Topology in space, time, and space-time

In recent years, topological phenomena in photonic systems have attracted much attention, with their striking features arising from robust states in the energy gaps of spatially periodic media. However, light waves are entities that extend in space as well as time, such that one may ask whether topological effects can also occur in the temporal domain, or even space-time. Intuitively, systems that are periodic in time may be gapped in momentum, leading to topological states localized at time interfaces. However, time - in contrast to space - exhibits a unique unidirectionality often referred to as the “arrow of time”. Inspired by these features, I will present our most recent experiments on topological states residing at temporal interfaces. Moreover, I will discuss the formation of spacetime-topological events and demonstrate unique features such as their limited collapse under disorder and causality-suppressed coupling.