In November 2022, the China Space Station (CSS) was equipped with a cold atomic microwave clock and a Sr optical lattice clock with stabilities of $5\times {10}^{-14}/\sqrt{\tau }$ and $2\times {10}^{-15}/\sqrt{\tau }$ (where $\tau$ is the integration time in seconds), respectively, which provides an excellent opportunity to test gravitational redshift (GRS) with higher accuracy than previous results. Based on high-precision frequency links between the China Space Station and a ground station, we formulated a model and provided simulation experiments to test GRS. Simulation results suggest that this method could test the GRS at the accuracy level of $5\times {10}^{-7}$, more than 2 orders in magnitude higher than the result of the experiment of a hydrogen clock on board a flying rocket more than 40 years ago.

Summary: Traditional methods for measuring geopotential difference using optical fiber frequency transfer or satellite-based time-frequency transfer, based on general relativity, require the use of two clocks and the calibration of these clocks. Here we present a simplified clock transportation experiment using a single hydrogen clock to measure the geopotential difference between two time-frequency stations, separated by 129 km with a height difference of 1,245 m, by GNSS precise point positioning time-frequency transfer. Taking the reference clock of International GNSS Service (IGS) time as a ‘bridge’, we extract the gravity frequency shift between the two stations by comparing the fractional frequency differences between the hydrogen clock and the ‘bridge’ before and after clock transportation. The determined geopotential difference between the two stations is 12075.9$\pm $118.5 m²/s², which closely aligns with the value computed by the EIGEN-6C4 global gravity field model, with a difference of -78.7 m²/s². These results validate the feasibility of geopotential difference measurements with a single clock and highlight several advantages compared to the dual-clock method: elimination of inter-clock calibration, low operational complexity and equipment cost, high data utilization efficiency but similar precision of geopotential difference measurement. Furthermore, this method can be extended to other similar techniques to measure geopotential differences, provided that they enable users to connect to a stable time-frequency reference.

Earth rotation parameters (ERPs) are fundamental to geodetic and astronomical studies. With its high measurement accuracy and stability, the Very Long Baseline Interferometry (VLBI) plays an irreplaceable role in estimating the ERPs and maintaining the earth reference frame. However, the imperfect global station distribution, observation discontinuity, and vast cost of the VLBI make the GNSS a more attractive technique. In 2020, the third generation of the BeiDou Navigation System (BDS), namely BDS-3, was constructed completely. In this study, we conducted a series of experiments to estimate Earth’s rotation parameters based on the continuous BDS-3 observation data, the discontinuous VLBI observation data, and the combined BDS-3 and discontinuous VLBI observation data. We used two methods, namely the weighted averaging method and the normal equation combination method, to obtain ERP combination solutions. The results are compared with the International Earth Rotation and Reference Systems Service (IERS) EOP 20C04 at 00:00:00 UTC. Final results show that (a) the estimation accuracy becomes stable when the number of BDS-3 tracking stations is more than 40. At the same time, both the number of stations and the volume of polyhedrons formed by the observing stations affect the accuracy of the ERPs estimated by the BDS-3 or VLBI. (b) Results have also shown that the inclusion of the BDS-3 IGSO and GEO satellites contributes little to the ERP estimation. (c) For the BDS-3-only MEO satellites solution, the root mean square (RMS) was 113.2 µas, 102.8 µas, and 13.1 µs/day for X-pole coordinate, Y-pole coordinate, and length of day (LOD), respectively. For the VLBI solution, the RMSs of the X-pole, Y-pole, and LOD were 100.4 µas for the X-pole, 94.2 µas for the Y-pole, and 14.1 µs/day. The RMS was 82.6 µas, 70.3 µas, and 10.5 µs/day for the combined X-pole, Y-pole, and LOD using the weighted averaging method. It was 78.2 µas, 62.6 µas, and 8.6 µs/day when the normal equation combination method was applied. This demonstrates that by taking advantage of the BDS-3 and VLBI technique combinations, accuracy in estimating the ERPs can be improved over that using either of them, in addition to enhanced stability and reliability.

The Atomic Clock Ensemble in Space (ACES) mission, currently operating aboard the International Space Station (ISS), is designed to provide high-precision time and frequency measurements and to test fundamental aspects of relativistic physics. Gravitational redshift (GRS), a fundamental prediction of General Relativity (GR), implies that clocks positioned at different gravitational potentials experience relative time dilation. Previous GRS experiments have focused primarily on microwave technologies, with negligible experimental coverage in the optical domain, particularly for ground-to-space links. Motivated by the European Laser Timing (ELT) experiment and the high-precision laser-cooled cesium clock aboard ACES, we introduce and evaluate an optical time-transfer method designed to achieve high-accuracy measurements of GRS. In the absence of actual ELT/ACES optical data, a high-fidelity numerical simulation framework was developed to assess the performance of this method. The framework incorporates representative ELT/ACES mission parameters, including the space-based cesium clock and the H-MASER clock located at the reference ground station, both providing frequency stability at the level of ${10}^{-15}$ for 1000 s averaging time. Applying a $\pm 1\sigma$ filtering criterion, we obtain a simulated dataset comprising 33 ELT/ACES passes, representing a total observation time of 4.38 h over a single week. Analysis of this high-fidelity dataset reveals a GRS deviation from GR of $(-7.19\pm 0.63)\times {10}^{-5}$, achieving a 3.4 orders of magnitude improvement over the best previous laser-ranging experiment conducted at the University of Maryland (UMD), USA, 51 years ago. These simulation results demonstrate that the optical time-transfer link constitutes a powerful tool for testing fundamental physics and, when combined with next-generation optical atomic clocks, enables unprecedented capabilities in space-based timekeeping and geoscience applications.

Space-based atomic clocks provide unique conditions for testing General Relativity (GR) due to their stability in a low-disturbance environment and their exposure to significant variations in gravitational potential. Gravitational redshift (GRS), a direct consequence of the Einstein Equivalence Principle (EEP), causes clocks at different gravitational potentials to experience relative time dilation. Ground-to-space GRS experiments measure frequency shifts arising from differences in gravitational potential through signal exchange between ground and satellite clocks. While past experiments have relied on microwave links for time–frequency comparisons, optical time and frequency transfer has recently emerged as a promising alternative due to its immunity to ionospheric effects, reduced sensitivity to atmospheric delays, higher modulation bandwidth, and improved signal clarity. In this work, we investigate the GRS using ground-to-space observations from the Time Transfer by Laser Link (T2L2) experiment onboard the Jason-2 mission. Relative to the pioneering 1975 University of Maryland experiment, USA, the T2L2 mission achieves over an order-of-magnitude improvement in measurement precision, demonstrating the power of modern optical time transfer techniques. By comparing a ground-based hydrogen maser and a space-based ultra-stable quartz oscillator, with respective stabilities of $$10^{-15}$$ 10 - 15 and $$10^{-13}$$ 10 - 13 at 1000s, over 47 independent T2L2/Jason-2 passes (approximately 12 h total), we obtain a GRS deviation from GR of $$(-0.77 \pm 3.54) \times 10^{-3}$$ ( - 0.77 ± 3.54 ) × 10 - 3 . These results demonstrate that optical time-transfer links can achieve high-precision tests of GR, underscoring their potential for future space-based optical timing missions.