| Citation: | WANG Xu, GAO Xue-rong, LI Pan, QI Ke-qi, LIU He-shan. Design and experimental verification of unequal-arm interferometric frequency stabilization scheme in taiji program[J]. Chinese Optics, 2026, 19(4): 887-894. doi: 10.37188/CO.2026-0029
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Laser frequency noise is the dominant noise source in space-based gravitational wave detection systems, which can be reduced by a multi-stage suppression approach employing PDH (Pound-Drever-Hall) cavity-locking pre-stabilization, arm-locking, and time-delay interferometry. However, with the advancement of picometer-level measurement, unequal-arm interferometric frequency stabilization using free-space laser links has emerged as a popular alternative to the PDH cavity-locking pre-stabilization scheme. This approach can effectively utilize existing space laser interferometers without requiring additional ultra-stable reference cavities. Based on the first-generation interferometric optical platform of the Taiji program, this paper verifies the feasibility and effectiveness of an unequal-arm interferometer frequency stabilization scheme using the existing interferometric optical path. Experimental results show that the free-running laser frequency noise is reduced by approximately one order of magnitude overall, reaching 3 kHz/Hz1/2 at 1 Hz. Noise analysis reveals that in the 0.2 Hz–1 Hz band, the main limiting factor is the background noise of the interferometer; in the 0.1 Hz–1 mHz band, the dominant noise source is the power noise of the free-running laser. Future work will focus on further reducing the interferometer noise to 1 pm/Hz1/2 and exploring the feasibility of replacing the PDH cavity-locking scheme with frequency stabilization using the existing interferometric optical path.
| [1] |
HU W R, WU Y L. The Taiji Program in Space for gravitational wave physics and the nature of gravity[J]. National Science Review, 2017, 4(5): 685-686. doi: 10.1093/nsr/nwx116
|
| [2] |
LUO Z R, GUO Z K, JIN G, et al. A brief analysis to Taiji: Science and technology[J]. Results in Physics, 2020, 16: 102918. doi: 10.1016/j.rinp.2019.102918
|
| [3] |
LUO J, CHEN L SH, DUAN H Z, et al. TianQin: a space-borne gravitational wave detector[J]. Classical and Quantum Gravity, 2016, 33(3): 035010. doi: 10.1088/0264-9381/33/3/035010
|
| [4] |
LUO J, BAI SH J, BAI Y ZH, et al. Progress of the TianQin project[J]. Classical and Quantum Gravity, 2025, 42(17): 173001. doi: 10.1088/1361-6382/adda8a
|
| [5] |
The LISA Pathfinder Team, The eLISA Consortium. LISA and its pathfinder[J]. Nature Physics, 2015, 11(8): 613-615. doi: 10.1038/nphys3420
|
| [6] |
王娟, 齐克奇, 王少鑫, 等. 面向空间引力波探测的激光干涉技术研究进展及展望[J]. 中国科学: 物理学 力学 天文学, 2024, 54(7): 270405. doi: 10.1360/SSPMA-2024-0111
WANG J, QI K Q, WANG SH X, et al. Advance and prospect in the study of laser interferometry technology for space gravitational wave detection[J]. Scientia Sinica Physica, Mechanica & Astronomica, 2024, 54(7): 270405. (in Chinese). doi: 10.1360/SSPMA-2024-0111
|
| [7] |
刘河山, 王娟, 高瑞弘, 等. 太极二号干涉仪系统噪声与指标分解[J]. 空间科学学报, 2025, 45(4): 1047-1057. doi: 10.11728/cjss2025.04.2025-yg02
LIU H SH, WANG J, GAO R H, et al. Noise and index decomposition of Taiji-2 interferometer system[J]. Chinese Journal of Space Science, 2025, 45(4): 1047-1057. (in Chinese). doi: 10.11728/cjss2025.04.2025-yg02
|
| [8] |
FAN X, FAYER S E, MYERS T G, et al. Switchable damping for a one-particle oscillator[J]. Review of Scientific Instruments, 2021, 92(2): 023201. doi: 10.1063/5.0038005
|
| [9] |
LI Y Q, LUO Y, LAI J T, et al. An advanced digital controller with automatic design for laser frequency stabilization in space[J]. Review of Scientific Instruments, 2025, 96(8): 084502. doi: 10.1063/5.0272346
|
| [10] |
骆颖欣. 星载激光稳频原理演示系统的研制[D]. 武汉: 华中科技大学, 2016.
