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Laser Beam Shaping

Free-space local nonseparability dynamics of parabolic vector modes

Carmelo Rosales‐Guzmán, Xiaobo Hu, Valeria Rodríguez-Fajardo, Raúl I. Hernández-Aranda, Andrew Forbes, Benjamin Perez-García

Published Jul 30, 2021• 1 citation
Publisher

Abstract

It is well known that entanglement is invariant to local unitary transformations, this implies the degree of entanglement or non-separability remains constant during free-space propagation, which is true for both quantum and classically-entangled modes. Here we demonstrate an exception to this rule using a carefully engineered vectorial light field, and study its non-separability dynamics upon free-space propagation. We show that the local non-separability between the spatial and polarisation degrees of freedom dramatically decays to zero, while preserving the purity of the state and hence the global non-separability. We show this by numerical simulations and corroborate it experimentally. Our results evince novel properties of classically-entangled modes, point to the need for new measures of non-separability for such vectorial fields, while paving the way to novel applications for customised structured light.

DOI
10.1117/12.2603091

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It is well known that entanglement is invariant to local unitary transformations, this implies the degree of entanglement or non-separability remains constant during free-space propagation, which is true for both quantum and classically-entangled modes. Here we demonstrate an exception to this rule using a carefully engineered vectorial light field, and study its non-separability dynamics upon free-space propagation. We show that the local non-separability between the spatial and polarisation degrees of freedom dramatically decays to zero, while preserving the purity of the state and hence the global non-separability. We show this by numerical simulations and corroborate it experimentally. Our results evince novel properties of classically-entangled modes, point to the need for new measures of non-separability for such vectorial fields, while paving the way to novel applications for customised structured light.
One of the most prominent features of quantum entanglement is its invariability under local unitary transformations, which implies that the degree of entanglement or nonseparability remains constant during free-space propagation, true for both quantum and classically entangled modes. Here we demonstrate an exception to this rule using a carefully engineered vectorial light field, and we study its nonseparability dynamics upon free-space propagation. We show that the local nonseparability between the spatial and polarization degrees of freedom dramatically decays to zero while preserving the purity of the state and hence the global nonseparability. We show this by numerical simulations and corroborate it experimentally. Our results evince novel properties of classically entangled modes and point to the need for new measures of nonseparability for such vectorial fields, while paving the way for novel applications for customized structured light.
One of the most prominent features of quantum entanglement is its invariability under local unitary transformations, which implies the degree of entanglement remains constant during free-space propagation. While this is true for quantum and classically--entangled modes, here we demonstrate a novel type of classically-entangled modes that experience an entanglement decay upon free-space propagation. We show this by numerical simulations and corroborate experimentally. Our results evinces novel properties of classically-entangled modes, which pave the way to novel applications.
It is well known that the entanglement of a quantum state is invariant under local unitary transformations. This rule dictates, for example, that the entanglement of internal degrees of freedom of a photon remains invariant during free-space propagation. Here, we outline a scenario in which this paradigm does not hold. Using local Bell states engineered from classical vector vortex beams with non-separable degrees of freedom, the so-called classically entangled states, we demonstrate that the entanglement evolves during propagation, oscillating between maximally entangled (purely vector) and product states (purely scalar). We outline the spin-orbit interaction behind these novel propagation dynamics and confirm the results experimentally, demonstrating spin-orbit coupling in paraxial beams. This demonstration highlights a hitherto unnoticed property of classical entanglement and simultaneously offers a device for the on-demand delivery of vector states to targets, for example, for dynamic laser materials processing, switchable resolution within stimulated emission depletion (STED) systems, and a tractor beam for entanglement.
It is well known that the entanglement of a quantum state is invariant under local unitary transformations. It dictates, for example, that the degree of entanglement of a photon pair in a Bell state remains maximally entangled during propagation in free-space. Here we outline a scenario where this paradigm does not hold. Using local Bell states engineered from classical vector vortex beams with non-separable degrees of freedom, so-called classically entangled states, we demonstrate that the entanglement evolves during propagation, oscillating between maximally entangled (purely vector) and product states (purely scalar). We outline the theory behind these novel propagation dynamics and confirm the results experimentally. Crucially, our approach allows delivering a tunable degree of local entanglement to a distant receiver by simply altering a modal phase delay holographically, or, in essence, a tractor beam for entanglement. This demonstration highlights a hitherto unnoticed property of classical entanglement and offers at the same time a device for on-demand delivery of vector states to targets, e.g., for dynamic laser materials processing as well as switchable resolution within STED systems.
Nonseparability in classical and quantum states of light gives rise to the notions of classical (local) and quantum (nonlocal) entanglement, usually defined as global features of the fields and states. Here we use concurrence as a measure of this nonseparability and show that it can be spatially resolved, revealing regions of maximum nonseparability and regions with no nonseparability. We use the topical examples of vectorial structured light and its quantum analog, a hybrid spatial mode and polarization entangled states, to test the approach on both local and nonlocal forms of entanglement. Our work has wide reaching implications, for instance, in understanding the spatial dependence of coherence and polarization in vectorial light, as well as in quantum entangled states for imaging, where spatial correlations are vital.
One of the most captivating properties of diffraction-free optical fields is their ability to reconstruct upon propagation in the presence of an obstacle, both classically and in the quantum regime. Here we demonstrate that the local entanglement, or nonseparability, between the spatial and polarization degrees of freedom also experience self-healing. We measured and quantified the degree of nonseparability between the two degrees of freedom when propagating behind various obstructions, which were generated digitally. Experimental results show that even though the degree of nonseparability reduces after the obstruction, it recovers to its maximum value within the classical self-healing distance. To confirm our findings, we performed a Clauser-Horne-Shimony-Holt Bell-like inequality measurement, proving the self-reconstruction of nonseparability. These results indicate that local entanglement between internal degrees of freedom of a photon, can be recovered by suitable choice of the enveloping wave function.