Recently, the all-optical quantum information team at Southeast University has achieved important progress in the field of topological quantum physics. Using a photonic quantum walk experimental platform, the team has realized, for the first time, the quantum simulation of a Floquet non-Abelian topological insulator (FNATI). The results were published in Nature Photonics under the title “Simulation of a Floquet non-Abelian topological insulator with photonic quantum walks” .
Topological phases of matter have become an important research direction in condensed matter physics and quantum information in recent years. Unlike conventional phases described by symmetry breaking, topological phases are characterized by global topological invariants and can host boundary states that are robust against perturbations. The non-Abelian topological phases proposed in recent years further extend the scope of topological matter. In such systems, the topological properties are characterized by non-Abelian topological charges, whose mathematical structure is related to the non-Abelian quaternion group (Q8), making the topology more complex and richer.
In their previous theoretical work [Nat. Commun. 14, 6418 (2023)], the team found that a novel topological phase, namely the Floquet non-Abelian topological insulator (FNATI), can emerge in periodically driven systems. Unlike conventional static topological systems, FNATI features a multigap topological structure, where the relation between edge states and topological charges is intricate: the same topological charge may correspond to multiple distinct edge-state configurations, leading to a more complex bulk–boundary correspondence. It has been shown that the topological properties of the system can be characterized by Dirac-type singularities in the phase bands, which carry non-Abelian topological charges. In systems with domain-wall configurations, the difference between the topological charges of the left and right bulks can be characterized by the residual configuration of phase-band singularities, which uniquely determines the form of edge states at the domain wall, thereby establishing a Floquet bulk–boundary correspondence governed by the configuration of phase-band singularities. This intricate bulk–boundary correspondence, together with the intrinsic complexity of non-Abelian topological charges, makes the experimental realization of FNATI highly challenging.
To realize the experimental simulation of FNATI, the team constructed a three-band discrete-time quantum walk system. Photons are used as walkers, and the periodically driven Floquet evolution operator is implemented via a time-multiplexed optical network. The three-dimensional coin states of photons are encoded jointly in polarization and spatial-path modes, forming a three-band structure and satisfying the required symmetry conditions.
As shown in Fig. 1(a), the experiment constructs the quantum-walk network using fiber loops and linear optical elements, where rotation and shift operations are implemented using devices such as polarizing beam splitters and electro-optic modulators, thereby simulating a periodically driven topological system. Figure 1(b) illustrates the possible bulk–boundary correspondences in this system. In non-Abelian topological systems, the same topological charge can correspond to different edge-state configurations, leading to complex bulk–boundary correspondence.
Figure 1: Experimental schematic of the photonic quantum-walk simulation of a Floquet non-Abelian topological insulator.
In this quantum-walk system, the team extracts the non-Abelian topological charge via dynamical measurements. By reconstructing the evolution operator through quantum-state tomography, the trajectories of eigenstates in different bands as functions of momentum can be obtained. As shown in Figs. 2(a, b), the eigenstates of different bands form closed trajectories on the unit sphere. The topological structure of these trajectories encodes the quaternion topological charge of the system. The experimental results demonstrate that the system possesses a nontrivial non-Abelian topological structure. Based on this, the team further constructs two regions with different topological charges and forms a topological domain wall between them. As shown in Fig. 2(c), localized topological edge states appear near the domain wall, with spatial distributions clearly distinct from bulk states. To directly detect these edge states experimentally, the team proposes a spatially resolved injection spectroscopy method. By injecting photons near the domain wall and analyzing their dynamical evolution, the quasienergy spectrum of the edge states can be extracted. As shown in Fig. 2(d), the experimental results agree with theoretical predictions, confirming the existence of edge states determined by the topology.
Figure 2: Experimental measurement of bulk topological charge and edge states.
This work realizes and systematically characterizes the Floquet non-Abelian topological insulator experimentally for the first time, and develops a dynamical-measurement-based method for detecting non-Abelian topology. The observed edge-state structures are in strong agreement with the Floquet non-Abelian topological invariants predicted by the topological configuration of phase-band singularities. This work establishes a controllable photonic quantum simulation platform, providing a new experimental tool for studying complex non-Abelian topological systems. In the future, this platform can be extended to higher-band structures and more complex periodically driven topological systems, offering an important experimental basis for exploring new topological quantum phases.
The first authors of the paper are Dr. Quan Lin (Southeast University) and Associate Researcher Tianyu Li (South China Normal University). Important collaborators include Researcher Haiping Hu from the Institute of Physics, Chinese Academy of Sciences, and Professor Wei Yi from the University of Science and Technology of China. The School of Physics at Southeast University is the primary affiliation for this work. This research was supported by the National Key R&D Program, the National Natural Science Foundation of China, the China Postdoctoral Science Foundation, and the Basic Research Program of Jiangsu.
Link：https://www.nature.com/articles/s41566-026-01854-x
