Systems that become $\cal{PT}$ symmetric through interaction

TL;DR

This paper investigates how interaction-induced $ ext{PT}$ symmetry in optical systems influences their dynamics, especially focusing on non-reciprocal behavior and symmetry breaking bifurcations, comparing with traditional loss-gain $ ext{PT}$ symmetric systems.

Contribution

It introduces and analyzes a class of $ ext{PT}$ symmetric systems where interaction induces symmetry, highlighting their non-reciprocal properties and symmetry breaking phenomena.

Findings

Interaction can induce $ ext{PT}$ symmetry in systems.

Non-reciprocal behavior is not universal in $ ext{PT}$ systems.

Symmetry breaking bifurcations occur in both reciprocal and non-reciprocal $ ext{PT}$ systems.

Abstract

In this article, we consider an interesting class of optical and other systems in which the interaction or coupling makes the systems to be $\cal{PT}$-symmetric. We aim to compare their dynamical behaviors with that of the usual $\cal{PT}$ symmetric systems with intrinsic loss-gain terms. In particular, we focus on the interesting non-reciprocal nature of the $\cal{PT}$ symmetric systems which has a promising application in optical diodes and optical isolators. We check whether the non-reciprocal nature is common to all $\cal{PT}$ symmetric systems and, if not, what are the situations under which it can be observed. Due to the recent interest in studying spontaneous symmetry breaking in coupled waveguide systems, we here present such symmetry breaking bifurcations in certain reciprocal and non-reciprocal $\cal{PT}$ symmetric systems.