Adding Doublons to a Photonic Floquet-Topological Insulator

Topological photonics with laser-inscribed waveguides in glass is a way to implement a large class of time-dependent hopping Hamiltonians and to solve the corresponding time-dependent Schrödinger equation [1]. We characterize a Floquet-topological insulator on a finite square lattice [2] with an additional on-site potential along the diagonal. In addition to the usual bulk and edge states, this system also exhibits doublon states along the diagonal. The doublons' energies increase with the diagonal potential, which leads to crossings and avoided crossings with other states.

In real-time propagation, an edge state traveling along the system's boundary will split when hitting the diagonal and continue propagating along the edge and the diagonal simultaneously. We find and explain a temporal delay between the two contributions traveling around and through the system. The strength of the diagonal potential determines the ratio between both parts. This behavior could allow for the non-destructive measurement of topological edge states.

[1] Segev, M. & Bandres, M. A. Topological photonics: Where do we go from here? Nanophotonics 10, 425–434 (2021).

[2] Rudner, M. S., Lindner, N. H., Berg, E. & Levin, M. Anomalous Edge States and the Bulk-Edge Correspondence for Periodically Driven Two-Dimensional Systems. Phys. Rev. X 3, 031005 (2013).