Non-Hermitian swallowtail catastrophe revealing transitions among diverse topological singularities

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.

Automated summary

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.