Strain Induced Curvature in a Photonic Floquet Topological Insulator

The research on topological states of matter of the past few decades has mainly focused on Euclidean or flat lattice geometries. Only very recently, the topological phenomena in negatively curved or Hyperbolic lattices have attracted significant attention and Hyperbolic lattice tilings were studied especially in electronic circuits and circuit QED. In this talk, we present a different approach to Hyperbolic geometries which can be applied in optical systems such as photonic waveguides or fiber loop setups. By straining a topological Floquet- or time-periodically driven- graphene lattice, we simulate a pseudomagnetic field as well as negative Gaussian curvature. This allows us to move smoothly from Euclidean to Hyperbolic space and tune the curvature continuously, which is impossible by studying different Hyperbolic tilings. In this talk we explore the interplay between this curvature and the topology of the Floquet system and discuss phenomena unobserved in Euclidean lattice geometries.