Raising the $\mathcal{PT}$ transition threshold by strong coupling to neutral chains

TL;DR

This paper demonstrates that coupling $ ext{PT}$ symmetric systems to multiple neutral chains significantly raises the symmetry-breaking threshold, offering new ways to engineer $ ext{PT}$ properties in experiments.

Contribution

It introduces a method to increase the $ ext{PT}$ transition threshold by strongly coupling to neutral chains, supported by analytical and numerical analysis.

Findings

Threshold increases proportionally with the number of neutral chains.

Adding neutral sites more than doubles or triples the $ ext{PT}$ threshold.

The approach provides a practical way to enhance $ ext{PT}$ symmetry stability.

Abstract

The $\mathcal{PT}$ symmetry breaking threshold in discrete realizations of systems with balanced gain and loss is determined by the effective coupling between the gain and loss sites. In one dimensional chains, this threshold is maximum when the two sites are closest to each other or the farthest. We investigate the fate of this threshold in the presence of parallel, strongly coupled, Hermitian (neutral) chains, and find that it is increased by a factor proportional to the number of neutral chains. We present numerical results and analytical arguments for this enhancement. We then consider the effects of adding neutral sites to $\mathcal{PT}$ symmetric dimer and trimer configurations and show that the threshold is more than doubled, or tripled by their presence. Our results provide a surprising way to engineer the $\mathcal{PT}$ threshold in experimentally accessible samples.