Direct measurement of topological invariants in photonic superlattices

Abstract

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 nanoscattering structures. We employ a two-waveguide bulk excitation scheme to the superlattice, enabling the identification 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.