# Experimental observation of exceptional surface in synthetic dimensions with magnon polaritons

## TL;DR

This paper reports the first experimental observation of a three-dimensional exceptional surface in a magnon polariton system, revealing new high-dimensional control possibilities in non-Hermitian physics.

## Contribution

It demonstrates the formation of an exceptional surface and saddle point in a synthetic four-dimensional space using magnon polaritons, a novel experimental achievement.

## Key findings

- Observation of a three-dimensional exceptional surface
- Identification of an exceptional saddle point with anisotropic properties
- First experimental realization of high-dimensional non-Hermitian control

## Abstract

Exceptional points (EPs) are singularities of energy levels in non-Hermitian systems. In this Letter, we demonstrate the surface of EPs on a magnon polariton platform composed of coupled magnons and microwave photons. Our experiments show that EPs form a three-dimensional exceptional surface (ES) when the system is tuned in a four-dimensional synthetic space. We demonstrated that there exists an exceptional saddle point (ESP) in the ES which originates from the unique couplings between magnons and microwave photons. Such an ESP exhibits unique anisotropic behaviors in both the real and imaginary part of the eigenfrequencies. To the best of our knowledge, this is the first experimental observation of ES, opening up new opportunities for high-dimensional control of non-Hermitian systems.