Atom interferometer as a freely falling clock for time-dilation measurements

Light-pulse atom interferometers based on single-photon transitions are a promising tool for gravitational-wave detection in the mid-frequency band and the search for ultralight dark-matter fields. Here we present a novel measurement scheme that enables their use as freely falling clocks directly measuring relativistic time-dilation effects. The proposal is particularly timely because it can be implemented with no additional requirements in Fermilab's MAGIS-100 experiment or even in the 10-m prototypes that are expected to start operating very soon. This will allow the unprecedented measurement of gravitational time dilation in a local experiment with freely falling atoms, which is out of reach even for the best atomic-fountain clocks based on microwave transitions. The results are supported by a comprehensive treatment of relativistic effects in this kind of interferometers as well as a detailed analysis of the main systematic effects. Furthermore, the theoretical methods developed here constitute a valuable tool for modelling light-pulse atom interferometers based on single-photon transitions in general.