Braiding of Light

Physicists have proposed a way to braid three beams of light by guiding the beams along swirling, vortex-shaped defects in the optical medium through which the beams travel. The braided light would have an unusual “non-Abelian” nature, meaning that its phase would depend on the exact order in which the defects are wound around each other.

Researchers have created photonic analogues of [braided light] topological zero modes in photonic lattices. They demonstrated that these “topological guided modes” can be understood at both the quantum and classical levels when the photons in the waveguide array are weakly interacting. They further proposed a photonic non-Abelian interferometer, feasible with current technology, to detect unambiguous signatures of the non-Abelian Berry phases that result from braiding these topological guided modes

Many topological phenomena first proposed and observed in the context of electrons in solids have recently found counterparts in photonic and acoustic systems. Researchers demonstrated that non-Abelian Berry phases can arise when coherent states of light are injected into “topological guided modes” in specially fabricated photonic waveguide arrays. These modes are photonic analogues of topological zero modes in electronic systems. Light traveling inside spatially well-separated topological guided modes can be braided, leading to the accumulation of non-Abelian phases, which depend on the order in which the guided beams are wound around one another. Notably, these effects survive the limit of large photon occupation, and can thus also be understood as wave phenomena arising directly from Maxwell’s equations, without resorting to the quantization of light. They propose an optical interference experiment as a direct probe of this non-Abelian braiding of light.

Schematic of the proposed photonic non-Abelian interferometer. A coherent laser beam (one of three, one for each vortex in a lattice) passes through a 50/50 beam splitter (blue) and simultaneously enters two separate photonic lattices fabricated with the two braids to be compared. The two output beams are reflected by mirrors (grey) into another beam splitter that interferes the two signals and outputs the sum and difference to separate screens (black). For the choice of braids used here, one screen shows a bright and two dark spots, while the other screen shows the “logical complement” of the first, with one dark and two bright spots.

Arxiv – Non-Abelian braiding of light (18 pages)

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