  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.
