Quantum simulation technology utilizes controllable experimental systems to study the properties and evolution of quantum physical models of interest. In the research of topological materials, to overcome the limitations of three-dimensional spatial dimensions, researchers have proposed a quantum simulation method known as synthetic dimensions. This approach realizes effective synthetic dimensions by coupling different modes of a particle's independent degrees of freedom (such as the frequency or polarization of photons) in a specific manner. When combined with real geometric dimensions, this method enables the simulation of unique properties of higher-dimensional topological materials beyond three dimensions.
Photons carrying vortex-phase wavefronts possess orbital angular momentum (OAM), exhibiting a doughnut-shaped energy distribution with a central hole in space. The orbital angular momentum degree of freedom of photons has been recognized as an excellent carrier for synthetic dimensions, enabling researchers to successfully simulate one-dimensional topological chains.
Among material topological properties, a phenomenon called edge states holds significant physical and practical value. As manifestations of a material's global characteristics at boundaries, edge states exhibit robustness against local defects and disturbances—a property known as topological protection. These edge states show potential applications in stable signal transmission and laser efficiency enhancement.
Since the topological charges of photon orbital angular momentum modes are theoretically unbounded, the constructed synthetic dimension can extend infinitely without natural boundaries, making it difficult to directly observe topological edge states. The key challenge for expanding the simulation capabilities of OAM synthetic dimension experimental platforms lies in how to create boundaries within this system.
To address this challenge, the team led by CAS Academician Guang-Can Guo at the University of Science and Technology of China, including Chuan-Feng Li, Jin-Shi Xu, and Mu Yang, proposed an experimental scheme employing laser-processed perforated waveplates to construct boundaries in orbital angular momentum (OAM) synthetic dimensions. This approach successfully detected distinct edge states in OAM synthetic lattices and investigated topological properties such as bulk-boundary correspondence. Relevant research results were recently published in Photonics Research, Volume 13, Issue 1, 2025.[Yu-Wei Liao, Mu Yang, Hao-Qing Zhang, Zhi-He Hao, Jun Hu, Tian-Xiang Zhu, Zong-Quan Zhou, Xi-Wang Luo, Jin-Shi Xu, Chuan-Feng Li, Guang-Can Guo, "Realization of edge states along a synthetic orbital angular momentum dimension," Photonics Res. 13, 87 (2025)]
In this work, the research team designed and fabricated a birefringent crystal plate with a small pinhole of a specific size, based on the spatial distribution characteristics of the optical field of photon orbital angular momentum modes, as shown in Fig. 1(a) and (b). The size of the hole allows photons in the Gaussian fundamental mode (topological charge m = 0) to pass through, so that the plate only operates on photons with OAM order m> 0. This design achieves controlled manipulation of the OAM spatial modes, enabling the truncation of the Su-Schrieffer-Heeger (SSH) model chain on the synthetic dimension of OAM in the degenerate optical cavity to create a boundary, as illustrated in Fig. 1(c). Fig. 1(d) displays the topological phase diagram of the system.
Figure 1 The degenerate cavity designed to form the OAM synthetic lattice and the topology of the bulk. (a) The degenerate cavity contains diverse OAM modes. WP: waveplate. (b) The WP with a centered hole in the cavity, where only optical modes with topological charge m=0 pass through the hole. (c) The schematic of the synthetic lattice formed by OAM modes with different spins. The 1-D chain in synthetic space is cut off between the different polarized fundamental Gaussian modes (m=0). (d) The diagram of the topological phase.
By continuously exciting different synthetic dimension lattice sites within the cavity using a laser (Fig. 2(c) and (e)), the research team first theoretically simulated the distribution of edge states (Fig. 2(a) and (b)), and then directly detected topological edge states distributed at various positions in the experiment (Fig. 2(d) and (f)). The team validated the bulk-boundary correspondence through measurements of the system's bulk topological invariants. Further investigations revealed the topological protection of OAM synthetic dimension edge states and single boundary interference effects, demonstrating the advantages of this proposed approach.
Figure 2 Theoretical simulated results and the experimental observation of the energy band structures of the edge states. (a) The theoretical energy spectrum with edge states. (b) Distributions of the edge states. (c), (e) The schemes of the OAM lattice model when exciting different sites. (d), (f) The normalized transmission intensity spectra with edge state when pumping the cavity with a left circularly polarized fundamental Gaussian mode (d) or right circularly polarized m=2 OAM mode (f).
Professor Jin-Shi Xu remarked, "By designing the punched wave plate within the degenerate cavity, this work ingeniously enables controlled manipulation of synthetic dimension lattice sites and the creation of boundaries. This greatly expands the capabilities of synthetic dimension quantum simulation systems and contributes to a deeper understanding of the topological properties of complex systems."
This study represents a significant advancement following the team's previous work on simulating one-dimensional topological lattices (Nature Communications 13, 2040 (2022)) and exploring the properties of non-Hermitian exceptional points (Science Advances 9, eabp8943 (2023)), both of which were also based on orbital angular momentum synthetic dimensions. This work establishes a foundation for simulating boundary effects in non-Hermitian systems and refining generalized bulk-boundary correspondence theories. It also creates opportunities for developing OAM synthetic-dimension-based optical devices, such as optical switches and topological lasers.
