Spatiotemporal Topological Phase Transition in non-Hermitian Photonic System

While energy band topology in spatial photonic crystals (PCs) and momentum-band topology in temporal crystals have each served as powerful probes of topological phases in their respective domains, their unification in a static platform remains unexplored. In this Letter, we bridge this gap by introducing a waveguide assisted non-Hermitian SSH model, in which controlled tuning of loss and coupling drives PT-symmetry breaking and enables a continuous transition between energy- and momentum-gap regimes. This allows us to construct a complete spatiotemporal topological phase diagram in a unified parameter space. By mapping this phase diagram onto a spatially graded PC, we experimentally observe multiple Bloch momentum-band gaps and a continuous spatiotemporal topological transition via translating across the static sample, enabling real-time control over the evolution pathway of the band topology. Our work creates a versatile, bias-free platform for exploring synthetic spacetime physics and opens new avenues for controlling light via non-Hermitian band engineering.