Gouy phase and visibility in the double-slit experiment

We study a matter wave double-slit experiment with unequal aperture widths in order to evaluate the effect of the Gouy phase on the visibility/predictability. While the predictability changes as one increases the width of one of the slits, the visibility receives a contribution from the Gouy phase at a specific point in the detection screen. Consequently such apparatus constitutes a simple device for measuring the Gouy phase of matter waves. We illustrate it numerically for neutrons.