Quasi Parity-time Symmetric Dynamics And Spin Josephson Effect In Non-Hermitian Systems

For non-Hermitian systems satisfying Parity-Time(PT)symmetry,there exist a real energy spectrum like that of the Hermitian system,thus ensuring the observability of the energy.Studying PT-symmetric properties in nonHermitian systems,on the one hand,extend the traditional Hermitian quantum theory and are closely related to open or dissipative systems;on the other hand,semi-classical or quantum systems with novel non-Hermitian properties could be constructed,for example,the equivalent PT-symmetric quantum Hamiltonian are successfully constructed in the experimental platform of quantum systems such as photons,cold atoms,and ion traps.Based on the previous works,this paper focuses on the PT symmetry and spin-related tunneling dynamics in two-level non-Hermitian open systems and double-well non-Hermitian open systems.The main contents are as follows:The article briefly present the development of non-Hermitian PT symmetric systems and related experiments,identify the theoretical basis required for this paper,and accomplish the following:(1)quasi-PT symmetric dynamics in periodically driven two-level non-Hermitian system.By phase-space analysis find that there exist so-called pseudo fixed points in phase space representing the Floquet solutions.According to these pseudo fixed points,we analytically construct a non-unitary evolution operator and then explore the dynamic behaviors of the non-PT-symmetric two-level quantum system in different parameter regions.We confirm both analytically and numerically that the two-level non-Hermitian Floquet quantum system,still features a phase transition with the quasi-energy spectrum changing from all-real to all-complex energy spectrum,just like the PT symmetric systems.Furthermore,we reveal that a novel phenomenon called quasi-PT symmetric dynamics occurs in the time evolution process.(Ⅱ)Spin Josephson effects of spin-orbit-coupled Bose-Einstein condensates in a non-Hermitian double well.Under high-frequency driving,we obtain the effective time-averaged Hamiltonian by using the standard timeaveraging method,and analytically calculate the quasienergies,revealing that PT-symmetry-breaking phase transition appears even for arbitrarily small non-Hermitian parameters when the spin-orbit coupling strength takes half-integer value,irrespective of the values of other parameters used.At the same time,we also find that the spin Josephson effects(total atomic current can be zero,which leads to a pure spin current)still exists in the broken PT-symmetric phase of the system.Finally,we make a summary of the thesis and make a prospect for future research work.