Universal Quantum Fisher Information and Simultaneous Occurrence of Landau-Class and Topological-Class Transitions in Non-Hermitian Jaynes-Cummings Models

Light-matter interactions provide an ideal testground for interplay of critical phenomena, topological transitions, quantum metrology, and non-Hermitian physics with high controllability and tunability. The present work considers two fundamental non-Hermitian Jaynes-Cummings models in light-matter interactions that possess real energy spectra in parity-time (PT) symmetry and anti-PT symmetry. The quantum Fisher information is shown to be critical around the transitions at the exceptional points and exhibit a super universality, with respect to different parameters, all energy levels, both models, symmetric phases, and symmetry-broken phases, which guarantees a universally high measurement precision in quantum metrology. In particular, the transitions are found to be both symmetry-breaking Landau-class transitions (LCTs) and symmetry-protected topological-class transitions (TCTs), thus realizing a simultaneous occurrence of critical LCTs and TCTs that are conventionally incompatible due to contrary symmetry requirements. Besides establishing a paradigmatic case to break the incompatibility of the LCTs and the TCTs in non-Hermitian systems, the both availabilities of the sensitive critical feature and the robust topological feature can also provide more potential for designing quantum devices or sensors.