Higher-order exceptional lines in a non-Hermitian Jaynes-Cummings triangle

Higher-order exceptional points (EPs) in non-Hermitian systems showcase diverse physical phenomena but require more parameter space freedom or symmetries. We report the observation of a third-order exceptional surface and line in a Jaynes-Cummings triangle. A fine-tuning artificial magnetic field enriches the emergence of the third-order exceptional lines (ELs), which require only three tuning parameters when protected by parity-time (PT) symmetry. Third-order ELs maintain robust enhanced sensitivity through a cube-root response mechanism, displaying a greater sensitivity than second-order EPs. We develop a nontrivial fidelity metric based on the biorthogonal associated-state approach that reliably detects EPs while eliminating the unphysical fidelity values in previous approaches. Furthermore, our method captures quench dynamics across EPs, revealing distinct behavior in both PT-symmetric and PT-broken regimes. Our work establishes a platform for studying higher-order geometry in light-matter interactions using circuit QED.