Differing Calculations of the Response of Matter-wave Interferometers to Gravitational Waves

TL;DR

This paper compares two different theoretical expressions for matter-wave interferometer phase shifts caused by gravitational waves, concluding that the geodesic deviation approach is correct at low frequencies.

Contribution

It clarifies which of the two existing formulas for gravitational wave-induced phase shifts in matter-wave interferometers is physically accurate.

Findings

The geodesic deviation-based phase shift matches expected low-frequency behavior.

The geodesic equation of motion-based phase shift is shown to be incorrect in this context.

The comparison highlights fundamental differences in the physics underlying the two approaches.

Abstract

There now exists in the literature two different expressions for the phase shift of a matter-wave interferometer caused by the passage of a gravitation wave. The first, a commonly accepted expression that was first derived in the 1970s, is based on the traditional geodesic equation of motion (EOM) for a test particle. The second, a more recently derived expression, is based on the geodesic deviation EOM. The power-law dependence on the frequency of the gravitational wave for both expressions for the phase shift is different, which indicates fundamental differences in the physics on which these calculations are based. Here we compare the two approaches by presenting a series of side-by-side calculations of the phase shift for one specific matter-wave-interferometer configuration that uses atoms as the interfering particle. By looking at the low-frequency limit of the different expressions for the phase shift obtained, we find that the phase shift calculated via the geodesic deviation EOM is correct, and the ones calculated via the geodesic EOM are not.