Spatiotemporal topological phase transitions in photonic spacetime crystals

Topological phase transitions, characterized by the closing and reopening of band gaps and a concomitant change in topological invariants, have played a central role in topological physics. However, such transitions have so far been restricted to spatial crystals, relying solely on energy band gaps and spatial interfaces. Here, we transcend this conventional framework and report, for the first time, spatiotemporal topological phase transition in photonic spacetime crystals - structures that are periodically modulated in both space and time. Using a dynamically modulated transmission line metamaterial, we theoretically propose and experimentally demonstrate complete spatiotemporal topological phase transitions characterized by the closing and reopening of both energy and momentum band gaps, alongside changes in spatiotemporal topological invariants and topological phases. Furthermore, in a genuine photonic spacetime crystal that possesses a complete energy-momentum band gap, we directly observe a space-time topological event that localizes in both space and time, exhibiting relativistic-causality-governed excitation and robustness against spatiotemporal disorders. Our findings reveal the interplay among space, time, and topology, establishing a unified framework that provides a comprehensive picture of the emerging topological space-time physics and opening new avenues for robust spatiotemporal topological wave manipulations.