Research teams led by Academician DU Jiangfeng and Prof. RONG Xing from CAS Key Laboratory of Microscale Magnetic Resonance of University of Science and Technology of China (USTC) have systematically studied the relations between symmetries and high-order non-Hermitian exceptional points (EPs), and observed the third-order exceptional line (EL) in a nitrogen-vacancy (NV) spin system.

EPs are singularities in non-Hermitian systems, where there are 2 or more eigenvalues and eigenstates coalesce. Many exotic topological phenomena and novel dynamic features occur thanks to the unique characteristics of EPs. EPs have played an essential role in understanding edge-cutting areas like quantum computing and topological phase transitions.

High-order EPs exhibit richer topological characteristics and better sensing performance than second-order EPs. However, to realize high-order EPs is rather difficult since it relies on the simultaneous tuning of multiple system parameters, and the higher the order of the EPs, the more system parameters need to be tuned simultaneously, making the realization process challenging.

Researchers have utilized a single NV center, an atomic-scale defect in diamond, and the nuclear spin system to realize the non-Hermitian systems which embrace both PT symmetry and pseudochirality. Furthermore, the experimental observation of third-order EL in two-dimensional parameter space was reported.

By systemically investigating the role of symmetry in high-order EP geometries, researchers revealed that third-order EPs can exist as isolated points when there was only PT symmetry in the non-Hermitian Hamiltonian.

Researchers further explored the relationship between the third-order EPs and the symmetries of the non-Hermitian Hamiltonians. It turned out that there was no third-order EP when the non-Hermitian Hamiltonian has no symmetry, which exhibited the importance of symmetries in studying the structure of high-order EPs.

It was worth mentioning that the successful observation of high-order EP geometries benefited a lot from the former studies in diamonds. Prof. WANG Ya, in particular, has been devoted in synthesis and production of high-quality diamonds for many years, which has laid a solid foundation for this work.

This work is of fundamental importance to non-Hermitian studies, on the one hand, it can be further applied to explore high-order EP-related topological physics at the atomic scale, and on the other, to shed light for the quantum control and quantum-enhanced metrology.