Measuring topological invariants for higher-order exceptional points in quantum three-mode systems.

Owing to the presence of exceptional points (EPs), non-Hermitian (NH) systems can display intriguing topological phenomena without Hermitian analogs. However, experimental characterizations of exceptional topological invariants have been restricted to second-order EPs (EP2s) in classical or semiclassical systems. We here propose an NH multi-mode system with higher-order EPs, each of which is underlain by a multifold-degenerate multipartite entangled eigenstate. We implement the NH model by controllably coupling a Josephson-junction-based electronic mode to two microwave resonators. We experimentally quantify the topological invariant for an EP3, by mapping out the complex eigenspectra of the tripartite system along a loop surrounding this EP3 in the parameter space. The nonclassicality of the realized topology is manifested by the observed quantum correlations in the corresponding eigenstates. Our results extend research of exceptional topology to fully quantum-mechanical models with multipartite entangled eigenstates.