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

Abstract

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.