In quantum mechanics,the Hermiticity of the Hamiltonian ensures that the system has a purely real eigenenergy and unitary time evolution.With the study of nonHermitian theory,a class of non-Hermitian systems with PT symmetry has attracted the attention of researchers.The researchers found that non-Hermitian Hamiltonian still have real eigenvalues under the protection of PT symmetry,and it can selfconsistently construct a system of non-Hermitian PT-symmetric quantum theory.This has largely enriched the content of quantum mechanics.On the other hand,quantum information and quantum computing,as a new interdisciplinary subject formed by the interplay of quantum mechanics and classical informatics,is gradually becoming a hot research area.Because the non-classical effects generated by the interaction between quantum systems can be used as effective physical resources in the field of quantum information,the study of non-classical effects such as quantum entanglement has important theoretical research significance.In this paper,we focus on the non-classical effects such as quantum entanglement and scattering properties of coupled quantum systems with PT symmetry,and obtain some meaningful results.The main research contents and results of this paper are as follows:1.We study the PT symmetry,dynamic evolution,entanglement evolution and the atomic population inversion of the non-Hermitian double Jaynes-Cummings model with PT symmetry based on a given initial entangled state.The results show that the presence of non-Hermtian terms divides the entire parameter region into two distinct phases,and the system generates different dynamical behaviors in these two different phases.In the PT symmetry phase,stable interactions between photons and atoms occur because the system is protected by the PT symmetry.This leads to the evolution of probabilities with time in the form of Rabi oscillations and entanglement will exhibit the phenomena of "entanglement sudden death" and "entanglement sudden birth".Meanwhile,the atomic population inversion also changes periodically with time.As non Hermiticity increases,the system gradually transforms from PT symmetry phase to PT symmetry broken phase.In the PT symmetry broken phase,the probability and entanglement evolutions will tend to a certain non-zero value under appropriate parameter selection,and the atomic population inversion will eventually stabilize with time.This study can help us understand the effect of symmetry on the interaction between photons and atoms in non-Hermitian systems,and is important for achieving long-distance quantum communication,maintaining long entanglement time,and enhancing entanglement anti-interference.2.We study the scattering characteristics of single photon confined in onedimensional infinite coupled resonator waveguid with PT symmetry,where two resonators applying gain and loss are embedded with the same two-level atom respectively.By using the scattering matrix method,we find that the transmission of single photon will produce the phenomenon of complete reflection without transmission at the resonance point.Under the condition that the parameters are adjusted properly,the system will also have unidirectional invisible transmission phenomenon.As the parameters are adjusted,the system will experience a phase transition from PT symmetry phase to spontaneously PT symmetry breaking phase.In this process,we solve the exceptional points numerically and give the discriminant to judge the phase transition of the system.In the spontaneously PT symmetry breaking phase,we also find that there will be a unique phenomenon called CPA-Laser in this model.This work provides theoretical support for further study the transmission of single photon,and provides a theoretically feasible way for manufacturing quantum devices.3.We study the single photon scattering properties of a non-Hermitian AharonovBohm model modulated by magnetic flux.We generally prove that the magnetic flux gauge invariance is still satisfied in non-Hermitian system.With proper parameter adjustment,we find that the single photon transmission will produce a wide-range of unidirectional reflectioness and unidirectional invisible transmission phenomenon.The system will experience a phase transition from PT symmetry phase to spontaneously PT symmetry breaking phase.In the PT symmetry breaking phase,the synthetic magnetic flux can be used as a good method to judge the occurrence of the CPA-Laser phenomenon.This work provides relevant theoretical preparation for revealing the effect of synthetic magnetic flux on the transmission of light and provides a theoretically feasible way for the design and application of related quantum devices.4.We study quantum entanglement and quantum coherence in two coupled twolevel systems with PT symmetry in an open environment.First,we briefly introduce the master equation describing the dynamics of non-Hermitian open systems.Then,the equation is solved by matrix approach,and the analytical expressions of the timedependent density matrix,quantum entanglement and quantum coherence of the system are obtained.The results show that quantum entanglement and quantum coherence of this system can exhibit novel characteristics due to the combination of gain and loss non-Hermitian effects in non-Hermitian systems and dissipation effects in the open environment.Finally,we find that there will be a new class of higher-order exceptional points in this system.This work has some theoretical implications for the understanding and further study of non-Hermitian open systems. |