Experimental research on low-noise and high-gain balanced detectors in mHz−MHz band

LU Bo; SHI Shaoping; GAO Li; WANG Xuan; LIN Yisong; TIAN Long; LI Wei; WANG Yajun; ZHENG Yaohui

doi:10.7498/aps.74.20250640

Abstract

Balanced detector is a fundamental component for the accurately measuring quantum state fluctuations, especially quantum noise, which is crucial for future quantum-enhanced interferometric gravitational wave detectors utilizing squeezed light. By using a transimpedance amplifier (TIA) model core for balanced detection, a detailed theoretical and practical analysis is conducted on the electronic factors that affect the performance of the detector in the target ultra-low-frequency range. The TIA stage is meticulously designed using a high-performance integrated operational amplifier characterized by low offset voltage drift. In order to ensure the critical gain stability for ultra-low-frequency operation, this design adopts low temperature-drift metal foil resistors. Subsequent voltage amplification is achieved using a noninverting amplifier configuration to attain the necessary high electrical gain, while strictly managing overall electronic noise. By recognizing the criticality of common-mode noise rejection for quantum noise measurements, the photodiode (PD) nonlinear response compensation mechanism is analyzed and optimized. This is achieved through the innovative implementation of a differential fine-tuning circuit (DFTC) coupled with an adjustable bias voltage (ABV) compensation scheme. Experimental validation confirms the effectiveness of the optimized design. The compensation scheme utilizing DFTC and ABV successfully achieves a high common mode rejection ratio (CMRR) exceeding 75 dB@500 Hz. Crucially, the detector achieves an electronic noise spectral density of 3.5 × 10^–5 V/Hz^1/2 within the 1 mHz–1 Hz band, exceeding the requirements for laser intensity noise (1 × 10^–4 V/Hz^1/2) in space-based gravitational wave detection. Furthermore, the detector demonstrates high gain capability and bandwidth: with an incident detection light power of 4 mW, the balanced detector achieves a gain of 20 dB maintained in a wide frequency range from 1 mHz to 1 MHz. This work presents the design, detailed analysis, and experimental realization of optimized balanced detectors specifically tailored for high-sensitivity measurements in the millihertz gravitational wave frequency band. The achieved low electronic noise base below 1 Hz and high CMRR meet the key requirements for future space-based gravitational wave detectors to detect squeezed states of light. This optimized balanced detector provides important components and technical support for the next-generation space-based gravitational wave detection and millihertz squeezed light characterization.

Keywords:

Authors and contacts

1.
State Key Laboratory of Quantum Optics Technologies and Devices, Institute of Opto-Electronics, Shanxi University, Taiyuan 030006, China
2.
Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan 030006, China
3.
College of Physics and Electronic Engineering, Shanxi University, Taiyuan 030006, China

Corresponding author: SHI Shaoping, ssp4208@sxu.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 62035015, 62225504, 62027821, U22A6003, 12304399, 12174234, 12274275, 62375162), the Fundamental Research Program of Shanxi Province, China (Grant Nos. 202303021212003, 202303021224006), and the Key R&D Program of Shanxi Province, China (Grant No. 202302150101015).

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References

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Cited By

图 1 基于TIA的平衡光电探测器示意图(OPA1/2, 运算放大器1/2; PD, 光电二极管; V_bias, 偏置电压; V_AC, 交流电压信号; V_DC, 直流电压信号)

Figure 1. Schematic diagram of the balanced detector based on TIA. OPA1/2, operational amplifier 1/2; PD, photodiode; V_bias, bias voltage; V_AC, AC voltage signal; V_DC, DC voltage signal.

DownLoad: Full-Size Img PowerPoint

图 2 光电二极管和TIA的等效电路模型

Figure 2. Noise response model of photodiode and TIA.

DownLoad: Full-Size Img PowerPoint

图 3 平衡光电探测器电路原理图(FER, 磁珠; RP, 滑动变阻器)

Figure 3. Circuit layout of balanced detector. FER, ferrite bead; RP, variable resistor.

