Test of the gravitational redshift with single-photon-based atomic clock interferometers

The gravitational redshift (GR), as predicted by Einstein’s general theory of relativity, posits that two identical clocks situated at different gravitational potentials will tick at different rates. In this study, we explore the impact of the GR on a single-photon-based atom interferometer and propose a corresponding testing scheme. Our approach conceptualizes the atom interferometer as two coherent atomic clocks positioned at distinct elevations, which is referred to as an atomic clock interferometer, allowing us to derive the GR-induced phase shift. This effect becomes significant due to the notable energy difference between the two atomic internal states, comparable to other relativistic effects in single-photon-based atomic clock interferometers. Furthermore, our proposed scheme incorporates the velocity of the laser device to effectively mitigate other relativistic effects. The ensuing analysis indicates an anticipated GR test precision at the 10⁻⁵ level for our proposed approach.