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Physica Scripta

Non-locality and geometric potential provide the phenomenology of the double-hole single massive particle and light interference

Román Castañeda, Pablo Bedoya-Ríos, Gioṙgio Matteucci

Published Nov 30, 2021• 13 citations

Abstract

Abstract In spite of its accurate prediction of the experimental outcomes of double-hole single particle interference, quantum mechanics does not provide a phenomenological description of the individual realizations of the experiment. By defining a non-locality function and considering the non-paraxial solution of the time-independent Schrödinger equation by the Green’s theorem, we introduce a geometrical potential which leads to an outstanding result. The geometric potential allows the description of spatially structured Lorentzian wells in the volume between the double-hole mask and the detector. The buildup of the interference patterns results from the confined propagation of single particles through these Lorentzian wells. The phenomenological implications of this description are discussed and illustrated by numerical examples, and its compatibility with quantum mechanical predictions is also shown. A further, non-trivial advantage of this model over the conventional formalism, is that the present quantum probability density can be exactly calculated both in the near and far field conditions.

DOI: 10.1088/1402-4896/ac3ea5

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Abstract In spite of its accurate prediction of the experimental outcomes of double-hole single particle interference, quantum mechanics does not provide a phenomenological description of the individual realizations of the experiment. By defining a non-locality function and considering the non-paraxial solution of the time-independent Schrödinger equation by the Green’s theorem, we introduce a geometrical potential which leads to an outstanding result. The geometric potential allows the description of spatially structured Lorentzian wells in the volume between the double-hole mask and the detector. The buildup of the interference patterns results from the confined propagation of single particles through these Lorentzian wells. The phenomenological implications of this description are discussed and illustrated by numerical examples, and its compatibility with quantum mechanical predictions is also shown. A further, non-trivial advantage of this model over the conventional formalism, is that the present quantum probability density can be exactly calculated both in the near and far field conditions.

The wave superposition is considered the phenomenological principle of light interference, as well as an accurate procedure to calculate the quantum probability of the buildup of single matter particle interference patterns.However, it cannot provide a unified phenomenological framework to explain both types of interference.In this paper, a unified framework is proposed which leads to a unique principle for interference of both light waves and single matter particles.It is shown that the term interference denotes the confinement of the light irradiance or the single matter particles in spatially structured Lorentzian wells, due to the geometric potential determined by the prepared non-locality at the mask plane.This new description does not resort to the assumption of wave superposition, so that the setup configuration plays the main role.

Abstract Non-paraxial interference has recently been explained as light energy confinement in spatially structured Lorentzian wells. This theory describes, in the same way, single particle interference in ordinary space too. Such an alternative thought is discussed here in the framework of a quantum formalism, which introduces confinement operators and density matrices of space states for the first time. Therefore, Lorentzian wells are characterized as the base states of space, which are excited by the geometric potential to produce interference. Geometrical uncertainty and space entanglement are discussed as novel features that approach the proposed theory in the quantum context. This formalism provides insight into the role of space in interference.

An exact and exhaustive phenomenology of interference in ordinary space describes it in terms of confinement in geometric states of space. Under high prepared non-locality, such space states exhibit spatial entanglement, a behavior not reported in the standard interference formalism of optics and quantum mechanics. In this paper, the fundamental theoretical features of the spatial entanglement of geometric states of space are discussed and illustrated with numerical simulations of non-paraxial Young interference.

Recently, the novel confinement principle in spatially-structured Lorentzian wells was reported to describe in a unified way the interference of classical waves and singular quantum particles in a causal framework in ordinary space. The phenomenology derived from this principle offers significant advantages over the conventional classical and quantum formalisms of interference founded on wave superposition. This paper presents a conceptual analysis of such a principle and its main implications indicating its fundamental differences from the standard descriptions.

Non-paraxial interference in ordinary space has been described as the confinement of light, photons, and matter particles in geometric states of space, which are realized as spatially structured Lorentzian wells in the setup volume. Michelson interference is discussed in this framework by regarding the space states dependence from lengths of interferometer arms. It is optically equivalent to considering the space state vertices distributed in a three-dimensional region before the detector plane. This description is potentially relevant in devices where light comes from three-dimensional distributions of points, for instance, the outputs of waveguide arrays in optical or integrated photonics elements.

A new type of indetermination is discussed in the framework of the exact (non-paraxial) and generalized description of interference in ordinary space for light, photons and matter particles. This description is based on the novel phenomenological principle of confinement in geometric states of space. It is shown that space states with vertices within a sphere of diameter no greater than a fixed value must be ground states of space, which can be represented by a single ground state with vertex at any point of this sphere. This geometric uncertainty differs from Heisenberg's uncertainty which was established for matter particles and deals with dynamical quantities. However, it is shown that geometric uncertainty establishes limitations for Heisenberg's uncertainty.