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National Meeting on Optics and Andean and Caribbean Conference on Optics and its Applications (ENO-CANCOA)

Spatial Entanglement of Geometric States of Ordinary Space in Non-paraxial Inteference

Samuel Huertas, Daniel Peláez, Valentina López, Laura Bravo, Román Castañeda

Published Jun 12, 2024• 0 citations
Publisher

Abstract

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.

DOI
10.1109/eno-cancoa61307.2024.10751559

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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.
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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.
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.
In this article, a novel meaning for the notion of uncertainty is discussed, within the framework of the non-paraxial interference theory based on confinement in geometric states of space. This novel meaning refers to the fact that, for any set of space states whose vertices are distributed in an arbitrary array of size less than λ 10, both the excitation provided by the geometric potential and the positions of the vertices of the states are completely uncertain, such that the complete set is represented by the Lorentzian well of an individual ground state of space, with vertex at any of the points of the array, even if the set is under the maximum prepared non-locality (i.e., under a strong geometric potential). It is shown that the geometric uncertainty is different but compatible with the Heisenberg uncertainty principle. In fact, geometrical uncertainty establishes both the upper limit of momentum uncertainty and the lower limit of position uncertainty in the Heisenberg principle.
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