Light carries both spin (polarization) and orbital angular momentum. Combining these degrees of freedom produces hybrid spin-orbit states that live in a high-dimensional Hilbert space, offering greater information capacity and robustness for optical communication, quantum technologies, and metrology. However, generating arbitrary states in these spaces and characterizing them efficiently has remained difficult. Here we show a compact metasurface that generates arbitrary spin-orbit states in a four-dimensional Hilbert space, visualized on a Poincaré hypersphere, with straightforward scalability to higher dimensions. Using a tetratomic unit cell, the single-layer device precisely controls complex amplitude, phase, and polarization. We further introduce an efficient interferometric scheme that reconstructs the full density matrix of any N-dimensional spin-orbit state using only three interferograms. This approach uncovers an intrinsic spin-orbit parity order that governs the symmetry of projected intensity patterns, independent of the weighting of the eigenmodes, and enables controlled mode transformations through higher-order geometric phases. These advances establish a versatile platform for high-dimensional photonic technologies.
Light carries both spin (polarization) and orbital angular momentum. Combining these degrees of freedom produces hybrid spin-orbit states that live in a high-dimensional Hilbert space, offering greater information capacity and robustness for optical communication, quantum technologies, and metrology. However, generating arbitrary states in these spaces and characterizing them efficiently has remained difficult. Here we show a compact metasurface that generates arbitrary spin-orbit states in a four-dimensional Hilbert space, visualized on a Poincaré hypersphere, with straightforward scalability to higher dimensions. Using a tetratomic unit cell, the single-layer device precisely controls complex amplitude, phase, and polarization. We further introduce an efficient interferometric scheme that reconstructs the full density matrix of any N-dimensional spin-orbit state using only three interferograms. This approach uncovers an intrinsic spin-orbit parity order that governs the symmetry of projected intensity patterns, independent of the weighting of the eigenmodes, and enables controlled mode transformations through higher-order geometric phases. These advances establish a versatile platform for high-dimensional photonic technologies.
High-dimensional photonic states have significantly advanced the fundamentals and applications of light. However, it remains huge challenges to quantify arbitrary states in high-dimensional Hilbert spaces with spin and orbital angular momentum bases. Here we introduce a geometric method to quantify arbitrary states in a 4D Hilbert space by interferometrically mapping them to unified centroid ellipses. Specifically, nine Stokes parameters can be deduced from three ellipses to quantify the 4D spin-orbit states described by SU(4) Poincaré hypersphere. We verify its feasibility by detecting these spin-orbit states gotten by both free-space wave plates and few-mode fibers. For the first time, we completely quantify and reconstruct higher-order modal group evolution of a weakly guiding few-mode fiber under twist perturbation. This geometric quantification, beyond the classical Stokes polarimetry, may pave the way to multi-dimensional optical metrology, sensing, and high-dimensional classical or quantum communications.
Twisted photons, carrying spin and orbital angular momentum (OAM) in an unbounded-dimensional Hilbert space, has recently sparked significant interest, leading to the discovery of new physics in both classical and quantum optics, furthering our understanding and incubating applications in classical and quantum communication. At the heart of this emerging field is the requirement for versatile, efficient, and robust generation of novel photonic spin-orbit states involving both spin and OAM degrees of freedom (DoFs). However, so far, the generation and manipulation of spin–orbit photons have primarily relied on free-space bulk optics, which, due to their lack of compactness and stability, are unsuitable for large-scale applications. In this work, we address this challenge by dynamically generating and manipulating the photonic spin-orbit states in both integrated microlaser and single photon source systems, leveraging non-Hermitian photonics and chiral quantum optics. We further investigated the generation and control of quantum entanglement between the spin and OAM DoFs of photons via integrated photonic circuits. Moreover, we successfully generated photonic spin-orbit states with intricate Skyrmionic topological structures and demonstrate the robustness of their topological properties during the quantum teleportation process. The integrated spin-orbit control toolbox for various structured photons, combined with the robustness of their topological properties, holds significant potential for developing large-channel capacity, noise-resilient information systems within a unique multidimensional space.
