Weak‑Light Phase‑Locked Ground‑Based Experimental Validation and Noise Analysis of the Taiji Program

Chen Wang; Xuerong Gao; Keqi Qi; Shaoxin Wang; Pan Li; Peng Dong; Heshan Liu; Ziren Luo

doi:10.3788/CJL241485

Chinese Journal of Lasers, Volume. 52, Issue 11, 1101004(2025)

Weak‑Light Phase‑Locked Ground‑Based Experimental Validation and Noise Analysis of the Taiji Program

Chen Wang^1,2,3,4, Xuerong Gao⁴, Keqi Qi⁴, Shaoxin Wang⁴, Pan Li⁴, Peng Dong¹, Heshan Liu^4、*, and Ziren Luo^2,4

¹School of Fundamental Physics and Mathematical Sciences, Hangzhou Institute for Advanced Study, UCAS, Hangzhou 310024, Zhejiang , China

²National Space Science Center, Chinese Academy of Sciences, Beijing 100190, China

³University of Chinese Academy of Sciences, Beijing 100049, China

⁴Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, China

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Figures & Tables(11)

Fig. 1. Schematic of a double-star laser interferometric ranging

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Fig. 2. Experimental program design diagram

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Fig. 3. System physical drawing. (a) Laser; (b) four-chip interferometer and photodetector; (c) Moku: Pro integrated controller

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Fig. 4. Schematic of phasemeter

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Fig. 5. PID control loop diagram

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Fig. 6. Amplitude spectral density (ASD) of residual locked phase error at different powers

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Fig. 7. Weak light phase-locking noise analysis

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Table 1. Arm length and relative velocity for different space-based gravitational wave detection programs
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Table 1. Arm length and relative velocity for different space-based gravitational wave detection programs
Program Arm length /m
Maximum relative
velocity /（m/s）
Taiji 3×10⁹ ±10
LISA 2.5×10⁹ ±10
Tianqin $\sqrt[]{3} \times 10^{5}$ ±5

Table 2. Main parameters of the experimental equipment

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Table 2. Main parameters of the experimental equipment

Experimental equipment

Main parameter

Laser

（Mephisto 500NEFC）

Wavelength：1064 nm

PZT port adjustment rate： 1 MHz/V

TEC port adjustment rate： -3 GHz/V

PZT port response bandwidth： 100 kHz

TEC port response bandwidth： 1 Hz

Photodetector

（Thorlabs APD430M/C）

Response bandwidth： 0‒400 MHz

Adjustable gain range： 4‒20

APD responsivity： 12 A/W

Transimpedance amplifier resistor： 5000 Ω/10000 Ω

Phasor， PID controller， acquisition card （Moku：Pro）

Number of input connectors： 4

Input interface maximum bandwidth： 600 MHz

Maximum sampling rate of input interface： 1.25 GSa/s

Number of output connectors： 4

Output interface sample rate： 1.25 GSa/s

ADC quantization bits： 10 bit

Table 3. PID Control loop parameters

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Table 3. PID Control loop parameters

Part	Parameter name	Value	Unit
General	Sampling frequency $f_{s a m p l i n g}$	78.125	MHz
	Quantization $N$	24	bit
	Phase amplification factor $k_{1}$	120	mV/cycle
LPF （Butterworth）	Cutoff frequency $f_{c u t}$	50	kHz
	$a_{0}$	1
	$a_{1}$	2.6131259
	$a_{2}$	3.4142136
	$a_{3}$	2.6131259
PI-I⁺（PZT）	Proportional gain $k_{P Z T}$	-28	dB
	Integrator crossover frequency $f_{P Z T ‑ I}$	8	kHz
	Integrator crossover frequency $f_{P Z T ‑ I^{+}}$	300	Hz
PI （TEC）	Proportional gain $k_{T E C}$	-40	dB
PI （TEC）	Integrator crossover frequency $f_{T E C ‑ I}$	500	mHz

Table 4. Measured phase noise at different weak-light powers

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Table 4. Measured phase noise at different weak-light powers

Weak-light power /nW	Carrier power C /dBm	Noise power spectrum density N₀ /（dBm/Hz）	CNR noise S_CNR / （rad/Hz^1/2）	Shot noise S_shot / （rad/Hz^1/2）	Experimental results / （rad/Hz^1/2）
0.49	-42.7	-128.7	5.01×10^-5	1.95×10^-5	6×10^-5
3.08	-30.4	-128.7	1.22×10^-5	7.78×10^-6	1.9×10^-5
12.33	-26.21	-128.7	7.51×10^-6	3.89×10^-6	9.5×10^-6
49.31	-19.5	-128.7	3.47×10^-6	1.95×10^-6	5.5×10^-6

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Chen Wang, Xuerong Gao, Keqi Qi, Shaoxin Wang, Pan Li, Peng Dong, Heshan Liu, Ziren Luo. Weak‑Light Phase‑Locked Ground‑Based Experimental Validation and Noise Analysis of the Taiji Program[J]. Chinese Journal of Lasers, 2025, 52(11): 1101004

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