LUO Y X. Establishment of a preliminary prototype of the spaceborne laser-frequency-stabilization system[D]. Wuhan: Huazhong University of Science and Technology, 2016. (in Chinese).
|
| [11] |
彭建康. 星载全固态Nd: YAG单块非平面环形腔激光及稳频用参考腔的研制[D]. 武汉: 中国科学院大学(中国科学院精密测量科学与技术创新研究院), 2025.
PENG J K. Development of a spaceborne all-solid-state Nd: YAG nonplanar-ring-oscillator laser and the reference cavity for frequency stabilization[D]. Wuhan: University of Chinese Academy of Sciences, 2025. (in Chinese).
|
| [12] |
程飞虎. 用于长度标准的532 nm碘分子频率标准的研究[D]. 武汉: 华中科技大学, 2021.
CHENG F H. Study of a 532-nm molecular-iodine frequency standard as a length standard[D]. Wuhan: Huazhong University of Science & Technology, 2021. (in Chinese).
|
| [13] |
支允琳. 碘分子激光稳频及其中剩余幅度调制的研究[D]. 武汉: 中国科学院大学(中国科学院精密测量科学与技术创新研究院), 2022.
ZHI Y L. Laser frequency stabilization with iodine molecules and investiagation on residual amplitude modulation[D]. Wuhan: University of Chinese Academy of Sciences, 2022. (in Chinese).
|
| [14] |
董靖. 超低噪声光纤干涉仪稳频激光器实验研究[D]. 北京: 中国科学院大学, 2016.
DONG J. Experimental research on ultra-low noise fiber interferometer stabilized laser[D]. Beijing: University of Chinese Academy of Sciences, 2016. (in Chinese).
|
| [15] |
SHI B, EDREIRA I B, DING M, et al. Laser stabilized to a fiber interferometer with close-to-zero temperature sensitivity[J]. Laser & Photonics Reviews, 2026, 20(8): e02000. doi: 10.1002/lpor.202502000
|
| [16] |
GERBERDING O, ISLEIF K S, MEHMET M, et al. Laser-frequency stabilization via a quasimonolithic mach-zehnder interferometer with arms of unequal length and balanced dc readout[J]. Physical Review Applied, 2017, 7(2): 024027. doi: 10.1103/PhysRevApplied.7.024027
|
| [17] |
HUARCAYA V, ÁLVAREZ M D, PENKERT D, et al. 2×10-13 fractional laser-frequency stability with a 7-cm unequal-arm mach-zehnder interferometer[J]. Physical Review Applied, 2023, 20(2): 024078. doi: 10.1103/PhysRevApplied.20.024078
|
| [18] |
DI FRONZO C, HOLLAND N A, MITCHELL A L, et al. Laser frequency stabilization with the use of homodyne quadrature interferometers[J]. Classical and Quantum Gravity, 2024, 41(6): 065010. doi: 10.1088/1361-6382/ad13c4
|
| [19] |
HUARCAYA V, DOVALE ÁLVAREZ M, YAMAMOTO K, et al. Single-element dual-interferometer for precision inertial sensing: sub-picometer structural stability and performance as a reference for laser frequency stabilization[J]. Sensors, 2023, 23(24): 9758. doi: 10.3390/s23249758
|
| [20] |
ARMANO M, AUDLEY H, BAIRD J, et al. Sensor noise in LISA Pathfinder: in-flight performance of the optical test mass readout[J]. Physical Review Letters, 2021, 126(13): 131103. doi: 10.1103/PhysRevLett.126.131103
|
| [21] |
ARMANO M, AUDLEY H, BAIRD J, et al. Sensor noise in LISA Pathfinder: an extensive in-flight review of the angular and longitudinal interferometric measurement system[J]. Physical Review D, 2022, 106(8): 082001. doi: 10.1103/PhysRevD.106.082001
|
| [22] |
WANG J, QI K Q, LIU H SH, et al. An integrated fiber phase modulation device for optical path noise suppression[J]. Classical and Quantum Gravity, 2026, 43(1): 015001. doi: 10.1088/1361-6382/ae28ac
|
| [23] |
CAO B, JIA F L, YANG M L, et al. Suppression of frequency-mixing effect for pm-level heterodyne interferometers based on “zero coupling” optical path length control[J]. Optics Letters, 2024, 49(12): 3300-3303. doi: 10.1364/OL.523455
|
| [24] |
范习谦, 刘河山, 罗子人, 等. 基于MHz深度频率调制激光干涉的相位测量技术[J]. 中国光学(中英文), 2025, 18(3): 622-630.
