Experimental demonstration of photonic anomalous Floquet topological insulators

Summary form only given. In the field of topology, it is commonly accepted that for two-dimensional spin-decoupled structures a complete topological characterization is provided by the Chern numbers of the system[1]. The number of the extraordinarily robust chiral edge modes residing in a band gap is given by the sum of the Chern numbers of all bands below this gap. However, this is strictly true only for systems with a Hamiltonian which is constant in the evolution coordinate. For characterizing periodically driven (Floquet) systems it was shown recently that the appropriate topological invariants are winding numbers [2]. They utilize the information in the Hamiltonian for all times within a single driving period.In our work, following our recent efforts in the field of topological photonics [3], we experimentally demonstrate so-called anomalous Floquet topological insulators (A-FTI) with chiral edge states being present although the Chern numbers of all bands are zero. To this end, we employ arrays of evanescently coupled waveguides with the light evolution governed by a Schrodinger equation. We consider a bipartite square lattice with two site species A and B (with same on-site potential), as it was suggested in [2]. Along the propagation direction, the structure consists of four sections with different coupling steps as sketched in Fig.1(a) building up one period. The inter-site coupling in the individual sections is experimentally achieved by appropriately engineering directional couplers (Fig.1(a)) with complete coupling into the respective neighboring waveguide per step. Due to the periodicity along the propagation direction, Floquet theory can be applied to derive a quasi-energy band structure [2]. The bulk bands of the system are flat and degenerate such that there is no transport after a full period (Fig.1(b)) and have a Chern number equal to zero. We experimentally implement the lattices using photonic laser-written waveguides. When launching light into a bulk waveguide, we indeed observe localization, as enforced by the flat band (see Fig.1(d) for one example). However, at the edges chiral edge states exist (Fig.1(b) and (c)) being also seen in the experiment. We observe the edge state traveling dispersionless and without any scattering along edges and around corners (Fig. 1(e)). This highly robust, unidirectional state is a clear signature of topological protection.