Non-Hermitian swallowtail catastrophe revealing transitions among diverse topological singularities

Hu，Jing1; Zhang，Ruo Yang1; Wang，Yixiao1; Ouyang，Xiaoping2; Zhu，Yifei3; Jia，Hongwei1,4; Chan，Che Ting1

2023

10.1038/s41567-023-02048-w

Nature Physics   影响因子和分区

1745-2473

1745-2481

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.

SCI ; EI

英语

NI论文

通讯

Research Grants Council of Hong Kong["AoE/P-502/20","16307821","KAUST20SC01","16307621"] ; National Natural Science Foundation of China[11701263]

Physics

Physics, Multidisciplinary

WOS:000981353200003

NATURE PORTFOLIO

20231914066629

Disasters ; Eigenvalues and eigenfunctions ; Topology

Combinatorial Mathematics, Includes Graph Theory, Set Theory:921.4

2-s2.0-85158003492

Scopus

1.Department of Physics,Hong Kong University of Science and Technology,Hong Kong
2.School of Materials Science and Engineering,Xiangtan University,Xiangtan,China
3.Department of Mathematics,Southern University of Science and Technology,Shenzhen,China
4.Institute for Advanced Study,Hong Kong University of Science and Technology,Hong Kong

Hu，Jing,Zhang，Ruo Yang,Wang，Yixiao,et al. Non-Hermitian swallowtail catastrophe revealing transitions among diverse topological singularities[J]. Nature Physics,2023,19(8):1098-1103.

Hu，Jing.,Zhang，Ruo Yang.,Wang，Yixiao.,Ouyang，Xiaoping.,Zhu，Yifei.,...&Chan，Che Ting.(2023).Non-Hermitian swallowtail catastrophe revealing transitions among diverse topological singularities.Nature Physics,19(8),1098-1103.

Hu，Jing,et al."Non-Hermitian swallowtail catastrophe revealing transitions among diverse topological singularities".Nature Physics 19.8(2023):1098-1103.