# The Effect of non-Hermiticity on Adiabatic Elimination

## TL;DR

This paper explores how non-Hermitian properties affect adiabatic elimination in coupled waveguides, revealing phase-dependent validity and implications for laser cavity control and absorber design.

## Contribution

It demonstrates that adiabatic elimination remains valid in parity-time symmetric phases but fails in broken phases due to amplitude growth.

## Key findings

- Adiabatic elimination is unaffected in PT-symmetric phase.
- Broken phase causes loss of darkness, invalidating adiabatic elimination.
- Results aid in designing controllable laser cavities and absorbers.

## Abstract

We investigate the influence of non-Hermiticity on the adiabatic elimination in coupled waveguides. We show that adiabatic elimination is not affected when the system is in parity-time symmetric phase. However, in the broken phase the eliminated waveguide loses its darkness namely its amplitude starts increasing, which means adiabatic elimination does not hold in the broken phase. Our results can advance the control of the dynamics in coupled laser cavities, and help the design of controllable absorbers.