Time Topology in Synthetic Photonic Lattices

Waves are shaped in time and space by their energy and momentum, respectively. Energy gaps may have topological properties, giving rise to striking features such as robust states at spatial interfaces. However, time-varying systems such as temporal metamaterials may be gapped in momentum, leading to topological states localised at time interfaces. Inspired by this, here we explore this notion of time topology based not on energy but on momentum gaps. We show that synthetic photonic lattices with suitably tailored non-Hermitian temporal variations may exhibit momentum gaps hosting time-topological states.