The Spectral Role of Quantum Jumps for Atomic Open Systems

Non-Hermitian quantum physics provides a powerful framework for describing dynamics in open quantum systems, predicting striking phenomena such as exceptional and diabolical points. These effects are typically modeled using non-Hermitian Hamiltonians (NHHs), which have been successfully applied in platforms ranging from photonics to superconducting qubits, and are now being extended to atomic systems.
However, we show that for atomic open systems, NHHs alone fail to capture the full spectral structure. Using an effective-operator approach, we compare spectra obtained from NHHs and the full Liouvillian superoperator. This allows us to identify and contrast Hamiltonian and Liouvillian exceptional points, as well as diabolical points.
Our results reveal that quantum jumps are not a correction but a qualitatively essential ingredient. Their inclusion fundamentally reshapes the spectrum, leading to features that are entirely absent in the NHH description. Finally, we show that the hybrid-Liouvillian formalism provides a natural interpolation between the non-Hermitian Hamiltonian and full Liouvillian descriptions. This approach enables a unified treatment of partially non-conserving systems, capturing how quantum jumps progressively modify and complete the spectral structure beyond the NHH picture.