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.

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.

Gravitational redshift (GRS), a fundamental prediction of general relativity (GR), serves as a critical test of the Einstein Equivalence Principle (EEP) by comparing time flow rates between differing gravitational potentials. Over the decades, GRS experiments in astronomical observations, terrestrial measurements, and space-based investigations have achieved precision levels as fine as 10-5. However, most GRS experiments depend on microwave links for time and frequency transfer, with only a few exploring optical time and frequency transfer methods. Optical time transfer links provide a transformative alternative, offering superior resistance to atmospheric perturbations and higher modulation bandwidths, which enable sub-picosecond synchronization and exceptional time transfer precision. In 1975, Professor Carroll Alley (1927–2016) and his team at the University of Maryland (UMD), USA, demonstrated the feasibility of the optical time transfer method for GRS testing, achieving 10-2 accuracy using cesium clocks with 2×10-14 stability per day and laser pulses of 0.5 mJ energy, 0.1 ns duration, and 10 pulses per second. Modern advancements in optical timing experiments, such as the Chinese Laser Timing (CLT) on the China Space Station (CSS) mission, launched in October 2022, and the European Laser Timing (ELT), part of the upcoming Atomic Clock Ensemble in Space (ACES) mission aboard the International Space Station (ISS), promise unprecedented precision in future GRS experiments.This study investigates GRS testing by simulating ELT data. The ACES mission features atomic clocks with instabilities of about 2×10-16, including a hydrogen maser achieving 1.5×10-15 after 10,000 seconds and a cesium clock with stability of 1.1×10-13​√τ, where τ is the integration time in seconds. Additionally, the ELT payload is equipped with a novel single photon detector with a timing stability of < 3 ps @ 300 s and an event timer with precision of < 1 ps. Our simulation results indicate that using the two-way laser time transfer (TWLTT) link via the ELT experiment achieves precision levels 3–4 orders of magnitude higher than those obtained in the Alley experiment 50 years ago, thanks to the advanced atomic clocks aboard the ACES mission. This study is supported by the National Natural Science Foundations of China (NSFC) (Grant Nos. 42030105, 42388102, and 42274011) and the Space Station Project (2020-228).