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<p>Achieving ultra-stable optical frequency dissemination over long-haul fiber networks is essential for numerous applications. Although optical frequency transfer systems based on optical phase-locked loops (OPLLs) have achieved unprecedented stability levels, their performance is limited by continuous compensation bias caused by noise asymmetry from bidirectional frequency shifts and loss of lock in long-distance, high-noise links. Here, we propose a bias-free noise compensation method based on digital radio-frequency phase recording using a time-to-digital converter, which eliminates residual errors and offers a theoretically unlimited dynamic range for enhanced reliability. By incorporating multifunctional relay stations and hertz-level optical bandpass filtering to improve OPLL robustness, our scalable architecture achieves a frequency instability of <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(2.9\times {10}^{-21}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>2.9</mn> <mo>×</mo> <msup> <mrow> <mn>10</mn> </mrow> <mrow> <mo>−</mo> <mn>21</mn> </mrow> </msup> </mrow> </math></EquationSource> </InlineEquation> at 1 day over a 2067 km field fiber link under extreme noise conditions (5000 <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\({\mathrm{rad}}^{2}\,{\mathrm{Hz}}^{-1}\,{\mathrm{km}}^{-1}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mrow> <mi>rad</mi> </mrow> <mn>2</mn> </msup> <mspace width="0.25em" /> <msup> <mrow> <mi>Hz</mi> </mrow> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> <mspace width="0.25em" /> <msup> <mrow> <mi>km</mi> </mrow> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msup> </mrow> </math></EquationSource> </InlineEquation> at 1 Hz). Bias correction improves the instability by threefold and breaks through the theoretical limit of uncalibrated systems. The setup maintains continuous phase lock for over four days, and noise purification enables virtually unlimited link extension. This advance establishes a robust, field-deployable optical frequency network compatible with standard telecommunication infrastructure.</p>

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10−21-Level optical frequency dissemination over 2067 km of noise-loaded field-deployed fiber network

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年6月22日

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  • Fa-Xi Chen,
  • Li-Bo Li,
  • Jiu-Peng Chen,
  • Kan Zhao,
  • Jian-Yu Guan,
  • Yang Xu,
  • Lei Hou,
  • Fei Zhou,
  • Cheng-Zhi Peng,
  • Qiang Zhang,
  • Hai-Feng Jiang,
  • Jian-Wei Pan

摘要

Achieving ultra-stable optical frequency dissemination over long-haul fiber networks is essential for numerous applications. Although optical frequency transfer systems based on optical phase-locked loops (OPLLs) have achieved unprecedented stability levels, their performance is limited by continuous compensation bias caused by noise asymmetry from bidirectional frequency shifts and loss of lock in long-distance, high-noise links. Here, we propose a bias-free noise compensation method based on digital radio-frequency phase recording using a time-to-digital converter, which eliminates residual errors and offers a theoretically unlimited dynamic range for enhanced reliability. By incorporating multifunctional relay stations and hertz-level optical bandpass filtering to improve OPLL robustness, our scalable architecture achieves a frequency instability of \(2.9\times {10}^{-21}\) 2.9 × 10 − 21 at 1 day over a 2067 km field fiber link under extreme noise conditions (5000 \({\mathrm{rad}}^{2}\,{\mathrm{Hz}}^{-1}\,{\mathrm{km}}^{-1}\) rad 2 Hz − 1 km − 1 at 1 Hz). Bias correction improves the instability by threefold and breaks through the theoretical limit of uncalibrated systems. The setup maintains continuous phase lock for over four days, and noise purification enables virtually unlimited link extension. This advance establishes a robust, field-deployable optical frequency network compatible with standard telecommunication infrastructure.