Nonlinearly-PT-symmetric systems: spontaneous symmetry breaking and transmission resonances

TL;DR

This paper introduces a new class of PT-symmetric systems with nonlinear loss and gain, revealing unique symmetry-breaking phenomena and transmission resonances, including multistability and EIT-like effects, with potential applications in wave control.

Contribution

It presents an analytical study of nonlinear PT-symmetric dimers, uncovering new resonance behaviors and multistable states, expanding the understanding of non-Hermitian nonlinear systems.

Findings

Analytical solutions for symmetric and asymmetric eigenstates.

Discovery of novel nonlinear resonances with suppressed or amplified transmission.

Identification of EIT-like regimes in nonlinear PT-symmetric systems.

Abstract

We introduce a class of PT-symmetric systems which include mutually matched nonlinear loss and gain (inother words, a class of PT-invariant Hamiltonians in which both the harmonic and anharmonic parts are non-Hermitian). For a basic system in the form of a dimer, symmetric and asymmetric eigenstates, including multistable ones, are found analytically. We demonstrate that, if coupled to a linear chain, such a nonlinear PT-symmetric dimer generates new types of nonlinear resonances, with the completely suppressed or greatly amplified transmission, as well as a regime similar to the electromagnetically-induced transparency (EIT). The implementation of the systems is possible in various media admitting controllable linear and nonlinear amplification of waves.