Local Measurement Scheme of Gravitational Curvature using Atom Interferometers

TL;DR

This paper introduces a measurement scheme using co-located atom interferometers to accurately determine gravitational curvature, crucial for advanced gravitational experiments and calibration.

Contribution

The authors propose a novel differential measurement method with a well-controlled scale factor to infer gravitational curvature from atom interferometry signals.

Findings

Numerical simulation confirms robustness of phase shift in complex gravitational fields.

Defined an estimator for gravitational curvature in non-trivial fields.

Analyzed trade-offs between signal strength and estimation accuracy.

Abstract

Light pulse atom interferometers (AIFs) are exquisite quantum probes of spatial inhomogeneity and gravitational curvature. Moreover, detailed measurement and calibration are necessary prerequisites for very-long-baseline atom interferometry (VLBAI). Here we present a method in which the differential signal of two co-located interferometers singles out a phase shift proportional to the curvature of the gravitational potential. The scale factor depends only on well controlled quantities, namely the photon wave number, the interferometer time and the atomic recoil, which allows the curvature to be accurately inferred from a measured phase. As a case study, we numerically simulate such a co-located gradiometric interferometer in the context of the Hannover VLBAI facility and prove the robustness of the phase shift in gravitational fields with complex spatial dependence. We define an estimator of the gravitational curvature for non-trivial gravitational fields and calculate the trade-off between signal strength and estimation accuracy with regard to spatial resolution. As a perspective, we discuss the case of a time-dependent gravitational field and corresponding measurement strategies.