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

Area of Science:

• Quantum physics
• Non-Hermitian systems
• Topological phenomena

Background:

• Non-Hermitian systems exhibit unique topological phenomena linked to exceptional points (EPs).
• Experimental studies of topological invariants in EPs have been limited to second-order EPs (EP2s) in classical or semiclassical systems.

Purpose of the Study:

• To propose and experimentally realize a non-Hermitian multi-mode system featuring higher-order EPs.
• To investigate the topological invariants associated with these higher-order EPs in a quantum mechanical context.
• To explore the nature of multipartite entangled eigenstates underlying these phenomena.

Main Methods:

• Implementation of a non-Hermitian model using a Josephson-junction-based electronic mode coupled to two microwave resonators.
• Experimental quantification of the topological invariant for a third-order exceptional point (EP3).
• Mapping of complex eigenspectra around the EP3 in parameter space.

Main Results:

• Successful realization of a non-Hermitian system with higher-order EPs.
• Experimental quantification of the topological invariant for an EP3.
• Observation of multipartite entangled eigenstates and quantum correlations, confirming nonclassical topology.

Conclusions:

• The study extends the understanding of exceptional topology to fully quantum-mechanical models.
• Demonstrates the feasibility of characterizing higher-order EPs and their associated topological invariants in quantum systems.
• Highlights the role of multipartite entanglement in non-Hermitian topological phenomena.