Characterization of topological phases and selection of topological interface modes in the parity-time-symmetric quantum walk

We present a method to detect topological invariants in nonunitary parity-time-symmetric (PT-symmetric) quantum walks (QWs). The topological phases of a PT-symmetric QW can be characterized by the mean position of the walk, which is an experimentally observable quantity. This method can also be applied to reveal topological phases in the unitary split-step QW and lattice model. We also explore the selection of topological interface modes in the PT-symmetric QW. The introduction of nonunitarity into the PT-symmetric QW can render the eigenvalue of the topological interface mode larger than the bulk region modes, which leads to the selective excitation of the corresponding topological interface mode during the evolution. Contrary to the Su-Schrieffer-Heeger (SSH) lattice model, in the PT-symmetric QW, the transition between the amplification and the suppression of the topological interface mode may not occur. Our study of the selection of topological interface modes in the PT-symmetric QW provides a route to realize the lasing of specific modes within the system.