Fig. 2 Time dilation in different interferometer geometries.

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Presentation transcript:

Fig. 2 Time dilation in different interferometer geometries. Time dilation in different interferometer geometries. Spacetime diagrams for the light-pulse and gravitationally induced trajectories zk and zg, as well as the accelerations z¨k caused by the light pulses, together with the proper-time difference Δτ, the gravito-kick action ΔSgk, the electromagnetic contribution ΔSem/ℏ, and the total phase difference Δφ of an MZI (left), a symmetric RBI (center), and an asymmetric RBI (right). The first two geometries display a symmetric momentum transfer between the two branches, leading to vanishing proper-time differences. However, the asymmetric RBI features a proper-time difference that has the form of a recoil term. The spacetime diagrams also illustrate the connection to the twin paradox by displaying ticking rates (the dashes) of the two twins traveling along the two branches. Both quantum twins in the MZI and symmetric RBI experience the same time dilation, whereas in the asymmetric RBI, one twin stays at rest and the other one leaves and returns so that their proper times are different. The arrows in the plot of z¨k denote the amplitude of the delta functions that scale with ±ℏk/m. Because of the instantaneous nature of z¨k, the integration over time in Eqs. 4 and 6 reduces to a sampling of the positions zk and zg at the time of the pulses such that the respective phase contributions can be inferred directly from the figure. Sina Loriani et al. Sci Adv 2019;5:eaax8966 Copyright © 2019 The Authors, some rights reserved; exclusive licensee American Association for the Advancement of Science. No claim to original U.S. Government Works. Distributed under a Creative Commons Attribution NonCommercial License 4.0 (CC BY-NC).