Tunable Localisation in Parity-Time-Symmetric Resonator Arrays with Imaginary Gauge Potentials

TL;DR

This paper explores how tuning gain and loss in parity-time symmetric resonator arrays with imaginary gauge potentials can control localization and phase transitions, revealing new topological and non-Hermitian phenomena.

Contribution

It introduces a combined analytical and numerical study of non-Hermitian effects in subwavelength resonator arrays, demonstrating controllable phase transitions and topological state changes.

Findings

Eigenmode decoupling at exceptional points

Transition from unbroken to broken PT symmetry

Edge-localized condensated eigenmodes

Abstract

The aim of this paper is to illustrate both analytically and numerically the interplay of two fundamentally distinct non-Hermitian mechanisms in a deep subwavelength regime. Considering a parity-time symmetric system of one-dimensional subwavelength resonators equipped with two kinds of non-Hermiticity - an imaginary gauge potential and on-site gain and loss - we prove that all but two eigenmodes of the system decouple when going through an exceptional point. By tuning the gain-to-loss ratio, the system changes from a phase with unbroken parity-time symmetry to a phase with broken parity-time symmetry. At the macroscopic level, this is observed as a transition from symmetrical eigenmodes to condensated eigenmodes at one edge of the structure. Mathematically, it arises from a topological state change. The results of this paper open the door to the justification of a variety of phenomena arising from the interplay between non-Hermitian reciprocal and non-reciprocal mechanisms not only in subwavelength wave physics but also in quantum mechanics where the tight binding model coupled with the nearest neighbour approximation can be analysed with the same tools as those developed here.