Fig. 1: Schematic diagram of a reconfigurable non-Abelian photonic chip.
a Schematic diagram of a double-layered polymer photonic chip which performs the task of non-Abelian braiding of four photonic modes located in waveguides A to D (gray), respectively, with the assistance of several auxiliary waveguides (blue) and coupling waveguides (red). The chip consists of six two-mode braiding structures as building blocks (dashed region), where electrode heaters (yellow) are introduced on top of the braiding waveguides to tune their refractive index via the thermo-optic effect. b An enlarged view of one building block, where an auxiliary waveguide (S) is placed in layer I, while braiding waveguides (A and B) and coupling waveguides (X1, X2, and X3) are located in layer II. The whole two-mode braiding process can be divided into steps I, II, and III, plus a crossing step for the repositioning of the waveguides. When electrode heaters are turned off, the braiding results in a swap of the two modes in waveguides A and B via a non-Abelian holonomy process. When electrode heaters are turned on, the refractive index of the braiding waveguides is significantly lowered down, leading to that the output and input are in the same braiding waveguide. c A braiding diagram of the photonic chip, where each green box represents a tunable two-mode braiding building block. The abbreviation “TB” is short for tunable block, which has two working conditions associated with two geometric phase matrices U2, depending on the modulation. By separately tuning the six TBs, a variety of unitary matrices associated with the braid group B4 can be achieved in this single chip.
