Observation of exceptional arcs and cusp singularities in acoustics

The known fact that two singularities can be connected by geometric arcs reveals fundamental excitations of materials, such as Fermi arc and the associated interface modes. Such concepts have been generalized to non-Hermitian scenarios recently. For example, two order-2 exceptional points (EPs) are connected by the non-Hermitian Fermi arc. However, it is still an open question that which geometric structure connects two higher-order EPs. Here we demonstrate both theoretically and experimentally that it is the exceptional arc that bridges two order-3 EPs and produces the cusp singularity at the order-3 EP. The studied system is a threestate non-Hermitian system which has been realized by the ternary acoustic cavity system with dissipative losses. We show that an order-3 EP holds a fractional topological charge of 2/3. The exceptional arcs and the cusp singularity are observed in acoustic experiments. In addition, our study reveals surprising critical behaviors for both the eigenvalues and eigenvectors in the vicinity of the order-3 EP when it is approached from different directions. Our findings enrich the fundamental understanding of multi-state non-Hermitian systems and may open new opportunities for applications exploring non-Hermicity.