FAN X Q, LIU H SH, LUO Z R, et al. Phase measurement technique based on MHz-lever depth frequency modulated laser interferometry[J]. Chinese Optics, 2025, 18(3): 622-630. (in Chinese)
|
| [25] |
LIU H SH, WANG J, TAO W, et al. Recent development of the laser interferometer for Taiji Space gravitational wave detection[J]. Research, 2026, 9: 1252. doi: 10.34133/research.1252
|
| [26] |
FENG Y J, JIANG Y Z, CHEN L Y, et al. Influence mechanism of truncation on low-frequency phase measurement[J]. Measurement, 2026, 259: 119594. doi: 10.1016/j.measurement.2025.119594
|
| [27] |
YANG R, LUO Z R, LIU H SH. Limitations and improvements in low-frequency performance of phasemeter for space gravitational wave detection[J]. Measurement, 2026, 260: 119825. doi: 10.1016/j.measurement.2025.119825
|
| [28] |
YANG R, LIU H SH, LUO Z R. Optimization design of decimation filter for the phasemeter in the space gravitational wave detection[J]. IEEE Transactions on Instrumentation and Measurement, 2024, 73: 7006508. doi: 10.1109/tim.2024.3453345
|
| [29] |
张强涛, 刘河山, 罗子人. 面向空间激光干涉的多通道相位测量系统[J]. 中国光学(中英文), 2023, 16(5): 1089-1099. doi: 10.37188/CO.2022-0258
ZHANG Q T, LIU H SH, LUO Z R. Multi-channel phase measurement system for the space laser interferometry[J]. Chinese Optics, 2023, 16(5): 1089-1099. (in Chinese). doi: 10.37188/CO.2022-0258
|
| [30] |
王晨, 高雪荣, 齐克奇, 等. 太极计划的弱光锁相地面实验验证及噪声分析[J]. 中国激光, 2025, 52(11): 1101004. doi: 10.3788/CJL241485
WANG CH, GAO X R, QI K Q, et al. Weak-light phase-locked ground-based experimental validation and noise analysis of the Taiji Program[J]. Chinese Journal of Lasers, 2025, 52(11): 1101004. (in Chinese). doi: 10.3788/CJL241485
|
| [31] |
LIANG Y R, FENG Y J, XIAO G Y, et al. Experimental scheme and noise analysis of weak-light phase locked loop for large-scale intersatellite laser interferometer[J]. Review of Scientific Instruments, 2021, 92(12): 124501. doi: 10.1063/5.0058659
|
| [32] |
陈沛权, 邓汝杰, 张艺斌, 等. 太极计划星间激光通信测距的伪随机码选取[J]. 中国光学(中英文), 2025, 18(3): 547-556. doi: 10.37188/CO.2024-0033
CHEN P Q, DENG R J, ZHANG Y B, et al. Pseudo-random code selection for inter-satellite laser ranging and data communication in the Taiji program[J]. Chinese Optics, 2025, 18(3): 547-556. (in Chinese). doi: 10.37188/CO.2024-0033
|
| [33] |
LIANG H Q, YI ZH X, LING H L, et al. Modeling and simulation of inter-satellite laser communication for space-based gravitational wave detection[J]. Sensors, 2025, 25(4): 1068. doi: 10.3390/s25041068
|
| [34] |
张子恒, 范习谦, 靳刚, 等. 太极计划激光链路辅助功能方案设计及验证[J]. 中国激光, 2025, 52(11): 1106001. doi: 10.3788/CJL241483
ZHANG Z H, FAN X Q, JIN G, et al. Design and verification of a laser link auxiliary function scheme for the Taiji Program[J]. Chinese Journal of Lasers, 2025, 52(11): 1106001. (in Chinese). doi: 10.3788/CJL241483
|
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