Diagnosing Floquet Chern and anomalous topological insulators based on Bloch oscillations

Abstract: It is challenging to distinguish Floquet Chern insulator (FCI) and Floquet anomalous topological insulator (FATI) because of their common features of chiral edge states and far away from equilibrium. A hybrid straight-curved waveguide array is proposed to enable topological phase transitions from FCI to FATI and show how to diagnose the two phases using Bloch oscillations. As a proof of principle, the hybrid straight-curved waveguide array is designed as a straight honeycomb waveguide array nested in an asynchronous curved Kagome waveguide array. Under a two-dimensional (2D) tilted potential created by the spatial gradient of refractive indices, an initial Gaussian-like wavepacket undergoes 2D Bloch oscillations, displaying quasi-quantized displacement in the FCI and no drift in the FATI. This approach offers a direct and unambiguous method to diagnose Floquet topological phases from the bulk response.