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arXiv:2004.13773 · Physical Review A

Irrealism from fringe visibility in matter-wave double-slit interference with initial contractive states

Fabrício Lustosa, Pedro R. Dieguez, I. G. da Paz

Published Nov 4, 2020• 20 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physreva.102.052205

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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 elements of reality coined by Einstein, Podoslky, and Rosen (EPR) 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. By using a measure of realism, in this work, we use for the first time quantum correlations of noncommuting observables of a single particle to extract information about the behavior of a quantum system. We investigate the role of single particle position-momentum correlations for the degree of irrealism, the interference pattern, wavelike, and particle-like properties in the double-slit setup with matter waves. We find that there is a time of propagation which minimizes position-momentum correlations and this also generates a minimum in the irrealism. Curiously, we show that the maximum number of interference fringes is related with the minimum of the position-momentum correlations and irrealism.
The double-slit experiment has stood for a century as the paradigmatic demonstration of quantum superposition: the standard interpretation holds that a particle passes through both slits simultaneously, existing in a superposition of two spatially separated states. This paper proposes a physically distinct alternative: the particle's matter wave — a real physical wave propagating through space in accordance with de Broglie's relation λ = h/p — passes through both slits, while the particle itself (matter) remains in an undetermined state until a constructive interference maximum is formed at the detection screen. The particle does not simultaneously occupy two locations; the wave does. This distinction eliminates the need for superposition as an ontological commitment while fully reproducing the observed interference pattern. We further show that the disappearance of the interference pattern upon which-path measurement is explained without invoking wavefunction collapse: the measurement interaction redirects the matter wave to a single-slit geometry, eliminating the two-wave interference condition. Three experimentally testable predictions distinguish this framework from the standard interpretation: (1) weak-measurement trajectory reconstruction should reveal single particle paths inconsistent with simultaneous two-slit passage; (2) diffraction fringe spacing should depend on the mass density of the slit material, because denser slit edges generate a steeper refractive-index gradient for the matter wave; (3) the fringe pattern should exhibit a density-dependent phase shift measurable with current matter-wave interferometry technology. This reinterpretation requires no new mathematical formalism — the Schrödinger equation and Born's rule are retained — but replaces the ontological claim of simultaneous multi-location existence with the physically consistent picture of matter-wave propagation through an undetermined-state particle.
The debate instigated by the seminal works of Einstein, Podolsky, Rosen, and Bell put the notions of realism and nonlocality at the core of almost all philosophical and physical discussions underlying the foundations of quantum mechanics. However, while experimental criteria and quantifiers are by now well established for nonlocality, there is no clear quantitative measure for the degree of reality associated with continuous variables such as position and momentum. This work aims at filling this gap. Considering position and momentum as effectively discrete observables, we implement an operational notion of projective measurement and, from that, a criterion of reality for theses quantities. Then we introduce a quantifier for the degree of irreality of a discretized continuous variable which, when applied to the conjugated pair position-momentum, is shown to obey an uncertainty relation, meaning that quantum mechanics prevents classical realism for conjugated quantities. As an application of our formalism, we study the emergence of elements of reality in an instance where a Gaussian state is submitted to the dissipative dynamics implied by the Caldirola-Kanai Hamiltonian. In particular, at equilibrium, we make some links with the measurement problem and identify aspects that can be taken as the quantum counterpart for the notion of rest.
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 slowing of the decoherence effect in the double-slit experiment by considering an initially correlated Gaussian state. The effects of the decoherence are included in a specific propagator which we use to obtain the density matrix at the detection screen. We calculate the uncertainties in the position and momentum for the density matrix as a function of the decoherence at the detection screen. We show that for a contractive initial state and specific times of propagation the state at the detection screen is squeezed in position in comparison with the standard Gaussian superposition. For this squeezed Gaussian superposition state, we observe that the fringe visibility is more robust to the decoherence in comparison with the standard Gaussian superposition. Then, we calculate the negativity of the Wigner function and study its behavior as a function of the decoherence and correlation parameters at the detection screen. We observe that the negativity decreases more slowly for the squeezed Gaussian superposition.
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.