Third-order exceptional line in a nitrogen-vacancy spin system.

Exceptional points (EPs) are singularities in non-Hermitian systems, where k (k ≥ 2) eigenvalues and eigenstates coalesce. High-order EPs exhibit richer topological characteristics and better sensing performance than second-order EPs. Theory predicts even richer non-Hermitian topological phases for high-order EP geometries, such as lines or rings formed entirely by high-order EPs. However, experimental exploration of high-order EP geometries has hitherto proved difficult due to the demand for more degrees of freedom in the Hamiltonian's parameter space or a higher level of symmetries. Here we observe a third-order exceptional line in an atomic-scale system. To this end, we use a nitrogen-vacancy spin in diamond and introduce multiple symmetries in the non-Hermitian Hamiltonian realized with the system. Furthermore, we show that the symmetries play an essential role in the occurrence of high-order EP geometries. Our approach can in future be further applied to explore high-order EP-related topological physics at the atomic scale and, potentially, for applications of high-order EPs in quantum technologies.