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Modern Physics Letters A

Fringe visibility of exotic trajectories for matter waves in a double-slit experiment

Carlos H. S. Vieira, H. A. S. Costa, Gustavo de Souza, Marcos Sampaio, I. G. da Paz

Published Jul 16, 2019• 5 citations
Publisher

Abstract

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.

DOI
10.1142/s021773231950233x

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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.
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.
The elements of reality coined by Einstein, Podolsky, and Rosen promoted a series of fundamental discussions involving the notion of quantum correlations and physical realism. The superposition principle applied in the double-slit experiment with matter waves highlights the need for a critical review of the adoption of physical realism in the quantum realm. In this work, we employ a measure of physical irrealism and consider an initial contractive state in the double-slit setup for which position and momentum variables of a single particle are initially correlated. We investigate how the behavior of the irrealism can help us to obtain information about the interference pattern, wavelike, and particlelike properties in the double-slit setup with matter waves. We find that there is a time of propagation that minimizes the irrealism, and around this point the state at the detection screen is squeezed in position and momentum in comparison with the standard Gaussian superposition. Interestingly, we show that the maximum visibility and the number of interference fringes are related to the minimum of the irrealism. Moreover, we demonstrate a monotonic relation between the irrealism and visibility around the time of minimum. Then, we argue how to use these results to indirectly measure the irrealism for position variable from the fringe visibility.
The validity of the superposition principle and of Born’s rule are well-accepted tenants of quantum mechanics. Surprisingly, it has been predicted that the intensity pattern formed in a three-slit experiment is seemingly in contradiction with the most conventional form of the superposition principle when exotic looped trajectories are taken into account. However, the probability of observing such paths is typically very small, thus rendering them extremely difficult to measure. Here we confirm the validity of Born’s rule and present the first experimental observation of exotic trajectories as additional paths for the light by directly measuring their contribution to the formation of optical interference fringes. We accomplish this by enhancing the electromagnetic near-fields in the vicinity of the slits through the excitation of surface plasmons. This process increases the probability of occurrence of these exotic trajectories, demonstrating that they are related to the near-field component of the photon’s wavefunction. Looped trajectories of photons in a three-slit interference experiment could modify the resulting intensity pattern, but they are experimentally hard to observe. Here the authors exploit surface plasmon excitations to increase their probability, measuring their contribution and confirming Born’s rule.
When individual particles pass through a double slit, a fringe pattern appears on a screen. If an observer detects the path of the particle, the interference fringes disappear. This is called the quantum decoherence. In this paper, we discuss a parameter estimation problem using the quantum decohenrece in the double-slit experiment. As a simple model, we consider a massive scalar field interacting with the particle which have passed through the double slit. The scalar field, as well as the observer, can induce the loss of the fringe pattern of the particle. Because the interference fringes of the particle depend on the field mass and coupling, we can estimate the field parameters from the fringes. For qualitative analysis, we introduce the interferometric visibility of the fringe pattern and the Fisher information (FI) matrix of the field mass and coupling. Using the fringe pattern observed on the distant screen, we derive a simple relation between the visibility and the FI matrix. Also if we focus on FI of the mass, then we find that FI characterizes the wave-particle duality in the double-slit experiment.
The double-slit experiment is a fundamental experiment in physical optics, currently regarded as a demonstration of the wave-like properties of microscopic particles. This is due to the pattern of alternating bright and dark fringes that appear on the screen as a result of the experiment. However, another characteristic of the double-slit fringe pattern—the nested fringes—has not been previously discussed. In this paper, the authors propose a novel theory of double-slit separation based on this feature and design a new double-slit experimental apparatus to conduct the experiment, allowing for the adjustment of the slit width during the process and thus observing the variation in the fringe pattern. The experiment reveals that the double-slit fringe pattern is actually a localized magnification at the center of the Single filament diffraction pattern, inheriting the nested feature of the Single filament diffraction fringes. A set of obstruction theories utilizing relativity is summarized to explain the double-slit experiment. This new discovery opens up a fresh direction for research into the double-slit experiment.
We propose a trajectory density formulation of the double-slit interference pattern that reproduces observed fringe intensities without wave superposition. The intensity at screen position x is the weighted density of particle trajectories arriving there, suppressed exponentially by the deflection cost in energy space: I(x) = V_{Trit}(KE) \times \sum_n w_n \cdot \delta\!\left(x - \frac{n\lambda L}{d}\right) \cdot e^{-k|n|} where k = dθ_eff/λ_dB is the coherence parameter set by the effective illumination semiangle θ_eff, and V_Trit(KE) = 2γβ/(1+γ²β²) is a new energy-dependent visibility factor from the Trit framework [1–3]. The parameter k connects to the effective source temperature through the emission physics: higher source temperature → larger emission area → larger θ_eff → larger k → fewer visible fringes. We test the formula against five independent experiments across five orders of magnitude in particle energy and three particle types. For thermionic and Schottky electron sources the formula outperforms standard QM by a factor of 2–6× in R². For cold FEG sources and C60 molecules the formula correctly reduces to QM (k → 0). The C60 result leads to a clean new distinction: V_Trit(KE) applies to elementary particles, where the energy space geometry directly governs wave-particle balance; for composite particles V_Trit = 1 and interference is from the centre-of-mass de Broglie wave. This difference is falsifiable: varying electron energy should reveal a visibility peak at KE = 211.66 keV; varying C60 velocity should show no such peak.