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arXiv:1902.07988 · Physical Review A

Basis-independent tomography and nonseparability witnesses of pure complex vectorial light fields by Stokes projections

Adam Selyem, Carmelo Rosales‐Guzmán, Sarah Croke, Andrew Forbes, Sonja Franke‐Arnold

Published Dec 23, 2019• 85 citations
arXivHTMLPDF

Abstract

Complex vectorial light fields, nonseparable in their polarization and spatial degree of freedom, are of relevance in a wide variety of research areas encompassing microscopy, metrology, communication, and topological studies. Controversially, they have been suggested as analogs to quantum entanglement, raising fundamental questions on the relation between nonseparability in classical systems, and entanglement in quantum systems. We perform basis-independent tomography of arbitrary pure vectorial light fields using spatially resolved Stokes projections. Moreover, we propose and demonstrate that concurrence, as a nonseparability witness for any pure vectorial light field, can be extracted from global Stokes projections, without assessing the spatial degree of freedom.

DOI
10.1103/physreva.100.063842

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Complex vectorial light fields, nonseparable in their polarization and spatial degree of freedom, are of relevance in a wide variety of research areas encompassing microscopy, metrology, communication, and topological studies. Controversially, they have been suggested as analogs to quantum entanglement, raising fundamental questions on the relation between nonseparability in classical systems, and entanglement in quantum systems. We perform basis-independent tomography of arbitrary pure vectorial light fields using spatially resolved Stokes projections. Moreover, we propose and demonstrate that concurrence, as a nonseparability witness for any pure vectorial light field, can be extracted from global Stokes projections, without assessing the spatial degree of freedom.
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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.
As structured optical fields with spatially inhomogeneous polarization distributions, vector beams have attracted widespread attention for their great applications across multiple fields. The coupling between spatial modes and polarization states in vector beams results in nonseparability analogous to quantum entangled states, referred to as classical entanglement. This concept has garnered considerable scholarly interest, due to its capacity to facilitate quantum-inspired approaches for the characterization of vector optical fields, leading to noteworthy applications such as metrological sensing, communication encryption, and quantum computing. However, most investigations concerning classical entanglement have focused on vector optical fields within the spatial domain, while the classical entanglement characteristics of ultrafast vector beam pulses in the temporal domain remain to be revealed. Here, we investigate the classical local entanglement of ultrafast vector beam pulses in the temporal domain. Through theoretical interpretation and experimental verification, time-varying nonseparability has been demonstrated throughout the pulse duration. The dynamic evolution of spatially vectorial polarization states on femtosecond timescales was measured. The temporal evolution of the classical entanglement and the associated density matrix were analyzed using quantum state tomography. This research provides, to our knowledge, novel perspectives for investigating quantum-classical optical analogies in the temporal domain, advancing deeper fundamental understanding of entanglement.
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.
We present an experimental proof-of-principle for the generation and detection of pure two-qubit states that have been encoded in degrees of freedom that are common to both classical-light beams and single photons. Our protocol requires performing polarization tomography on a single qubit from a qubit pair. The degree of entanglement in the qubit pair is measured by concurrence, which can be directly extracted from intensity measurements-or photon counting-entering single-qubit polarization tomography.
Light beams having a vectorial field structure, or polarization, that varies over the transverse profile and a central optical singularity are called vector vortex (VV) beams and may exhibit specific properties such as focusing into ``light needles'' or rotation invariance. VV beams have already found applications in areas ranging from microscopy to metrology, optical trapping, nano-optics, and quantum communication. Individual photons in such beams exhibit a form of single-particle quantum entanglement between different degrees of freedom. On the other hand, the quantum states of two photons can be also entangled with each other. Here, we combine these two concepts and demonstrate the generation of quantum entanglement between two photons that are both in VV states: a form of entanglement between two complex vectorial fields. This result may lead to quantum-enhanced applications of VV beams as well as to quantum information protocols fully exploiting the vectorial features of light.