Experimental demonstration of the clock asynchrony model in space-borne gravitational wave detection

Space-borne gravitational wave detection will open the observation window in the 0.1 mHz$-$1 Hz bandwidth, playing a crucial role in the development of cosmology and physics. Precise clock synchronization among satellites is essential for the accurate detection of gravitational wave signals. However, the independent clock counting mechanisms of each satellite pose a significant challenge. This work reports the mathematical model of clock asynchrony, which is mainly dominated by the constant term factor and the linear term factor. Moreover, it experimentally verifies the clock asynchronization technique based on a dual-phasemeter system. Through experimentation, the impacts of these two aspects of clock asynchrony were confirmed, and post-processing techniques were employed to reduce these impacts to as low as $\rm 2\pi \times 10^{-6} rad/Hz^{1/2}@ 3mHz$. Specifically, the constant term factor is measured by Time-delay Interferometry Ranging (TDIR), while the linear term factor can be gauged by clock transmission link. This study provides a reference for understanding the clock asynchrony mechanism and processing clock synchronization issues. Additionally, a low additional noise clock synchronization test system is introduced to support such measurements.