Direct Measurement of Topological Properties of an Exceptional Parabola

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.

References in corpus (5)

• Making Sense of Non-Hermitian Hamiltonians
• The physics of exceptional points
• Topological Origin of Non-Hermitian Skin Effects
• Loss-induced suppression and revival of lasing
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• Realization and Topological Properties of Third-Order Exceptional Lines Embedded in Exceptional Surfaces
• Experimental Simulation of Symmetry-Protected Higher-Order Exceptional Points with Single Photons
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