Quantum Phase Diagram of PT-Symmetry or Broken in a Non-Hermitian Photonic Structure

Classically, PT symmetry or broken in photonic structures is well studied, where only average effect of gain and loss on each optical mode is considered. However, in quantum, the role of gain or loss in a non-hermitian system is totally different, the specific quantum optical effect induced by which has never been studied. Here, we analytically obtained the PT-symmetry and PT-broken regime bounded by two exceptional lines in a bi-photonic structure with both gain and loss simultaneously existing. For the consideration of reality, the steady state condition under the weak gain is identified. We defined the exchange operator to represent the photon exchange between two modes and further to characterize the transition from PT symmetry to broken. Also, in the PT broken bi-waveguide system, multi-photon state can be on-demand engineered through the quantum interference. Quantum PT-Phase diagram with steady state regime is the basis to study the quantum state fabrication, quantum interferences, and logic operations in non-hermitian quantum systems.