Researchers at TU Dortmund University have documented a phenomenon in which multiple time crystals operating within the same material can achieve synchronization of their electron-nuclear spin oscillations, according to findings published in Nature Communications. The discovery builds on prior work conducted earlier this decade that demonstrated continuous time crystals could persist within semiconductor materials for extended periods.
Time crystals represent physical systems whose internal patterns repeat regularly over time without requiring an external driving signal. In these experiments, the crystals formed within gallium arsenide semiconductors doped with indium and silicon, which creates localized electrons throughout the material. Operating at extremely cold temperatures near -270 °C, each electron interacts with approximately one million surrounding nuclear spins. Researchers use laser light to align electron spins initially, allowing the polarization to transfer to adjacent nuclear spins. When a weak magnetic field is applied, these nuclear spins begin rotating, with feedback between electron and nuclear spins sustaining the oscillatory behavior.
Due to microscopic variations within the semiconductor material, time crystals forming in separate regions naturally oscillate at slightly different frequencies. However, when multiple areas are illuminated simultaneously with a broad laser beam, the separate oscillations become coupled and lock into the same frequency. This synchronization mechanism differs from the classical example observed by Christiaan Huygens involving pendulum clocks attached to a shared support. In the semiconductor system, rather than mechanical vibrations transmitting through a physical structure, synchronization occurs through the movement of spin-polarized electrons that couple the separate time crystal regions.
The research team determined that time crystals positioned up to 40 micrometers apart could still achieve synchronization, a distance exceeding one thousand times the characteristic size of individual oscillators. When separation increases beyond this threshold, the time crystals no longer synchronize and maintain independent oscillation patterns. The findings illustrate non-local coupling phenomena between spatially separated spin systems and may establish foundations for developing networks of controllable spin oscillators, potentially enabling new applications in spin-based technology platforms.
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