Interferometric Readout of Momentum-Space Topology in a Programmable Dissipative Photonic Circuit

Topology under non-Hermitian dynamics is encoded in the phase of the bulk evolution, yet strong dissipation suppresses the amplitudes carrying it. We resolve this using a programmable photonic integrated circuit that implements such dynamics in synthetic momentum space through unitary dilation, with the phase recovered by phase-shifted interferometry. For the non-Hermitian Su-Schrieffer-Heeger model, the method distinguishes trivial and non-trivial Zak phases and yields a coherence winding q= plus or minus 1 induced by an exceptional point. Extending to a synthetic torus via a Rice-Mele pump gives the first Chern number Ch 1=0,1 for trivial and non-trivial cycles, showing a programmable route to momentum-space topology under strongly dissipative non-Hermitian dynamics.