Direct measurement of topological invariants in photonic superlattices

Since the discovery of topological insulators,topological phases have generated considerable attention across the physics community.The superlattices in particular offer a rich system with several degrees of freedom to explore a variety of topological characteristics and control the localization of states.Albeit their importance,characterizing topological invariants in superlattices consisting of a multi-band structure is challenging beyond the basic case of two-bands as in the Su-Schreifer-Heeger model.Here,we experimentally demonstrate the direct measurement of the topological character of chiral superlattices with broken inversion symmetry.Using a CMOS-compatible nanophotonic chip,we probe the state evolving in the system along the propagation direction using novel nano-scattering structures.We employ a two-waveguide bulk excitation scheme to the superlattice,enabling the iden-tification of topological zero-energy modes through measuring the beam displacement.Our measurements reveal quantized beam displacement corresponding to 0.088 and-0.245,in the cases of trivial and nontrivial photonic superlattices,respectively,showing good agreement with the theoretical values of 0 and-0.25.Our results provide direct identification of the quantized topological numbers in superlattices using a single-shot approach,paving the way for direct measurements of topological invariants in complex photonic structures using tailored excitations with Wannier functions.