High-dimensional broadband non-Abelian holonomy in silicon nitride photonics

Non-Abelian geometry phase has attracted significant attention for the robust holonomic unitary behavior exhibited, which arises from the degenerate subspace evolving along a trajectory in Hilbert space. It has been regarded as a promising approach for implementing topologically protected quantum computation and logic manipulation. However, due to the challenges associated with high-dimensional parameters manipulation, this matrix-valued geometry phase has not been realized on silicon integrated photonic platform, which is CMOS compatible and regarded as the most promising flatform for next-generation functional devices. Here, we demonstrate the first non-Abelian holonomic high-dimensional unitary matrices on multilayer silicon nitride integrated platform. By leveraging the advantage of integrated platform and geometry phase, ultracompact footprint, highest order (up to six) and broadband operation (larger than 100nm) non-Abelian holonomy unitary matrices are experimentally realized. Our work paves the way for versatile non-Abelian optical computing devices in integrated photonics.