中国物理B ›› 2026, Vol. 35 ›› Issue (1): 10602-010602.doi: 10.1088/1674-1056/ae1120

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Enhanced timing of a 113 km O-TWTFT link with complex maximum likelihood estimation process

Yu-Chen Fang(方宇辰)1,2,3,†, Jian-Yu Guan(管建宇)2,3,†, Qi Shen(沈奇)1,2,3, Jin-Jian Han(韩金剑)1,2,3, Lei Hou(侯磊)2,3, Meng-Zhe Lian(连蒙浙)1,2,3, Yong Wang(王勇)4, Wei-Yue Liu(刘蔚悦)2,3,5, Ji-Gang Ren(任继刚)1,2,3, Cheng-Zhi Peng(彭承志)1,2,3, Qiang Zhang(张强)1,2,3, Hai-Feng Jiang(姜海峰)1,2,3,‡, and Jian-Wei Pan(潘建伟)1,2,3   

  1. 1 Hefei National Research Center for Physical Sciences at the Microscale and School of Physical Sciences, University of Science and Technology of China, Hefei 230026, China;
    2 Shanghai Research Center for Quantum Sciences and CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China;
    3 Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China;
    4 Xinjiang Astronomical Observatory, Chinese Academy of Sciences, Urumqi 830011, China;
    5 Faculty of Information Science and Engineering, Ningbo University, Ningbo 315211, China
  • 收稿日期:2025-09-10 修回日期:2025-09-25 接受日期:2025-10-09 发布日期:2025-12-29
  • 通讯作者: Hai-Feng Jiang E-mail:hjiang1@ustc.edu.cn
  • 基金资助:
    This research was supported by the National Key Research and Development Programme of China (Grant Nos. 2020YFC2200103 and 2020YFA0309800), the National Natural Science Foundation of China (Grant No. T2125010), Strategic Priority Research Programme of Chinese Academy of Sciences (Grant No. XDB35030000), Anhui Initiative in Quantum Information Technologies (Grant No. AHY010100), Key R&D Plan of Shandong Province (Grant No. 2021ZDPT01), Shanghai Municipal Science and Technology Major Project (Grant No. 2019SHZDZX01), and Innovation Programme for Quantum Science and Technology (Grant Nos. 2021ZD0300100, 2021ZD0300300, and 2021ZD0300903).

Enhanced timing of a 113 km O-TWTFT link with complex maximum likelihood estimation process

Yu-Chen Fang(方宇辰)1,2,3,†, Jian-Yu Guan(管建宇)2,3,†, Qi Shen(沈奇)1,2,3, Jin-Jian Han(韩金剑)1,2,3, Lei Hou(侯磊)2,3, Meng-Zhe Lian(连蒙浙)1,2,3, Yong Wang(王勇)4, Wei-Yue Liu(刘蔚悦)2,3,5, Ji-Gang Ren(任继刚)1,2,3, Cheng-Zhi Peng(彭承志)1,2,3, Qiang Zhang(张强)1,2,3, Hai-Feng Jiang(姜海峰)1,2,3,‡, and Jian-Wei Pan(潘建伟)1,2,3   

  1. 1 Hefei National Research Center for Physical Sciences at the Microscale and School of Physical Sciences, University of Science and Technology of China, Hefei 230026, China;
    2 Shanghai Research Center for Quantum Sciences and CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Shanghai 201315, China;
    3 Hefei National Laboratory, University of Science and Technology of China, Hefei 230088, China;
    4 Xinjiang Astronomical Observatory, Chinese Academy of Sciences, Urumqi 830011, China;
    5 Faculty of Information Science and Engineering, Ningbo University, Ningbo 315211, China
  • Received:2025-09-10 Revised:2025-09-25 Accepted:2025-10-09 Published:2025-12-29
  • Contact: Hai-Feng Jiang E-mail:hjiang1@ustc.edu.cn
  • Supported by:
    This research was supported by the National Key Research and Development Programme of China (Grant Nos. 2020YFC2200103 and 2020YFA0309800), the National Natural Science Foundation of China (Grant No. T2125010), Strategic Priority Research Programme of Chinese Academy of Sciences (Grant No. XDB35030000), Anhui Initiative in Quantum Information Technologies (Grant No. AHY010100), Key R&D Plan of Shandong Province (Grant No. 2021ZDPT01), Shanghai Municipal Science and Technology Major Project (Grant No. 2019SHZDZX01), and Innovation Programme for Quantum Science and Technology (Grant Nos. 2021ZD0300100, 2021ZD0300300, and 2021ZD0300903).

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摘要： Optical two-way time-frequency transfer (O-TWTFT), utilizing optical frequency comb carriers and linear optical sampling, effectively enables space-to-ground optical frequency standard comparisons. Previously reported detection sensitivities of O-TWTFTs were typically in the nanoWatt level, necessitating high-power optical frequency combs to compensate for significant losses in high-orbit satellite-to-ground passes. Such hardware-based solutions, while effective, tend to be costly. This paper presents a novel data post-processing algorithm to enhance sensitivity. Unlike previous timing methods, which depend solely on optical phase data and discard intensity information — resulting in elevated errors, especially under low-reception power, our approach employs complex least squares (CLS) estimation in the complex frequency domain. By preserving all intermediate data and avoiding noise from phase unwrapping, it achieves superior sensitivity and accuracy. Experiments over a 113-kilometer free-space link validate the algorithm’s robustness, delivering a detection sensitivity of 0.1 nanoWatts — over tenfold better than prior techniques — despite a 100-decibel link loss, comparable to Earth-Moon optical links.

关键词: optical time-frequency transfer, linear optical sampling, frequency comb, complex least squares

Abstract: Optical two-way time-frequency transfer (O-TWTFT), utilizing optical frequency comb carriers and linear optical sampling, effectively enables space-to-ground optical frequency standard comparisons. Previously reported detection sensitivities of O-TWTFTs were typically in the nanoWatt level, necessitating high-power optical frequency combs to compensate for significant losses in high-orbit satellite-to-ground passes. Such hardware-based solutions, while effective, tend to be costly. This paper presents a novel data post-processing algorithm to enhance sensitivity. Unlike previous timing methods, which depend solely on optical phase data and discard intensity information — resulting in elevated errors, especially under low-reception power, our approach employs complex least squares (CLS) estimation in the complex frequency domain. By preserving all intermediate data and avoiding noise from phase unwrapping, it achieves superior sensitivity and accuracy. Experiments over a 113-kilometer free-space link validate the algorithm’s robustness, delivering a detection sensitivity of 0.1 nanoWatts — over tenfold better than prior techniques — despite a 100-decibel link loss, comparable to Earth-Moon optical links.

Key words: optical time-frequency transfer, linear optical sampling, frequency comb, complex least squares

中图分类号:  (Time and frequency)

  • 06.30.Ft
42.62.Eh (Metrological applications; optical frequency synthesizers for precision spectroscopy) 42.79.Sz (Optical communication systems, multiplexers, and demultiplexers?)