Vector beam with spin-orbital non-separable coupling acts as classically entangled state with two degrees of freedom, here we generalize the ray-wave structured vectorially structured light to create multi-degree-of-freedom control towards high-dimensional classical entanglement.
Classically entangled light is used to refer to a class of structured beams with space-polarization, polarization-time, and space-time non-separable states akin to entangled states, which enable novel quantum-analog methods and applications in structured light. Here, we argue that classical entanglement is also available for pure scalar beams with multiple non-separable spatial degrees of freedom (DoFs). We theoretically and experimentally demonstrate a class of scalar ray-wave structured light with multiple controllable local DoFs to emulate multipartite entangled states, including the Greenberger-Horne-Zeilinger states. Our work unveils a rich parameter space for high-dimensional and multi-DoF control of structured light to extend applications in classical-quantum regimes.
Vectorially structured light has emerged as an enabling tool in many diverse applications, from communication to imaging, exploiting quantum-like correlations courtesy of a non-separable spatially varying polarization structure. Creating these states at the source remains challenging and is presently limited to two-dimensional vectorial states by customized lasers. Here we invoke ray-wave duality in a simple laser cavity to produce polarization marked multi-path modes that are non-separable in three degrees of freedom and in eight dimensions. As a topical example, we use our laser to produce the complete set of Greenberger-Horne-Zeilinger (GHZ) basis states, mimicking high-dimensional multi-partite entanglement with classical light, which we confirm by a new projection approach. We offer a complete theoretical framework for our laser based on SU(2) symmetry groups, revealing a rich parameter space for further exploitation. Our approach requires only a conventional laser with no special optical elements, is easily scaleable to higher dimensions, and offers a simple but elegant solution for at-the-source creation of classically entangled states of structured light, opening new applications in simulating and enhancing high-dimensional quantum systems.
Vector beams, non-separable in spatial mode and polarisation, have emerged as enabling tools in many diverse applications, from communication to imaging. This applicability has been achieved by sophisticated laser designs controlling the spin and orbital angular momentum, but so far is restricted to only two-dimensional states. Here we demonstrate the first vectorially structured light created and fully controlled in eight dimensions, a new state-of-the-art. We externally modulate our beam to control, for the first time, the complete set of classical Greenberger-Horne-Zeilinger (GHZ) states in paraxial structured light beams, in analogy with high-dimensional multi-partite quantum entangled states, and introduce a new tomography method to verify their fidelity. Our complete theoretical framework reveals a rich parameter space for further extending the dimensionality and degrees of freedom, opening new pathways for vectorially structured light in the classical and quantum regimes.
Structured light refers to the arbitrarily tailoring of optical fields in all their degrees of freedom (DoFs), from spatial to temporal. Although orbital angular momentum (OAM) is perhaps the most topical example, and celebrating 30 years since its connection to the spatial structure of light, control over other DoFs is slowly gaining traction, promising access to higher-dimensional forms of structured light. Nevertheless, harnessing these new DoFs in quantum and classical states remains challenging, with the toolkit still in its infancy. In this perspective, we discuss methods, challenges, and opportunities for the creation, detection, and control of multiple DoFs for higher-dimensional structured light. We present a roadmap for future development trends, from fundamental research to applications, concentrating on the potential for larger-capacity, higher-security information processing and communication, and beyond.
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.
Structured light has become topical of late, where controlling light in all its degrees of freedom has offered novel states of light long predicted, enhanced functionality in applications, and a modern toolbox for probing fundamental science. Structuring light as single photons and entangled states allows the spatial modes of light to be used to encode a large alphabet, accessing high dimensional Hilbert spaces for fundamental tests of quantum mechanics and improved quantum information processing tasks. In this tutorial, we outline the basic concepts of high dimensional quantum states expressed in a basis of spatial modes (structured light) and explain how to create, control, and detect such quantum states in the laboratory with a focus on transverse spatial modes such as the orbital angular momentum and pixel (position) modes. Finally, we highlight some example applications of such quantum structured light, from communications to imaging.