Transmission phase lapse in the non-Hermitian Aharonov-Bohm interferometer near the spectral singularity

TL;DR

This paper investigates how PT-symmetric imaginary potentials in an Aharonov-Bohm interferometer influence transmission phases, revealing spectral singularities at specific momenta and phase jumps, with implications for quantum interference control.

Contribution

It provides an exact solution showing the occurrence of spectral singularities at specific conditions and analyzes the associated critical behavior and phase lapses in a non-Hermitian quantum system.

Findings

Spectral singularity occurs at k=±π/2 for various fluxes and potentials.

Transmission phase jumps by π at the spectral singularity.

Pulse-like phase lapse appears near the spectral boundary.

Abstract

We study the effect of PT-symmetric imaginary potentials embedded in the two arms of an Aharonov-Bohm interferometer on the transmission phase by finding an exact solution for a concrete tight-binding system. It is observed that the spectral singularity always occurs at k=${\pm}${\pi}/2 for a wide range of fluxes and imaginary potentials. Critical behavior associated with the physics of the spectral singularity is also investigated. It is demonstrated that the quasi-spectral singularity corresponds to a transmission maximum and the transmission phase jumps abruptly by {\pi} when the system is swept through this point. Moreover, We find that there exists a pulse-like phase lapse when the imaginary potential approaches the boundary value of the spectral singularity.