A characteristic feature of non-Hermitian systems is the presence of exceptional points, where eigenvalues and eigenstates coalesce. Additionally, non-Hermitian systems can exhibit a richer degeneracy morphology known as the swallowtail catastrophe. In this study, the authors demonstrate the existence of the swallowtail catastrophe in non-Hermitian systems with both parity-time and pseudo-Hermitian symmetries, and experimentally observe its degeneracy features.
A characteristic feature of non-Hermitian systems is an exceptional point at which eigenvalues and eigenstates coalesce. They also support richer degeneracies-a swallowtail catastrophe-that reveals transitions among three different types of singularity. Exceptional points are a unique feature of non-Hermitian systems at which the eigenvalues and corresponding eigenstates of a Hamiltonian coalesce. Many intriguing physical phenomena arise from the topology of exceptional points, such as bulk Fermi arcs and the braiding of eigenvalues. Here we report that a structurally richer degeneracy morphology, known as the swallowtail catastrophe in singularity theory, can naturally exist in non-Hermitian systems with both parity-time and pseudo-Hermitian symmetries. For the swallowtail, three different types of singularity exist at the same time and interact with each other-an isolated nodal line, a pair of exceptional lines of order three and a non-defective intersection line. Although these singularities seem independent, they are stably connected at a single point-the vertex of the swallowtail-through which transitions can occur. We implement such a system in a non-reciprocal circuit and experimentally observe the degeneracy features of the swallowtail. Based on the frame rotation and deformation of eigenstates, we further demonstrate that the various transitions are topologically protected.
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