Reconfigurable non-Abelian integrated photonics.

Current integrated photonics typically utilizes the dynamical phase associated resonant on-chip components, leading to bandwidth-limited devices with perturbation-sensitive performance. Multi-mode geometric phase matrix, arising from the non-Abelian holonomy which is a non-resonant and global effect, has been recently introduced to integrated photonics for the design of broadband and robust on-chip photonic devices. Achieving reconfigurable on-chip non-Abelian photonic devices is a crucial step towards practical applications, which however remains elusive. Here, we propose a universal approach by employing the thermo-optic effect to tune the system's Hamiltonian and thus the holonomy induced geometric phase matrix. We implement this concept in double-layered polymer integrated platforms, experimentally demonstrating a four-mode non-Abelian braiding device comprising six sets of tunable two-mode braiding building blocks. Through modulations, the device can be reconfigured to generate up to 24 unitary matrices belonging to the braid group B(4). Our work paves the way for non-Abelian integrated photonics towards abundant applications.