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arXiv:1510.04186 · Physical Review A

Gouy phase in nonclassical paths in a triple-slit interference experiment

I. G. da Paz, Carlos H. S. Vieira, R. Ducharme, Luís A. Cabral, H. Alexander, Marcos Sampaio

Published Mar 14, 2016• 15 citations
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Abstract

We propose a simple model to study the Gouy phase effect in the triple-slit experiment in which we consider a nonclassical path. The Gouy phase differs for classical and nonclassical paths as it depends on the propagation time. In this case the Gouy phase difference changes the Sorkin parameter $\ensuremath{\kappa}$ used to estimate the nonclassical path contribution in a nontrivial way, shedding some light on the implementation of experiments to detect nonclassical path contributions.

DOI
10.1103/physreva.93.033621

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We propose a simple model to study the Gouy phase effect in the triple-slit experiment in which we consider a nonclassical path. The Gouy phase differs for classical and nonclassical paths as it depends on the propagation time. In this case the Gouy phase difference changes the Sorkin parameter \ensuremathκ\ensuremath{\kappa}\ensuremathκ used to estimate the nonclassical path contribution in a nontrivial way, shedding some light on the implementation of experiments to detect nonclassical path contributions.
In which-way double-slit experiments with perfect detectors, it is assumed that having a second detector at the slits is redundant because it will not change the interference pattern. We, however, show that if higher-order or nonclassical paths are accounted for, the presence of the second detector will have an effect on the interference pattern. Accounting for these nonclassical paths also means that the Sorkin parameter in triple-slit experiments is only an approximate measure of Born-rule violation. Using the difference between single and double which-way detectors, we give an alternative parameter which is an exact measure of Born-rule violation.
We study the observation of exotic looped trajectories in double-slit experiments with matter waves. We consider the relative intensity at x=0x=0x=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 ∣κmax∣≈0.2|κ_{max}|\approx0.2∣κmax​∣≈0.2, which is the value of the fringe visibility.
In a double slit interference experiment, the wave function at the screen with both slits open is not exactly equal to the sum of the wave functions with the slits individually open one at a time. The three scenarios represent three different boundary conditions and as such, the superposition principle should not be applicable. However, most well-known text books in quantum mechanics implicitly and/or explicitly use this assumption that is only approximately true. In our present study, we have used the Feynman path integral formalism to quantify contributions from nonclassical paths in quantum interference experiments that provide a measurable deviation from a naive application of the superposition principle. A direct experimental demonstration for the existence of these nonclassical paths is difficult to present. We find that contributions from such paths can be significant and we propose simple three-slit interference experiments to directly confirm their existence.
We theoretically study the fringe visibility of exotic looped trajectories in double-slit experiments with matter waves. We consider the relative intensity at [Formula: see text] 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 with the contribution to the interference pattern given by exotic looped trajectories. We demonstrate that the Sorkin parameter is given in terms of this visibility and of the axial phases which include the Gouy phase. Thus, the effect of exotic looped trajectories can be attested by measuring deviations from unity for the fringe visibility. We show that the effect of exotic trajectories can be increased by adjusting the parameters of the double-slit apparatus in the Fresnel regime.
The Gouy phase is essential for accurately describing various wave phenomena, ranging from classical electromagnetic waves to matter waves and quantum optics. In this work, we employ phase-space methods based on the cross-Wigner transformation to analyze spatial and temporal interference in the evolution of matter waves characterized initially by a correlated Gaussian wave packet. First, we consider the cross-Wigner of the initial wave function with its free evolution, and second for the evolution through a double-slit arrangement. Different from the wave function which acquires a global Gouy phase, we find that the cross-Wigner acquires a Gouy phase difference due to different evolution times. The results suggest that temporal like-Gouy phase difference is important for an accurate description of temporal interference. Furthermore, we propose a technique based on the Wigner function to reconstruct the cross-Wigner from the spatial intensity interference term in a double-slit experiment with matter waves.
Type-I spontaneous parametric down-converted biphotons can be described approximately by a double-Gaussian wave function in configuration space. Using an effective propagator in the Fresnel approximation, the time evolution and transversal spreading of the two-particle biphoton wave function allow us to evaluate the Sorkin parameter $\ensuremath{\kappa}$, which results from nonclassical path contributions of the kink type and loops to double- and triple-slit interferometry. This simple unidimensional model for the evaluation of $\ensuremath{\kappa}$ predicts that kinked nonclassical paths may lead to $\ensuremath{\kappa}\ensuremath{\approx}{10}^{\ensuremath{-}5}$ for degenerate biphotons. We show that such a model reproduces well the Sorkin parameter for matter waves found in more involved approaches in the literature. Moreover, we establish a hierarchy of approximations based on the shape of the nonclassical paths for matter waves and compare their size with leading relativistic corrections to the propagator.