Observation of knot topology of exceptional points

Exceptional points (EPs), which refer to degeneracies in non-Hermitian systems, have garnered significant attention in the last few years due to their potential applications in the fields of sensing, single-mode lasing, and others. Recently, the complete classification of isolated EPs based on homotopy theory has been proposed, where the topology of energy spectra around EPs can be fully characterized by the braiding group and knot topology. However, there have been few experimental observations of EPs with different knot topologies due to the need for tunable, nonlocal, and nonreciprocal couplings in the proposed non-Hermitian lattice model. Here, we report experimental observation of EPs with different types of knots/links by non-Hermitian electric circuits with voltage-tunable node couplings. Specifically, a second-order EP with trefoil knot topology and a third-order EP with 633 link topology (according to Rolfsen's table) are achieved. Moreover, we also provide a method on the construction of higher-order Dirac EPs with nested-link topologies, and experimentally construct a sixth-order Dirac EP. Our work provides an artificial platform for exploring EPs with knot and link topologies, offering potential applications in designing EP-based electronic devices.