Complex Berry phase instability in PT-symmetric coupled waveguides

TL;DR

This paper investigates how the geometric phase in PT-symmetric coupled waveguides can become purely imaginary, leading to instabilities that are amplified near exceptional points and cause early PT-symmetry breaking.

Contribution

It reveals that the geometric phase in non-Hermitian PT-symmetric systems can be imaginary, linking it to system instabilities and non-adiabatic effects near exceptional points.

Findings

Instability peaks correspond to the spectrum of the derivative of the geometric function.

Instabilities are magnified near the exceptional point.

PT-symmetry breaks earlier than predicted due to non-adiabatic effects.

Abstract

We show that the analogue of the geometric phase for non-Hermitian coupled waveguides with PT-symmetry and at least one periodically varying parameter can be purely imaginary, and will consequently result in the manifestation of an instability in the system. The instability peaks seen in the spectrum of the system's eigenstates after evolution along the waveguides can be directly mapped to the spectrum of the derivative of the geometric function. The instabilities are magnified as the exceptional point of the system is approached, and non-adiabatic effects begin to appear. As the system cannot evolve adiabatically in the vicinity of the exceptional point, PT-symmetry will be observed breaking earlier than theoretically predicted.