Fig. 1. Schematic diagram of ultra-stable laser system assembly (AVI represents the active vibration isolation platform, VC is the vacuum chamber, TC is temperature control, ISO stands for optical isolator, and PD denotes photo detector. The red lines represent the optical paths, the blue lines represent the electrical circuits, and the black connecting lines represent optical fibers)

Fig. 2. Comparison of error signal stability under different optical path isolation configurations (The left axis is the error signal voltage value. The right axis represents the ratio of the frequency deviation converted from the error signal slope to the cavity linewidth, and the corresponding frequency stability of the frequency deviation divided by optical frequency)

Fig. 3. Frequency locking circuit design schematic, where the ⊗ symbol represents a mixer, and arrows indicate the direction of signal flow

Fig. 4. Circuit pure proportional gain bandwidth (The solid line represents the gain at different frequencies, while the dot dash line represents the corresponding phase angles)

Fig. 5. Spectrum of the error signal after laser frequency locking

Fig. 6. Comparison of error signal stability before and after frequency locking

Fig. 7. Vibration sensitivity test for the two reference cavities

Fig. 8. Plot of beat frequency variation over time after inner cavity temperature change ("data" represents the measured beat frequency values, "fit" is the fitted beat frequency curve, "temp" indicates the cavity temperature change over time predicted by the fitting model, and T₀ represents the temperature at which the cavity's thermal expansion coefficient crosses zero)

Fig. 9. Temperature stability of the vacuum chamber and internal insulation layer. (a)(b) Temperature variation graphs over time for the inner and outer layers of No. 1 and No. 2 reference cavities, respectively; (c)(d) corresponding Allan deviations calculated using the temperature data from figures (a) and (b)

Fig. 10. Beat frequency data plots. (a) Beat frequency variation over time with the linear drift of 11.8 mHz/s removed; (b) Allan deviation of the beat frequency calculated from the data in figure (a)