DownLoad: Full-Size Img PowerPoint

图 4 基于LTspice软件的电路仿真图　(a) 时域参数扫描分析图; (b) 频域参数扫描分析图

Figure 4. Electronic circuit simulation based on LTspice software: (a) Time domain parameter scan analysis results; (b) frequency domain parameter scan analysis results.

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图 5 平衡光电探测器性能测试评估装置图(ISO, 光学隔离器; HWP, 半波片; PBS, 偏振分束器; EOAM, 电光振幅调制器; SG, 信号发生器; BHD, 平衡光电探测器; SA, 频谱分析仪; OSC, 示波器; Meter, 高精度数字万用表)

Figure 5. Balanced detector performance test and evaluation device. ISO, isolator; HWP, half-wave plate; PBS, polarization beam splitter; EOAM, electro-optic amplitude modulator; SG, signal generator; BHD, balanced homodyne detector; SA, spectrum analyzer; OSC, oscilloscope; Meter, high-precision digital multimeter.

DownLoad: Full-Size Img PowerPoint

图 6 平衡光电探测器CMRR测试图

Figure 6. CMRR of the balanced detector.

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图 7 平衡光电探测器线性度测试噪声谱表征　(a) 1 kHz—1.5 MHz频段性能的测量结果; (b) 1 mHz—1 Hz频段性能的测量结果

Figure 7. Balanced detector linearity test noise spectral characterization: (a) Measured noise spectra from 1 kHz to 1.5 MHz; (b) noise power spectrum from 1 Hz downwards to 1 mHz.

