Finite-Speed-of-Light Effects in Atom Interferometry: Diffraction Mechanisms and Resonance Conditions

TL;DR

This paper develops a theoretical framework to understand how finite light speed affects phase measurements in atom interferometers, highlighting the importance of diffraction mechanisms and geometry for high-precision relativistic measurements.

Contribution

It introduces a comprehensive theory for finite-speed-of-light effects in atom interferometry, considering relativistic effects and diffraction mechanisms, with practical implications for precision measurements.

Findings

Finite light speed induces phase perturbations in atom interferometers.

Diffraction mechanism and geometry critically influence the magnitude of effects.

Laser tuning, rather than atomic velocity, is key to resonance in Mach-Zehnder setups.

Abstract

Light-pulse atom interferometers serve as tools for high-precision metrology and are targeting measurements of relativistic effects. This development is facilitated by extended interrogation times and large-momentum-transfer techniques generating quantum superpositions of both interferometer arms on large distances. Due to the finite speed of light, diffracting light pulses cannot interact simultaneously with both arms, inducing phase perturbations that compromise the accuracy of the sensor -- an effect that becomes progressively important as spatial separations increase. For a consistent framework, we develop a theory for finite-speed-of-light effects in atom interferometers alongside with other relativistic effects such as the mass defect. Our analysis shows that their magnitude depends crucially on the diffraction mechanism and the specific interferometer geometry. We demonstrate that the velocity of the atomic cloud at the mirror pulse of a Mach-Zehnder interferometer is less critical than the precise tuning of the lasers for resonant diffraction. Finally, we propose an experiment to test our predictions based on recoilless transitions and discuss mitigation strategies to reduce the bias in gravimetric applications.