Can a Matter-Wave Interferometer Detect Translational Speed?

TL;DR

This paper explores whether matter-wave interferometers can detect translational speeds by deriving a phase difference expression analogous to the Sagnac effect, suggesting potential for high-sensitivity speed measurement and implications for a preferred reference frame.

Contribution

It derives a phase difference formula for matter-wave interferometers under translation, proposing experimental setups to detect translational speeds and discussing implications for reference frames.

Findings

Derived phase difference formula for matter waves under translation

Proposed experimental configurations for detecting translational speed

Indicated potential for high-sensitivity speed measurement

Abstract

Based only on the Galilean addition of velocities and the de Broglie relation, it is deduced that in a matter-wave interferometer with slow-speed particles, a moving segment of deltaL with a velocity V contributes deltaPhi = (2Pi/vlamda)VdotdeltaL to the total phase difference of the interferometer, where v is the speed of the particles and lamda is the wavelength.. This expression is exactly the same as the generalized Sagnac effect for light waves found by experiments except that v is replaced by c. For a rotational motion, it leads to the Sagnac effect. Additionally, the scientific value of this relationship is also to explore the possibility of detecting translation speeds by a matter-wave interferometer. Two configurations of the experimental setup have been indicated and the key element is that the paths of the interfering beams constitute a loop with an opening. If the possibility is confirmed by experiments, the conclusions will be that there is a preferred reference frame for matter waves and a speedometer with a very high sensitivity is possible.