DownLoad: Full-Size Img PowerPoint

DownLoad: Full-Size Img PowerPoint

[1]	Abbott R, Abbott T D, Abraham S, Acernese F, Ackley K, Adams A, Adams C, Adhikari R X, Adya V B, Affeldt C 2020 Phys. Rev. Lett. 125 101102 Google Scholar
[2]	Vitale S 2021 Science 372 eabc7397 Google Scholar
[3]	Abbott T D, Abraham S, Acernese F, et al. 2020 Astrophys. J. Lett. 896 L44 Google Scholar
[4]	李庆回, 李卫, 孙瑜, 王雅君, 田龙, 陈力荣, 张鹏飞, 郑耀辉 2022 物理学报 71 164203 Google Scholar Li Q H, Li W, Sun Y, Wang Y J, Tian L, Chen L R, Zhang P F, Zheng Y H 2022 Acta Phys. Sin. 71 164203 Google Scholar
[5]	王在渊, 王洁浩, 李宇航, 柳强 2023 物理学报 72 054205 Google Scholar Wang Z Y, Wang J H, Li Y H, Liu Q 2023 Acta Phys. Sin. 72 054205 Google Scholar
[6]	Jia W X, Xu V, Kuns K, et al. 2024 Science 385 1318 Google Scholar
[7]	McCuller L, Whittle C, Ganapathy D, Komori K, Tse K, Fernandez-Galiana A, Barsotti L, Fritschel P, MacInnis M, Matichard F, Mason K, Mavalvala N, Mittleman R, Yu H C, Zucker M E, Evans M 2020 Phys. Rev. Lett. 124 171102 Google Scholar
[8]	Aasi J, Abadie J, Abbott B P, Abbott R, et al. 2013 Nat. Photonics 7 613 Google Scholar
[9]	Acernese F, Agathos M, Aiello L, et al. 2019 Phys. Rev. Lett. 123 231108 Google Scholar
[10]	Mikhail K, Ma Y Q, Chen Y B, Schnabel R 2019 Light: Sci. Appl. 8 118 Google Scholar
[11]	Harry G M, LIGO Scientific Collaboration 2010 Classical Quantum Gravity 27 084006 Google Scholar
[12]	Matichard F, Lantz B, Mittleman R, et al. 2015 Classical Quantum Gravity 32 185003 Google Scholar
[13]	Thorne K S, Winstein C J 1999 Phys. Rev. D 60 082001 Google Scholar
[14]	Acernese F, Agathos M, Agatsuma K, et al. 2014 Classical Quantum Gravity 32 024001 Google Scholar
[15]	Luo J, Chen L S, Duan H Z, Gong Y G, Hu S C, Ji J H, Liu Q, Mei J W, Milyukov V, Sazhin M, Shao C G, Toth V T, Tu H B, Wang Y M, Wang Y, Yeh H C, Zhan M S, Zhang Y H, Zharov V, Zhou Z B 2016 Classical Quantum Gravity 33 035010 Google Scholar
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[17]	Luo Z R, Wang Y, Wu Y L, Hu W R, Jin G 2021 Prog. Theor. Exp. Phys. 2021 05A108 Google Scholar
[18]	Luo Z R, Guo Z K, Jin G, Wu Y L, Hu W R 2020 Results Phys. 16 102918 Google Scholar
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[28]	Gao L, Zheng L A., Lu B, Shi S P, Tian L, Zheng Y H 2024 Light: Sci. Appl. 13 294 Google Scholar
[29]	Yang W H, Jin X L, Yu X D, Zheng Y H, Peng K C 2017 Opt. Express 25 24262 Google Scholar
[30]	王炜杰, 李番, 李健博, 鞠明健, 郑立昂, 田宇航, 尹王保, 田龙, 郑耀辉 2022 红外与激光工程 51 20220300 Google Scholar Wang W J, Li F, Li J B, Ju M J, Zheng L A, Tian Y H, Yin W B, Tian L, Zheng Y H 2022 Infrared Laser Eng. 51 20220300 Google Scholar
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[32]	Shi S P, Tian L, Wang Y J, Zheng Y H, Xie C D, Peng K C 2020 Phys. Rev. Lett. 125 070502 Google Scholar
[33]	史少平, 武奕淼, 刘璇, 田龙, 郑耀辉 2024 量子光学学报 30 040102 Google Scholar Shi S P, Wu Y M, Liu X, Tian L, Zheng Y H 2024 J. Quantum Opt. 30 040102 Google Scholar
[34]	王鼎康, 武晋泽, 宋志刚, 李晋红 2024 量子光学学报 30 041001 Google Scholar Wang D K, Wu J Z, Song Z G, Li J H 2024 J. Quantum Opt. 30 041001 Google Scholar
[35]	Graeme J 1996 Photodiode amplifiers: op amp solutions (New York: McGraw-Hill) pp87–92
[36]	Lu Q, Shen Q, Cao Y, Liao S K, Peng C Z 2019 IEEE Trans. Nucl. Sci. 66 1048 Google Scholar
[37]	AD797: Ultralow Distortion, Ultralow Noise Op Amp Data Sheet (Rev. K) https://www.analog.com/media/en/technical-documentation/data-sheets/AD797.pdf [2025-5-12]
[38]	AD8671/AD8672/AD8674: Precision, Very Low Noise, Low Input Bias Current Operational Amplifiers Data Sheet (Rev. F) https://www.analog.com/media/en/technical-documentation/data-sheets/AD8671_8672_8674.pdf [2025-5-12]
[39]	Jin X L, Su J, Zheng Y H, Chen C Y, Wang W Z, Peng K C 2015 Opt. Express 23 23859 Google Scholar
[40]	李番, 王嘉伟, 高子超, 李健博, 安炳南, 李瑞鑫, 白禹, 尹王保, 田龙, 郑耀辉 2022 物理学报 71 209501 Google Scholar Li F, Wang J W, Gao Z C, Li J B, An B N, Li R X, Bai Y, Yin W B, Tian L, Zheng Y H 2022 Acta Phys. Sin. 71 209501 Google Scholar

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Vol. 74, Issue 18 - 2025-09-20

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