Exceptional Points And Dynamics Of A Non-hermitian Twolevel System Without PT Symmetry

In quantum mechanics,the Hamiltonian of a closed quantum system is usually required to be Hermitian,which guarantees the real energy spectrum and the unitary time evolution.In fact,any realistic quantum systems are open.Under certain conditions,open quantum systems may be effectively modeled by the non-Hermitian Hamiltonians(NHHs).For this reason,the investigation of open and,in particular,nonHermitian quantum systems has been among the main topics of physics over the past two decades.A hallmark of non-Hermitian quantum systems is the occurrence of a coalescence in its eigenvalues and eigenfunctions(eigenstates)with some particular system parameters.The point where the coalescence occurs,is usually called the exceptional point(EP).The EP named by Kato,is a spectral coalescent point giving rise to a great variety of exotic physical phenomena.It may cause counterintuitive physical results which allow one to explain some puzzling experimental results.EP has been studied in various non-Hermitian quantum systems,including optomechamical systems,coupled waveguides,coupled optical microresonators,cavity magnonics systems,superconducting circuit quantum electrodynamics systems,the non-Hermitian quantum systems of Euclidean Lie algebraic type and so on.In recent years,researchers’ interest in parity-time(PT)symmetric quantum systems beyond quantum mechanics has increased significantly.Specially,the nonHermitian operators with PT symmetry can possess either complex or real eigenvalues.Besides,EP appears in particular in PT symmetric quantum system.It turns out that the parameter values where the spontaneous breaking of PT symmetry occurs are just those values where an EP of the system appears.Meanwhile,the system undergoes a quantum phase transition(QPT)from the PT symmetric phase to the PT symmetry broken phase at the EP in the parameter space,so the EP is also known as the PT symmetry phase transition point.Therefore,to construct a non-Hermitian quantum system with the most general Hamiltonian and to study the non-Hermitian characteristics of the system with and without PT symmetry,respectively,have become the core of this research topic.In this dissertation,first of all,we take the non-Hermitian two-level system without PT symmetry and with the most general Hamiltonian into account,then study the EP of the model system and the non-Hermitian two-level system with PT symmetry(PT symmetric quantum system),respectively.Afterward,the generalized definition of the phase rigidity is given,and the phase rigidity near the EP in the model system and the PT symmetric quantum system is calculated numerically,which can correctly identify the positions of EP in the parameter space.Finally,the different dynamic behaviors of the two systems are studied in turn.