Breakup and Recovery of Topological Zero Modes in Finite Non-Hermitian Optical Lattices.

The topological edge state (TES) in a one-dimensional optical lattice has exhibited robust field localization or waveguiding against the structural perturbations that would give rise to fault-tolerant photonic integrations. However, the zero mode as a kind of TES usually deviates from the exact zero-energy state in a finite Hermitian lattice due to the coupling between these edge states, which inevitably weaken the topological protection. Here, we first show such a breakup of zero modes in finite Su-Schriffer-Heeger optical lattices and then reveal their recovery by introducing non-Hermitian degeneracies with parity-time (PT) symmetry. We carry out experiments in a finite silicon waveguide lattice, where a passive-PT symmetry was implemented with carefully controlled lossy silicon waveguides. The experimental results are fully compatible with the theoretical prediction. Our results show that the topological property of an open system can be tuned by non-Hermitian lattice engineering, which offers a route to enhance the topological protection in a finite system.