Nanophotonic Systems Generate Hyperentanglement with Discrete Rotational Symmetry for High-Dimensional Hilbert Space Preservation

Quantum communication relies on creating and manipulating entangled particles, and researchers continually seek methods to enhance the amount of information these entangled states can carry. Lior Fridman, Amit Kam, and Amir Sivan, all from the Technion, Israel Institute of Technology, alongside Guy Sayer, Stav Lotan, and Guy Bartal, demonstrate a new approach to generating hyperentanglement, a powerful form of entanglement that utilises multiple degrees of freedom simultaneously. Their work focuses on nanophotonic systems with unique polygonal shapes, which allow them to create a finite set of near-field modes and preserve a high-dimensional space for encoding quantum information. This breakthrough overcomes limitations found in traditional, rotationally symmetric systems, and establishes a promising pathway towards expanding the capacity of on-chip quantum communication networks by efficiently utilising both spin and orbital angular momenta.

Coupling between photons carrying angular momentum in nanophotonic systems with discrete rotational symmetry represents a significant advance in the field. The research focuses on coupling free-space photons into surface plasmon polaritons using a polygonal-shaped grating, which restricts the generated near-field modes to a finite set and establishes a novel mechanism for spatial mode entanglement. By encoding incoming photons with both spin and orbital angular momenta, the system preserves a high-dimensional space for quantum information, a crucial distinction from rotationally symmetric nanophotonic platforms where these degrees of freedom typically become inseparable, leading to information loss. Furthermore, the team demonstrates that careful engineering of the photons’ phase allows for precise control and manipulation of these entangled states, opening new avenues for quantum information processing and advanced optical technologies.

Polygonal Gratings Generate Hyperentangled Light States

Scientists developed a novel platform for generating hyperentanglement by harnessing the discrete rotational symmetry present in nanophotonic systems, specifically those with polygonal boundaries. The research team engineered a method to couple free-space light into surface plasmon polaritons using these polygonal gratings, effectively restricting the generated near-field modes to a finite set and creating a new mechanism for spatial mode entanglement. By encoding incoming light with both spin and orbital angular momenta, the study preserves a high-dimensional space for quantum information, overcoming limitations found in rotationally symmetric platforms where these degrees of freedom typically become indistinguishable, leading to information loss. This method utilizes the vector-field nature of the nanophotonic modes alongside the finite basis of states created by the polygonal boundaries, enabling complex entanglement generation.

To validate the theoretical model, scientists performed extensive numerical simulations using computational methods, comparing results with analytical approximations based on established principles of light propagation. These simulations, conducted on structures with dimensions of 15μm, demonstrated excellent agreement with theoretical predictions, with minor deviations attributed to the limitations of the modeling techniques. Researchers defined a mathematical operator to analyze the rotation of light fields, expressing it as a combination of translational movements. This operator’s eigenmodes represent light fields rotated by a specific angle, allowing the team to establish a direct relationship between free-space angular momentum and the resulting excitations within the nanophotonic system. Consequently, measuring any single component of the light field is sufficient to independently determine both the excitation’s spin and orbital angular momentum. This innovative approach paves the way for scalable, on-chip quantum photonic platforms by providing a robust mechanism for generating the complex entangled states necessary for efficient quantum computation.

Polygonal Grating Enables Hyperentanglement Generation

Scientists have achieved a breakthrough in quantum photonics by demonstrating a new method for generating hyperentanglement within nanophotonic systems. This work centers on manipulating the interaction between free-space photons and a specially designed nanophotonic platform featuring a polygonal grating coupler. The team discovered that by breaking the rotational symmetry typically found in these systems, they could preserve the high-dimensional space necessary for encoding and manipulating quantum information. The research demonstrates that a nanophotonic system carved with a polygonal slit supports a finite basis of discrete modes, effectively creating a system with discrete rotational symmetry.

Experiments reveal that by engineering the phase of incoming photons to match the discrete rotational symmetry of the polygonal boundary conditions, the system generates hyperentangled states utilizing both the vector-field nature of the nanophotonic modes and the finite basis of states. Specifically, the team showed that the system supports a finite set of modes, the number of which corresponds to the number of sides of the polygon, allowing for precise control over the quantum states. Measurements confirm that the electric field within this geometry can be characterized by rotating field components, each linked to a topological number representing the number of phase rotations. The team derived equations describing the electric field components, demonstrating how the system’s geometry dictates the behavior of the photons. This approach allows for the creation of entangled states where the topological number is limited to specific values, depending on the imprinted spin and orbital angular momentum, effectively increasing the space available for quantum information processing. The breakthrough delivers a pathway towards on-chip quantum communication and computation by expanding the possibilities for encoding and manipulating quantum information in compact, integrated devices.

Angular Momentum Preservation Enables Hyperentanglement

This research demonstrates a new approach to generating hyperentanglement within nanophotonic systems. By utilizing polygonal-shaped structures, the team created a platform where the angular momentum of incoming photons is preserved, unlike traditional rotationally symmetric designs which can lose information. This preservation is achieved through restricting the possible modes of light within the structure, effectively creating a finite set of states for entanglement. The team further established a direct relationship between the angular momentum of free-space photons and the resulting excitations within the nanophotonic system, meaning a direct correspondence exists between the properties of the incoming light and the generated entanglement. This allows for independent determination of both spin and orbital angular momentum, enhancing the potential for complex quantum state manipulation. These findings pave the way for developing scalable, on-chip quantum photonic platforms suitable for efficient quantum computation and communication.