PT-symmetry breaking for the scattering problem in a one-dimensional non-Hermitian lattice model

Abstract

We study the PT -symmetry breaking for the scattering problem in a one-dimensional (1D) nonHermitian 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 PT -symmetry phase to the phase with spontaneously breaking 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 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 PT -symmetric potentials.

PT-symmetric slowing down of decoherence

“…It expresses how systems remain unaffected by perturbations [4]. Therefore, a violation of symmetry (or its breakdown [5]) constitutes an irreplaceable source of valuable information regarding properties of physical systems [6][7][8]. There is an abundance of useful transformations providing necessary ingredients to understand and investigate quantum systems.…”

Unidirectional perfect absorber

“…Reciprocal transmissions are found in -symmetric optical structures 36 37 , in which the symmetry protects these reciprocal (symmetric) transmissions 46 47 48 49 50 . By applying the Aharonov-Bohm (AB) effect in dissipative optical systems, nonreciprocal (asymmetric) transmissions have been proposed 51 52 , where the magnetic field breaks the time-reversal symmetry and the reciprocality of light propagation.…”

Non-Hermitian scattering on a tight-binding lattice

“…In this work, we are concerned with the non-Hermitian physics of a quantum particle on a tight-binding lattice. Previous studies of non-Hermitian effects for a lattice particle include Anderson localization [49][50][51] and localization in quasiperiodic potentials [52,53], invisibiltiy (reflectionless scattering) due to non-Hermitian hopping [54] or oscillating imaginary scatterer [55], flatband physics [56], Bloch oscillations [57], PT symmetry obtained by combining an absorbing potential on one site with an emitting potential on another [58][59][60][61][62][63][64], etc. In addition, non-Hermitian tight-binding lattices form the basis of the study of non-Hermitian topological many-body systems, a topic of rapidly growing interest [65,66].…”