Quantum transport in non-Hermitian impurity array

Abstract

We study the formation of band gap bound states induced by a non-Hermitian impurity embedded in a Hermitian system. We show that a pair of bound states emerges inside the band gap when a parity-time ($\mathcal{P}\mathcal{T}$) imaginary potential is added in a strongly coupled bilayer lattices and the bound states become strongly localized when the system approaches to the exceptional point (EP). As a direct consequence of such $\mathcal{P}\mathcal{T}$ impurity-induced bound states, an impurity array can be constructed and protected by energy gap. The effective Hamiltonian of the impurity array is non-Hermitian Su-Schrieffer-Heeger (SSH) type and hosts Dirac probability-preserving dynamics. We demonstrate the conclusion by numerical simulations for the quantum transport of wave packet in right-angle bends waveguide and $Y$-beam splitter. Our finding provides alternative way to fabricate quantum device by non-Hermitian impurity.

10 pages, 6 figures

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