Subspace-induced Dirac point and nondissipative wave dynamics in a non-Hermitian optical lattice

Abstract

We propose a mechanism to achieve real energy spectra via Hermitian subspace in non-Hermitian systems. As an illustrative example, we investigate a system composed of two identical Su-Schrieffer-Heeger (SSH) chains connected by a lossy site in each unit cell. Although the system as a whole is non-Hermitian, it is able to support Dirac points that coexist with exceptional points, exactly exhibiting real eigenenergies. The real spectra and coexistence of different singularities are inherited from two virtual decoupled subsystems after a transformation that comprises a Hermitian SSH chain and a non-Hermitian Lieb lattice. Furthermore, we show the two subsystems both experience topological phase transition by tuning coupling strength, allowing the exploration of Hermitian and non-Hermitian topological edge modes at the same time. In aid of Hermitian subspace, the waves could evolve without dissipation depending on initial injection, which contributes to coherent splitters with locked phase and intensity in two SSH layers. The proposed model can be realized in evanescently coupled optical waveguide arrays and further extended to other tight-binding systems.