⚛️ quantum physics

Quantum skyrmion parallelism via metasurface-tailored high-dimensional entanglement

This paper demonstrates a method for generating multi-dimensional quantum skyrmions with multiple co-existing topologies by interfacing high-dimensional photonic entanglement with a metasurface, enabling the parallel transport of distinct topological states within a single compact device.

Original authors: Pedro Ornelas, Ramona Bedford, Fazilah Nothlawala, Chi Li, Haoyi Yu, Isaac Nape, Stefan A. Maier, Haoran Ren, Andrew Forbes

Published 2026-08-27

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CC BY 4.0

Original authors: Pedro Ornelas, Ramona Bedford, Fazilah Nothlawala, Chi Li, Haoyi Yu, Isaac Nape, Stefan A. Maier, Haoran Ren, Andrew Forbes

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

In the vast landscape of modern physics, light is often treated not just as a beam that illuminates a room, but as a carrier of intricate information. Scientists have long known that light possesses a property called spin, which relates to its polarization, or the direction in which its waves vibrate. They have also discovered that light can twist as it travels, carrying a form of angular momentum known as orbital angular momentum. When these two properties are linked together in a specific way, they can create a topological structure, a shape in the light's field that is robust and difficult to destroy, much like a knot in a rope that cannot be untied without cutting the rope itself. These structures, called skyrmions, have become a subject of intense interest because their resilience makes them ideal candidates for storing vast amounts of data or transmitting information through noisy environments. For years, researchers have been able to create these skyrmions using flat, engineered surfaces called metasurfaces, but there was a significant limitation: each surface could only produce one specific type of skyrmion at a time, determined by how the light entered it. This meant that to get a different shape, one had to build a new device or change the entire setup, restricting the amount of information that could be packed into a single beam of light.

A team of researchers has now broken this limitation by combining the power of quantum entanglement with these flat optical surfaces. In their work, they generated pairs of photons that were linked in a high-dimensional way, meaning their properties were correlated across a wide range of possibilities rather than just two simple states. They sent one photon from each pair through a specially designed metasurface that could twist the light's polarization and orbital momentum simultaneously. Because the photon entering the surface was part of an entangled pair, its exact state was not fixed until it was measured. This uncertainty allowed the single metasurface to act on all possible input states at once, effectively creating a superposition of many different skyrmion shapes within a single quantum state. The researchers demonstrated that by measuring the partner photon in a specific way, they could reveal which of these many co-existing topological structures was present. They showed that a single device could host multiple distinct skyrmions, each with its own unique topological number, effectively turning one surface into a parallel generator of complex quantum states.

The experiment began with a process that created pairs of entangled photons, where the orbital angular momentum of one photon was perfectly balanced by the opposite momentum of its partner. One of these photons was directed through a metasurface made of tiny silicon pillars, which acted as a J-plate to couple the photon's polarization with its orbital angular momentum. This interaction transformed the photon into a hybrid state where its spin and orbital motion were inextricably linked. Because the photon was entangled with its partner, the transformation applied by the metasurface was not limited to a single outcome. Instead, the system existed in a state where multiple topological configurations were present simultaneously, each correlated with a different orbital angular momentum value of the partner photon. The researchers found that by projecting the partner photon onto a specific orbital angular momentum state, they could select and reveal a particular skyrmion from this hidden landscape. They measured the resulting states and confirmed that they possessed the expected topological numbers, which describe how many times the light's field wraps around itself in space.

The team further explored the capabilities of this method by testing different configurations of the metasurface and the measurement settings. They successfully generated skyrmions with various topological numbers, including values of approximately one, two, and five, as well as their negative counterparts. In one set of experiments, they demonstrated that a single metasurface could produce three distinct topological states at the same time. By measuring the partner photon in three different ways, they could reveal each of these states individually, showing that the device was capable of parallel processing of topological information. They also pushed the boundaries further by projecting the partner photon onto a superposition of orbital angular momentum states, rather than a single state. This approach allowed them to create even more complex and exotic topological structures, revealing a richer landscape of shapes that included nested skyrmions and saddle-like features. These complex structures were not achievable with traditional methods using single photons or classical light beams, highlighting the unique advantage of using high-dimensional entanglement.

The results of this study confirm that it is possible to generate multiple, co-existing quantum skyrmions using a single passive device. The researchers measured the fidelity of these states, finding values around 0.77 to 0.87, which indicates a high degree of accuracy in the creation of the intended topological structures. They also calculated the topological numbers for the generated states, with measured values such as 0.97, 1.99, and 4.99, closely matching the theoretical predictions. The ability to switch between these different topologies simply by changing the measurement on the partner photon, without altering the physical device, represents a significant step forward in the field. It suggests a new pathway for creating compact systems that can handle complex quantum information, potentially leading to more robust methods for quantum communication and information processing. By interfacing structured entangled photons with structured matter, the researchers have established a new capability to enhance the topological information capacity of light, moving beyond the constraints of single-state generation and opening the door to multi-channel topological networks.

Technical Summary: Quantum Skyrmion Parallelism via Metasurface-Tailored High-Dimensional Entanglement

Problem Statement
Optical skyrmions, which are topologically non-trivial field configurations, have shown promise for robust information storage and communication due to their resilience in noisy environments. While recent advances in metasurfaces have enabled the compact generation of classical and quantum skyrmions, existing approaches face a fundamental limitation: they typically produce a single, pre-determined two-dimensional qubit state with a singular topological configuration at a time. This restricts the topological information capacity and prevents the parallel generation of diverse topological states using a single device. Furthermore, the generation of non-local skyrmionic states in the quantum regime using metasurfaces remains largely unexplored.