We propose a geometric hybrid Poincaré sphere (GHPS) as a unified geometrical framework for describing structured photon states with independently controllable spin angular momentum (SAM) and orbital angular momentum (OAM). Unlike the conventional higher-order Poincaré sphere, in which the SAM and OAM are intrinsically coupled through fixed basis states, the GHPS is constructed by defining its poles as direct products of arbitrary orthogonal bases on the Poincaré sphere (PS) and orbital Poincaré sphere (OPS) and by superposing these pole states. Using numerical simulations, we analyze representative GHPS states and show that the GHPS spherical coordinates govern the amplitude ratio and relative phase between the pole bases. This framework enables spatially inhomogeneous polarization distributions and intensity patterns, including nonseparable structures in which polarization and intensity are intrinsically intertwined, and provides a systematic state-space description for the coherent geometrical control of advanced structured light fields.
Abstract The hope for a futuristic global quantum internet that provides robust and high-capacity quantum information transfer lies largely on qudits, the fundamental quantum information carriers prepared in high-dimensional superposition states. However, preparing and manipulating N-dimensional flying qudits as well as subsequently establishing their entanglement are still challenging tasks, which require precise and simultaneous maneuver of 2 (N-1) parameters across multiple degrees of freedom. Here, using an integrated approach, we explore the synergy from two degrees of freedom of light, spatial mode and polarization, to generate, encode, and manipulate flying structured photons and their formed qudits in a four-dimensional Hilbert space with high quantum fidelity, intrinsically enabling enhanced noise resilience and higher quantum data rates. The four eigen spin–orbit modes of our qudits possess identical spatial–temporal characteristics in terms of intensity distribution and group velocity, thereby preserving long-haul coherence within the entirety of the quantum data transmission link. Judiciously leveraging the bi-photon entanglement, which is well preserved in the integrated manipulation process, we present versatile spin–orbit cluster states in an extensive dimensional Hilbert space. Such cluster states hold the promise for quantum error correction which can further bolster the channel robustness in long-range quantum communication.
The orbital angular momentum of photons, being defined in an infinite-dimensional discrete Hilbert space, offers a promising resource for high-dimensional quantum information protocols in quantum optics. The biggest obstacle to its wider use is presently represented by the limited set of tools available for its control and manipulation. Here, we introduce and test experimentally a series of simple optical schemes for the coherent transfer of quantum information from the polarization to the orbital angular momentum of single photons and vice versa. All our schemes exploit a newly developed optical device, the so-called "q-plate", which enables the manipulation of the photon orbital angular momentum driven by the polarization degree of freedom. By stacking several q-plates in a suitable sequence, one can also have access to higher-order angular momentum subspaces. In particular, we demonstrate the control of the orbital angular momentum m degree of freedom within the subspaces of |m| = 2h and |m| = 4h per photon.
Quantum skyrmions are topological structures that have garnered significant interest due to their demonstrated robustness and versatility across diverse optical platforms. However, existing approaches for their generation are limited to producing pre-determined two dimensional qubit states with a single topology. Here we create multi-dimensional topological states by introducing a non-local interaction between high-dimensional photonic entanglement and a metasurface, where the topological transformation induced by the metasurface is made non-deterministic by the probabilistic nature of the interfacing entangled state. Within this framework, we demonstrate that individual quantum states can host multiple co-existing topologies that are only revealed upon measurement, allowing for their parallel transport within distinct spatial mode channels. We confirm this by revealing the rich topological landscape within our modified Hilbert space while controlling the desired output topology by orbital angular momentum (OAM) projections on one of the entangled photons, producing multiple non-local polarization-OAM entangled states characterized by distinct topological classes, all from a single metasurface device. Our results reveal new capability when structured high-dimensional entanglement is interfaced with structured matter capable of coupling photonic degrees of freedom, establishing a new pathway for the compact generation of complex quantum states.