Braiding Light (and Majoranas too)
In this talk I will discuss platforms for the direct demonstration of non-Abelian Berry phases by braiding topological zero modes. To this end, we study novel ways to control and program the position of
topological zero modes in both photonic and electronic settings. In the photonic systems, we study coherent states of light injected into "topological guided modes" in specially-fabricated photonic waveguide
arrays. We show that light traveling inside well-separated topological guided modes can be braided, leading to the accumulation of non-Abelian phases, which depend on the order that the guided light beams are wound around each other. In electronic systems, we present a hierarchical architecture for building "logical" Majorana zero modes using "physical" Majorana zero modes at the Y-junctions of a hexagonal network of
semiconductor nanowires. In this network, the location of the topological zero modes can be moved by programming gate voltages to change as functions of time.