Methodology
The authors propose and experimentally demonstrate a scheme that overcomes these limitations by interfacing high-dimensional biphoton entanglement with a metasurface. The core methodology involves the following steps:

State Generation: A high-dimensional orbital angular momentum (OAM)-OAM entangled biphoton state ( $|\Psi\rangle_{AB}$ ) is generated via spontaneous parametric down-conversion (SPDC). The state is expressed as a superposition of OAM modes where the photons are anti-correlated ( $| \ell \rangle_A | -\ell \rangle_B$ ).
Metasurface Interaction: One photon (Photon A) is passed through a custom-designed "J-plate" metasurface. This metasurface decouples orthogonal polarization states and imparts distinct topological charges ( $m$ and $n$ ) to the horizontal ( $H$ ) and vertical ( $V$ ) polarization components, respectively. It also applies a linear phase gradient to separate the modulated field from zero-order light.
Non-Deterministic Transformation: The interaction transforms the initial state into a multi-dimensional hybrid state where the topological transformation is non-deterministic, governed by the probabilistic nature of the entangled state. The resulting state is a superposition of two high-dimensional states, each labeled by an orthogonal polarization of Photon A and shifted in OAM by $m$ and $n$ .
Parallel Topology Extraction: By performing OAM projections on Photon A (using a spatial light modulator and single-mode fiber), the system collapses into specific 2D hybrid states. Crucially, because the OAM of Photon A was unknown prior to measurement, the metasurface effectively acted on all input OAM modes in parallel. This allows distinct topological states, each correlated with a specific OAM mode, to coexist within the single quantum state.
Characterization: The researchers perform joint polarization and OAM projections on both photons to reconstruct the density matrix and calculate the quantum Stokes vector field. They quantify the topology using the Skyrmion number ( $N$ ), derived from the wrapping of the Poincaré sphere.

Key Contributions

Parallel Topological Generation: The work demonstrates that a single passive metasurface can generate multiple co-existing quantum topologies simultaneously. These topologies are embedded within the correlations of a single high-dimensional entangled state and are revealed only upon measurement.
High-Dimensional Enhancement: By leveraging high-dimensional entanglement, the authors show that the topological information capacity is enhanced beyond what is possible with single photons or coherent beams. The scheme shifts the complexity from state-generation optics to post-selection optics.
Tunability and Diversity: The authors demonstrate control over the output topology by varying the metasurface parameters ( $m, n$ ) and the projection basis. They successfully generated states with distinct topological numbers ( $N$ ) ranging from approximately $\pm 1$ to $\pm 5$ , as well as complex, nested topological structures.
Superposition Projections: The study extends beyond single OAM basis projections to arbitrary spatial mode bases (superpositions of OAM modes), revealing "exotic" topological structures, such as nested skyrmions and saddle-like features, which are not accessible through single-mode projections.

Results

Single Topology Control: Using a J-plate with parameters $(m, n) = (0, 1)$ , the team generated a quantum skyrmion with a measured topological number of $N = 0.97 \pm 0.25$ , confirming the first metasurface-generated quantum skyrmion.
Multiple Topological Classes: By varying $(m, n)$ to include values such as $(0, \pm 1), (0, \pm 2),$ and $(0, \pm 5)$ , the authors produced states belonging to six distinct topological classes with measured $N$ values of $\{-4.99, -1.99, -0.98, 0.97, 1.99, 4.99\}$ .
Polarity Flipping: Projecting Photon A onto different OAM modes (e.g., $|-1\rangle_A$ vs $|0\rangle_A$ ) with a fixed metasurface $(0, 1)$ resulted in a flip in the polarity of the topological state, changing $N$ from positive to negative.
Multi-Topology Coexistence: When projecting onto specific OAM modes with a metasurface $(0, 2)$ , the authors measured three distinct topological numbers ( $N \approx 0, \pm 2$ ) from the same initial state, demonstrating the simultaneous existence of multiple topologies.
Complex Structures: Projections onto superposition states (e.g., $|1\rangle_A + |3\rangle_A$ ) yielded complex topological numbers (e.g., $N \approx -2.87$ ) arising from nested structures, including Bloch-type and Néel-type skyrmions embedded within larger topological fields.

Significance and Claims
The paper claims to establish a new pathway for the compact generation of complex quantum states. By interfacing structured high-dimensional entanglement with structured matter (metasurfaces), the authors demonstrate a capability to directly enhance topological information capacity. The work suggests that this approach enables the creation of multi-channel topological networks where distinct topological states can be transported in parallel within distinct spatial mode channels.

The authors position this as a step toward robust, high-dimensional quantum communication and information processing. They note that while their experiment used separate components (nonlinear crystal and metasurface), the framework is compatible with future integration into ultra-compact platforms, such as lithium niobate non-local metasurfaces, which could generate these states directly at the source. The study emphasizes that the "parallelism" offered by high-dimensional entanglement breaks the bottleneck of single-topology generation, allowing for a richer, previously hidden topological landscape to be accessed and utilized.

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