Observing mixed-state Uhlmann winding numbers in integrated photonic quantum walks

arXiv:2611.07600v1 Announce Type: new Abstract: Integer winding numbers provide a well-established classification of topological phases protected by chiral symmetry at zero temperature, but extending this classification to thermal mixed states remains challenging. The Uhlmann phase, a mixed-state extension of the Berry phase, provides a geometric framework for characterizing finite-temperature topology. However, this geometric phase is restricted to two quantized values and therefore cannot resolve the multiple thermal regimes associated with high winding numbers. Here, we experimentally observe integer mixed-state winding numbers in a photonic quantum-walk chip. We prepare and reconstruct thermal states associated with high-winding chiral Hamiltonians and their spectrum-preserving dimensional extensions. The reconstructed Uhlmann overlaps form closed trajectories in the complex plane, and their integer windings around the zero-overlap point are directly observed. As temperature increases, the Uhlmann winding number undergoes multiple discrete changes, accompanied by switches of the Uhlmann phase and the successive disappearance of momentum-resolved topological kinks. These results highlight an integer-valued topological characterization alongside the mixed-state geometric phase.