# Symmetry recovery of exceptional points and their dynamical encircling in a two-state system

## TL;DR

This paper demonstrates that a two-state ferromagnetic waveguide system can exhibit exceptional points and symmetry recovery due to accidental degeneracies, with controllable encircling of these points revealing topological and chiral effects through microwave experiments.

## Contribution

It introduces a novel two-state system with controllable exceptional points and symmetry recovery, enabling exploration of topological phenomena in a simple lossless setup.

## Key findings

- Experimental confirmation of exceptional points in a two-state system.
- Observation of symmetry recovery due to accidental degeneracies.
- Demonstration of topological and chiral effects via dynamical encircling.

## Abstract

Exceptional points are degeneracies in non-Hermitian systems. A two-state system with parity-time (PT) symmetry usually has only one exceptional point beyond which the eigenmodes are PT-symmetry broken. The so-called symmetry recovery, i.e., eigenmodes become PT-symmetric again, typically occurs in multi-state systems. Here we show that a two-state ferromagnetic waveguide system can have an exceptional point and a subsequent symmetry recovery due to the presence of accidental degeneracy points when the system is lossless. By introducing a parameter space where both exceptional points reside, we designed a system in which the trajectory in the parameter space can be controlled in situ using an adiabatically tunable external field, allowing us to explore the topological and chiral character of the system by encircling zero, one or two exceptional points. We performed microwave experiments to demonstrate the presence of the exceptional point, symmetry recovery, and the effects arising from their dynamical encircling.

---
Source: https://tomesphere.com/paper/1701.03640