Direct Measurement of Topological Properties of an Exceptional Parabola

TL;DR

This paper experimentally investigates the topological properties of an exceptional parabola in non-Hermitian systems, revealing complex invariants like discriminant numbers and Berry phases through acoustic measurements.

Contribution

It provides the first experimental measurement of both discriminant numbers and Berry phases along a parabola-shaped EP trajectory in non-Hermitian systems.

Findings

EP trajectory has a non-trivial fundamental group with two non-homotopic classes

Eigenvalues and eigenfunctions measured to determine topological invariants

Experimental characterization of non-Hermitian topological invariants achieved

Abstract

Non-Hermitian systems can produce branch singularities known as exceptional points (EPs). Different from singularities in Hermitian systems, the topological properties of an EP can involve either the winding of eigenvalues that produces a discriminant number (DN) or the eigenvector holonomy that generates a Berry phase. The multiplicity of topological invariants also makes non-Hermitian topology richer than its Hermitian counterpart. Here, we study a parabola-shaped trajectory formed by EPs with both theory and acoustic experiments. By obtaining both the DNs and Berry phases through the measurement of eigenvalues and eigenfunctions, we show that the EP trajectory endows the parameter space with a non-trivial fundamental group consisting of two non-homotopic classes of loops. Our findings not only shed light on exotic non-Hermitian topology but also provide a route for the experimental characterization of non-Hermitian topological invariants.