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Analytical and numerical studies of periodic superradiance

Hideaki Hara1,*, Yuki Miyamoto1,†, Junseok Han1,2, Riku Omoto1, Yasutaka Imai1, Akihiro Yoshimi1, Koji Yoshimura1, Motohiko Yoshimura1, and Noboru Sasao1,‡

  • 1Research Institute for Interdisciplinary Science, Okayama University, Okayama, 700-8530, Japan
  • 2Department of Physics and Astronomy, Seoul National University, Seoul 08826, Korea

  • *Contact author: hhara@okayama-u.ac.jp
  • †Contact author: miyamo-y@cc.okayama-u.ac.jp
  • ‡Contact author: sasao@okayama-u.ac.jp
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Phys. Rev. A 113, 043713 – Published 8 April, 2026

DOI: https://doi.org/10.1103/fvvx-wtyd

Abstract

We conduct a theoretical study to understand the periodic superradiance observed in an Er:YSO crystal. First, we construct a model based on the Maxwell-Bloch equations for a reduced level system, a pair of superradiance states, and a population reservoir state. Analysis of the eigenvalues of the linearized differential equations shows that periodic superradiance can be realized only for certain parameters. We also derive two-variable equations consisting of the coherence and population difference between the two superradiance states, which contain the essential feature of the periodic superradiance. The two-variable equations clarify the mathematical structure of this periodic phenomenon and give analytical forms of the period, pulse duration, and number of emitted photons. Our model successfully reproduces the periodic behavior, but the actual experimental parameters are found to be outside the parameter region for the periodic superradiance. This result implies that some other mechanism(s) is (are) required. As one example, assuming that the field decay rate varies with the electric field, the periodic superradiance can be reproduced even under the actual experimental conditions.

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Phys. Rev. A 113, 043713– Published 8 April, 2026
  • Received 3 December 2024
  • Accepted 24 February 2026
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