# Exotic looped trajectories in double-slit experiments with matter waves

## TL;DR

This paper investigates how exotic looped trajectories influence matter wave interference in double-slit experiments, linking the Sorkin parameter to measurable fringe visibility and demonstrating how experimental adjustments can enhance these effects.

## Contribution

It introduces a method to quantify exotic looped trajectories using fringe visibility and the Sorkin parameter, providing practical ways to observe these effects in matter wave experiments.

## Key findings

- Maximum Sorkin parameter of about 0.2 for neutron interferometry.
- Exotic looped trajectories can be amplified by adjusting experimental parameters.
- The Sorkin parameter relates to fringe visibility and axial phases including Gouy phase.

## Abstract

We study the observation of exotic looped trajectories in double-slit experiments with matter waves. We consider the relative intensity at $x=0$ as a function of the time-of-flight from the double-slit to the screen inside the interferometer. This allows us to define a fringe visibility associated to the contribution to the interference pattern given by exotic lopped trajectories. We demonstrate that the Sorkin parameter is given in terms of this visibility and of the axial phases which include the Gouy phase. We verify how this parameter can be obtained by measuring the relative intensity at the screen. We show that the effect of exotic looped trajectories can be significantly increased by simply adjusting the parameters of the double-slit apparatus. Applying our results to the case of neutron interferometry, we obtain a maximum Sorkin parameter of the order of $|\kappa_{max}|\approx0.2$, which is the value of the fringe visibility.