## 1 Introduction  
The importance of artificial satellites in the modern society is increasing owing to their pivotal role in communication, navigation, and remote sensing applications in daily life, industrial production, scientific research, and innumerable other domains [1, 2, 3, 4]. To guarantee navigational and scientific operational precision, satellite payloads must be equipped with high-precision frequency or time references [5]. The time-frequency output of the satellite's onboard clock is a reference for the satellite ephemeris data and various onboard radio frequency (RF) and digital systems [6]. Currently, the high-precision frequency standards in space contribute considerably to solving astronomical issues pertaining to far-infrared, submillimeter, and millimeter wavelength ranges. This enables astronomers to observe the universe with unparalleled sensitivity and angular resolution [7; 8]. A prevalent approach to enhance the performance of spaceborne time and frequency references is to use onboard atomic clocks. Over time, the number of satellites equipped with atomic clocks has increased considerably, particularly for navigational applications [9]. The performance of these onboard atomic clocks directly determines the accuracy of navigational and positioning systems and is crucial for their precision and stability [10; 11; 12]. Navigation satellites, such as the Global Positioning System (GPS), GLONASS, BeiDou, and Galileo, are equipped with a cesium frequency standard (CFS), rubidium frequency standard (RFS), and passive hydrogen maser (PHM), which are fundamental to their time-frequency systems [13; 14]. The stability of these frequency sources has been evaluated using the Allan variance, a statistical measure for assessing the stability of frequency sources. In this context, the frequency stability of the CFS on GLONASS R17 can reach \(3\times 10^{-14}\) after averaging for approximately 16 h. The RFS on the GPS yields a \(3\times 10^{-15}\) 24 h frequency stability. The BeiDou PHM yields a \(7\times 10^{-15}\) 24 h frequency stability [15]. Despite advances in atomic clock miniaturization technology, balancing performance, size, and power consumption remains a challenge. Active hydrogen masers (AHMs), while offering exceptional short- and medium-term frequency stability--reaching levels such as \(1.27\times 10^{-15}\) at 10,000 s--are still constrained by their inherent physical size and environmental sensitivity. The microwave cavities in these systems occupy a large portion of the device volume. Although efforts have been made to reduce cavity size using new materials, current compact AHMs currently deployed aboard the Chinese space station still weigh around 35-40 kg and consume approximately 70 W of power [16]. These specifications, while improved over traditional laboratory-grade masers, still limit their integration into standard GEO communication satellite platforms or conventional GNSS satellite platforms. In contrast, optical clocks have demonstrated superior short- and medium-term frequency stability due to their high interrogation frequencies and ultra-narrow linewidths. They offer promising performance that could exceed that of traditional microwave atomic clocks by one to two orders of magnitude [17]. However, realizing these advantages in space remains challenging. Miniaturized optical clock systems must integrate ultra-stable lasers and thermal control subsystems, all within strict space-qualified SWaP (size, weight, and power) constraints [15]. Further engineering efforts are needed to ensure their long-term stability, mechanical robustness [18], and qualification for GNSS or geostationary satellite deployment. Satellites equipped with atomic clocks predominantly support navigation satellites, whereas commercial geostationary Earth orbit (GEO) communication satellites typically do not employ atomic clocks. Such satellites are increasingly being utilized as relays for time and frequency synchronization applications through free-space links [19; 20].