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<p>Synchronization resulting in unified collective behavior of the individual elements of a system that are weakly coupled to each other has long fascinated scientists. Examples range from the periodic oscillation of coupled pendulum clocks to the rhythmic behavior in biological systems. Here we demonstrate this effect in a solid-state platform: spatially remote, auto-oscillating electron-nuclear spin systems in a semiconductor. When two such oscillators separated by up to 40 <i>μ</i>m are optically pumped, their individually different frequencies lock to a common value, revealing long-range coupling. For larger separations, the synchronization breaks. The interaction distance matches the electron spin diffusion length, identifying spin transport as the coupling-mediating mechanism and maintaining correlated behavior over mesoscopic distances. As a consequence, a wide-area optical pump drives all oscillators within the illuminated spot into a single synchronized state, despite their inhomogeneity. This synchronization accounts for the exceptional stability of the resulting auto-oscillations, enabling collective motion in distributed spin systems and paving the way toward spin networks in spintronics.</p>

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Non-local synchronization of continuous time crystals in a semiconductor

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年7月22日

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  • Alex Greilich,
  • Nataliia E. Kopteva,
  • Vladimir L. Korenev,
  • Philipp A. Haude,
  • Linus Kunze,
  • Ben W. Grobecker,
  • Sergiu Anghel,
  • Markus Betz,
  • Manfred Bayer

摘要

Synchronization resulting in unified collective behavior of the individual elements of a system that are weakly coupled to each other has long fascinated scientists. Examples range from the periodic oscillation of coupled pendulum clocks to the rhythmic behavior in biological systems. Here we demonstrate this effect in a solid-state platform: spatially remote, auto-oscillating electron-nuclear spin systems in a semiconductor. When two such oscillators separated by up to 40 μm are optically pumped, their individually different frequencies lock to a common value, revealing long-range coupling. For larger separations, the synchronization breaks. The interaction distance matches the electron spin diffusion length, identifying spin transport as the coupling-mediating mechanism and maintaining correlated behavior over mesoscopic distances. As a consequence, a wide-area optical pump drives all oscillators within the illuminated spot into a single synchronized state, despite their inhomogeneity. This synchronization accounts for the exceptional stability of the resulting auto-oscillations, enabling collective motion in distributed spin systems and paving the way toward spin networks in spintronics.