Anomalous Parity-Time Symmetry Transition away from an Exceptional Point

TL;DR

This paper uncovers a novel PT symmetry transition in nonlinear systems that occurs away from exceptional points, challenging the traditional understanding that such transitions must pass through these points.

Contribution

It demonstrates an anomalous PT transition in nonlinear systems where the phase change occurs away from exceptional points, supported by coupled mode theory and wave propagation examples.

Findings

PT transition occurs away from exceptional points in nonlinear systems

Two PT-symmetric trajectories can collide and vanish without passing through an exceptional point

The phenomenon is illustrated through coupled mode theory and wave propagation models

Abstract

Parity-time (PT) symmetric systems have two distinguished phases, e.g., one with real energy eigenvalues and the other with complex conjugate eigenvalues. To enter one phase from the other, it is believed that the system must pass through an exceptional point, which is a non-Hermitian degenerate point with coalesced eigenvalues and eigenvectors. In this letter we reveal an anomalous PT transition that takes place away from an exceptional point in a nonlinear system: as the nonlinearity increases, the original linear system evolves along two distinct PT-symmetric trajectories, each of which can have an exceptional point. However, the two trajectories collide and vanish away from these exceptional points, after which the system is left with a PT-broken phase. We first illustrate this phenomenon using a coupled mode theory and then exemplify it using paraxial wave propagation in a transverse periodic potential.