Experimental proposal for measuring the Gouy phase of matter waves

TL;DR

This paper proposes an experiment using Ramsey interferometry with Rydberg atoms to measure the Gouy phase of matter waves, which could enable new quantum information processing techniques.

Contribution

It introduces a feasible experimental method to directly measure the Gouy phase of matter waves using atomic interferometry.

Findings

The proposed experiment can accurately determine the Gouy phase.

Experimental limitations are manageable with current technology.

Measuring the Gouy phase enables new quantum state manipulations.

Abstract

The Schr\"odinger equation for an atomic beam predicts that it must have a phase anomaly near the beam waist analogous to the Gouy phase of an electromagnetic beam. We propose here a feasible experiment which allows for the direct determination of this anomalous phase using Ramsey interferometry with Rydberg atoms. Possible experimental limitations are discussed and shown to be completely under control within the present day technology. We also discuss how this finding can open the possibility to use the spatial mode wavefunctions of atoms as q-dits, since the Gouy phase is an essential ingredient for making rotations in the quantum states.