Hyperentanglement in Nanophotonic Systems with Discrete Rotational Symmetry

TL;DR

The paper proposes a on-chip scheme to generate hyperentanglement by exploiting discrete rotational symmetry of polygonal nanophotonic couplers to restrict near-field modes to a finite basis, enabling simultaneous control of spin and orbital angular momentum. It derives a formal mapping between free-space angular momentum and nanophotonic near-field modes, and shows how phase-engineering and polygonal boundary conditions enable hyperentangled states that are preserved through coupling and out-coupling processes. Through analytical relations and FDTD simulations, it demonstrates an isomorphism between SAM/OAM in free space and TAM/rotation in the near field, and provides design rules (e.g., $N=4m$) for achieving hyperentanglement in various polygon geometries. The work presents a path toward scalable, high-dimensional on-chip quantum communication by expanding the usable Hilbert space and enabling robust generation and detection of hyperentangled photon states. It also provides a concrete experimental scheme for realizing and measuring these states in a nanophotonic platform. The results advance on-chip quantum photonics by marrying vector nanophotonic modes with discrete rotational symmetry to preserve and exploit multiple DoFs for quantum information processing.

Abstract

We propose a scheme to generate hyperentanglement between photons carrying angular momentum in nanophotonic systems with discrete rotational symmetry. Coupling free-space photons into surface plasmon polaritons by a polygonal-shaped grating restricts the basis of the generated near-field modes to a finite set, thus creating a new mechanism for spatial mode entanglement. By encoding the incoming photons with spin and orbital angular momenta, we find that the system preserves the high-dimensional Hilbert space, in contrast to rotationally symmetric nanophotonic platforms, where the inseparability of spin and orbital degrees of freedom results in loss of information. We further show that by properly engineering the phase of the photons to conform to the polygonal boundary conditions, we achieve a new scheme for generating hyperentangled states, utilizing both the vector-field nature of the nanophotonic modes and the finite basis of states in polygonal boundary conditions. Our approach paves the way for on-chip quantum communication by expanding the Hilbert space used in computation.

Figures (4)

• Figure 1: Eigenmodes of square boundary conditions - (a) An excitation from a square slit is modeled as 4 plane waves propagating along the slab nanophotonic system. (b) The field distribution of each field component. top - amplitude, bottom - phase.
• Figure 2: Out-coupled modes - a. the far-field (Fourier) plane amplitude of different out-coupled modes. b. calculated overlap integrals between the different modes. .
• Figure 3: Experimental system suggestion - $404_{nm}$ laser source is down-converted into a collinear photon pair. We split the photons based on polarization into a dual SLM configuration, each imprinting an identical spatial profile according to the sample excitation slit. Both photons are then combined and coupled to the nanophotonic system. Using another polarizing beam splitter, we then split the generated state and perform a correlation measurement in the selected basis.
• Figure 4: Numerical tilt angle calculation - Tilt angle of the excited modes as a function of the excitation topological charge for a square slit with side length $L=15_{\mu m}$. The lines represent tilt angles obtained by different methods: orange — prism approximation, blue — Huygens principle model, and purple — FDTD simulation, with the shaded band indicating ±1 circular standard deviation. Insets depict examples of rotated in-plane fields, with a blue horizontal line shown for reference and a green line indicating the tilt angle.