One-dimensional one-band topologically nontrivial non-Hermitian system simulated in optical cavities

Abstract

We propose a scheme for simulating a momentum dependent non-Hermitian Hamiltonian term by adding loss in the hopping process in a one-dimensional array of optical cavities, which leads to a one-band topological nontrivial non-Hermitian model. We find that there is a kind of transition from all real energy spectrum to all imaginary one under open boundary conditions: the eigenvalues are all real or imaginary dependent on which amplitude of the Hermitian or non-Hermitian part is dominant even though the eigenvalues of the bulk system are complex under the periodic boundary condition. In addition, for such a non-Hermitian Hamiltonian, the left eigenvectors are the mirror symmetry of the right eigenvectors. Finally, by using the input-output formula, we show that the distribution of the boundary states can be directly observed by detecting the optical transmission in both cases.