Measurement-induced photonic topological insulators.

Topological order in photonics, defined by pseudo-spin degrees of freedom, is traditionally static. By contrast, a unique quantum effect is that measurements alter system states. The convergence of these foundational concepts-measurement and topology-remains unexplored. Here, we demonstrate that topological order can be dynamically modified by repeated measurements. By fabricating a photonic lattice composed of an array of contiguous waveguides and incorporating 16,800 appended waveguide segments as discrete, nonindependent units, we established a classical-wave platform simulating the backaction from measurements and observed measurement-induced topological order in photonic lattices. Beyond topology, we further demonstrate that measurements can universally control the lattice by tailoring its Hilbert space and validate experimentally. Our study not only offers a quantum approach to dynamically tailor topological order but also unveils measurements as a powerful universal control tool, paving the way to on-chip topological materials and measurement-induced control over photonic systems.