$\mathcal{PT}$ symmetry breaking for the scattering problem in a one-dimensional non-Hermitian lattice model

TL;DR

This paper investigates the $ ext{PT}$-symmetry breaking transition in a 1D non-Hermitian lattice with balanced gain and loss, deriving an exact discriminant and identifying the exceptional point, revealing phenomena like coherent perfect absorption laser.

Contribution

The study provides an exact analytical discriminant for $ ext{PT}$-symmetry breaking and identifies the exceptional point in a simple 1D non-Hermitian lattice model.

Findings

Identified the exceptional point for symmetry breaking.

Derived an exact discriminant to distinguish symmetry phases.

Confirmed the occurrence of coherent perfect absorption laser.

Abstract

We study the $\mathcal{PT} $-symmetry breaking for the scattering problem in a one-dimensional (1D) non-Hermitian tight-binding lattice model with balanced gain and loss distributed on two adjacent sites. In the scattering process the system undergoes a transition from the exact $\mathcal{PT} $-symmetry phase to the phase with spontaneously breaking $\mathcal{PT} $-symmetry as the amplitude of complex potentials increases. Using the S-matrix method, we derive an exact discriminant, which can be used to distinguish different symmetry phases, and analytically determine the exceptional point for the symmetry breaking. In the $\mathcal{PT} $-symmetry breaking region, we also confirm the appearance of the unique feature, i.e., the coherent perfect absorption Laser, in this simple non-Hermitian lattice model. The study of the scattering problem of such a simple model provides an additional way to unveil the physical effect of non-Hermitian $\mathcal{PT} $-symmetric potentials.