Topological Temporal Boundary States in a Non-Hermitian Spatial Crystal

Periodic modulation of the material index in time opens momentum gaps. Such systems are regarded as the temporal analog of common spatial crystals, wherein the band gaps open in frequency space. Recent studies have also led to the theoretical prediction of topological temporal boundary states (TTBSs) in such momentum gaps. In this Letter, we report the discovery and experimental realization of a new type of TTBS, appearing in a non-Hermitian spatial crystal with spatially periodic loss and gain, wherein the emergence of the Bloch momentum gap is associated with a parity-time broken phase, instead of relying on temporal modulation. By inducing a sudden flip of signs of the loss and gain profile, a mode emerges in the middle of the Bloch momentum gap and peaks at the flipping instant, which is regarded as a temporal boundary. Remarkably, we found that the temporal flip induces a topological transition in time, and the said mode is a TTBS that is a temporal analog of the Jackiw-Rebbi state. The TTBS is experimentally observed in a one-dimensional active mechanical lattice, and it can generically emerge in a wide range of non-Hermitian systems. By linking non-Hermitian physics with spatiotemporal topological systems, our results not only deepen the understanding of temporal topological phases but also open new grounds for controlling transient waves by topological means.