Simulating Gravitational Redshift Test Using the European Laser Timing (ELT) Experiment on the ACES Mission

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).