Abstract Over the past decade, parity‐time (PT) symmetry and anti‐PT (APT) symmetry in various physical systems have been extensively studied, leading to significant experimental and theoretical advancements. However, physical systems that simultaneously exhibit both PT and APT symmetry have not yet been explored. This study constructs a phase‐sensitive non‐Hermitian wave mixing model that inherently possesses single‐mode APT symmetry. By tuning the phase of the pump field, this model simultaneously exhibits two‐mode quadrature PT symmetry. Moreover, the APT phase transition is accompanied by the emergence of quantum entanglement from absence to presence. This remarkable quantum effect, quantum entanglement is surprisingly linked to APT symmetry phase transition, which distinguishes itself from classical physics. This work investigates the relationship between two‐mode quantum entanglement and the pump field phase, providing insights into the generation and evolution of entanglement in the nonlinear system. This provides a new perspective on quantum information processing.
Huang et al. (Tue,) studied this question.