In recent years, remarkable breakthroughs have been achieved in the research and application of optical clocks. Various optical clocks have been developed by countries around the world. The systematic frequency uncertainty and stability of optical clocks are 2?3 orders lower than those of microwave fountain clocks, reaching levels of 10^-18?10^-19. The Bureau International des Poids et Measurements (BIPM) has adopted optical clocks as secondary frequency standards and is committed to redefining the second with optical clocks. Employing an optical clock to steer the local time scale is an effective method to improve autonomous timekeeping performance.

First, we introduce the main components of the time-keeping system. 1) The optical clock system, which is composed of a ⁴⁰Ca⁺ optical clock, an optical frequency comb, and a photogenic microwave system. It is responsible for probing, locking, and outputting an ultra-stable optical signal. The optical comb locks the signal and outputs the laser repetition frequency, the carrier-envelope phase offset frequency, and the beat frequency. The photogenic microwave system generates a 10 MHz signal through digital frequency synthesis based on the output frequency of the optical frequency comb. 2) The frequency steering platform consists of a hydrogen maser clock, two microphase steppers, and a phase comparator. Two local time scales, TS(H) and TS(Ca), are generated by steering the output frequency of the hydrogen maser clock with reference to UTC or the optical clock respectively. 3) The time system TS(BSNC) is responsible for establishing a time-transfer link to UTC to evaluate the performance of the local time scale. Second, the noise model of the hydrogen maser clock is developed based on the frequency deviation between the optical clock and the hydrogen maser clock. The noise components include white frequency noise, flicker frequency noise, random walk frequency noise, and frequency drift. Subsequently, we design two steering methods based on UTC and the optical clock to generate a local time scale. Finally, we analyze the timekeeping performance of TS(Ca) and TS(H) through the time-transfer link of TS (BSNC).

The run rate of an optical clock refers to the ratio of the duration of the clock’s normal time to the total duration of a specified period. From April 24 to September 30 in 2024, the run rate of the optical clock reaches 93.1% over 160 days. We evaluate the 11 common error sources associated with the optical clock, resulting in a systematic frequency uncertainty of 2.15×10^-17. The self-comparison frequency stability of the optical clock is assessed using the self-comparison frequency deviation of the three peak center frequencies. As shown in Fig. 5, the self-comparison frequency stability of the optical clock reaches a value of 8.28×10^-15/τ@(1-2)×10⁶ s. Over the 160 days, the final timekeeping deviations of TS(Ca), TS(H), and UTC(PTB) are 0.6 ns, -4.6 ns, and -1.0 ns respectively, with peak-to-peak time deviations of 1.5 ns, 4.9 ns, and 1.6 ns respectively. As shown in Fig. 14, when the averaging time ranges from 5 to 10 days, the frequency stabilities of UTC(PTB) and TS(Ca) are mainly influenced by time-transfer link white phase noise. When the averaging time exceeds 15 days, the influence of time-transfer link noise gradually decreases, with TS(Ca) exhibiting the best frequency stability, followed by UTC(PTB), and TS(H) showing the least stability. At an averaging time of 30 days, the frequency stabilities are 1.15×10^-16, 1.83×10^-16, and 4.42×10^-16 respectively.

In this study, we introduce a timekeeping system based on a ⁴⁰Ca⁺ optical clock at Beijing Satellite Navigation Center. The noise model of the hydrogen clock is accurately constructed using the frequency differences between the hydrogen clock and the optical clock. Two local time scales, TS(H) and TS(Ca), are generated and continuously operated for 160 days by steering the hydrogen clock with reference to UTC or the optical clock respectively. During the running period, the run rates of the optical clock and the whole optical system reach 93.1% and 88.4% respectively. The systematic frequency uncertainty of the optical clock is approximately 2.15×10^-17, and its frequency stability achieves 8.28×10^-15/τ@(1-2)×10⁶ s. The final and peak-to-peak time differences between TS(Ca) and UTC are better than 0.6 ns and 1.5 ns respectively. The frequency stability of TS(Ca) relative to UTC is 1.15×10^-16@30 d.