Indirect evidence for the Gouy phase for matter waves

TL;DR

This paper demonstrates that the Gouy phase, a geometric phase known in optics, also exists for matter waves in vacuum, linked to the Schrödinger-Robertson uncertainty principle, with experimental support from fullerene diffraction.

Contribution

It introduces the concept of the Gouy phase for matter waves and connects it to the covariance matrix and uncertainty principle, supported by recent diffraction experiments.

Findings

Gouy phase can be defined for matter waves in vacuum.

The physics of matter wave Gouy phase relates to the Schrödinger-Robertson uncertainty principle.

Experimental data from fullerene diffraction supports the existence of matter wave Gouy phase.

Abstract

We show that the well known geometric phase, the Gouy phase in optics can be defined for matter waves in vacuum as well. In particular we show that the underlying physics for the "matter waves" Gouy phase is the generalized Schroedinger-Robertson uncertainty principle, more specifically, the off diagonal elements of the covariance matrix. Recent experiments involving the diffraction of fullerene molecules and the uncertainty principle are shown to be quantitatively consistent with the existence of a Gouy phase for matter waves.