2024
  • Revised 6 August 2025
  • Accepted 16 October 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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