The Accelerated Topological Laser Induced by Non‐Hermitian Topological Flat Band in The Dimerized Lattice

A method of inverse Fourier transform engineering is demonstrated for constructing the topological flat band both in Hermitian and non‐Hermitian systems. In Hermitian dimerized lattice, the designed topological flat band is demonstrated to suppress the bulk diffusion of quantum walk. In non‐Hermitian dimerized lattice, the intrinsic connection between the topological flat band and non‐Hermitian phase transition is revealed, which is rarely mentioned in previous works. It is further shown that the non‐Hermitian effect can induce a topological laser in the quantum walk, and significantly, it can be markedly accelerated by the non‐Hermitian flat band. This accelerated transmission phenomenon is counterintuitive since the flat band usually means the localization in Hermitian system. This phenomenon is found to originate from the further destruction of orthogonality of quantum states induced by flat band in non‐Hermitian system, which shows the interesting interplay between non‐Hermitian effect and topological flat band. The investigations show the favorable effects of non‐Hermitian topological flat band on quantum transmission, which may promote the applications of non‐Hermitian topological system in quantum information processing.