Investigation Of Parity-Time Symmetry In A Single-ion System

PT symmetric systems,featuring real eigenvalues despite its non-Hermitian nature,undergo spontaneous PT symmetry breaking at the exceptional point(EP).The phase transition from PT symmetry to PT symmetry breaking has shown exotic functionalities in the classical realm.What are the novel phenomena and possible applications when PT symmetry breaking occurs in the quantum system?The main work of this thesis is to realize the quantum PT symmetric system and explore various physical properties of PT symmetry based on trapped ion quantum computation platform:1.We first simulate the static(Hamiltonian is time-independent)PT symmetric sys-tems.A theoretical model of a static PT symmetric system is established,and the model is realized experimentally with appropriate ion levels and laser settings(such as laser polar-ization,control timing,etc.).The experimental results show that when the PT symmetry is not broken,the quantum state oscillates with time,which is similar to the unitary evo-lution in the closed system.When the PT symmetry is broken,the quantum state evolves exponentially with time,and the evolution of the whole system tends to diverge.The PT symmetric system is successfully simulated on the trapped ion system,which provides a new candidate experimental platform for the further study of the quantum properties of the PT symmetric system.2.The spontaneous breaking of quantum PT symmetry is a quantum phase transition,the time average value of the populations of system(the energy of ion)Σ_Z(γ)and the time average value of the system quantum coherenceΣ_Y(γ)are selected as order parameters to describe the quantum phase transition.And the process from the PT symmetry non-breaking to breaking is successfully observed by using the order parameters.Compared with the observation of energy changes in the classical system to show the strange physical effects near the exceptional point(EP)of PT symmetric system,the order parameter selected in this paper can not only more accurately show the energy mutation behavior near EP,but also for the first time show the quantum coherence mutation behavior near EP.That is,the quantum coherence of the quantum system is maximized at EP.This indicates that the quantum coherence of the system near EP can be well protected,so the quantum properties of the system can be protected by PT symmetry.3.We simulate the Floquet PT symmetric system(Hamiltonian is time-dependent).Theoretically we calculate PT symmetric phase diagrams for two different types of pas-sive Floquet PT symmetric systems.Because of the periodic of the systematic Hamilto-nian,the PT symmetric unbreaking phase and PT symmetric breaking phase of the sys-tems alternate with parameter changes,which is quite different from the phase diagram of the static PT symmetric system.The dynamic evolution of the two passive Floquet PT symmetric systems is theoretically simulated and experimentally observed.It is found that the evolution characteristics of the systems are very similar in both the PT symme-try breaking phase and the unbreaking phase.The evolution of the passive systems is characterized by attenuation oscillation.Next,we study the evolution of the Floquet PT symmetric system.It is found that in the PT symmetry broken phase,the quantum states of the two Floquet PT symmetric systems may have oscillatory evolution with time in addition to exponential divergence evolution,which is completely different from the phe-nomena in the static PT symmetric system.It is not difficult to find that compared with static PT symmetric system,Floquet PT symmetric system can break PT symmetry in a smaller parameter range,which provides a design idea for new quantum sensor.4.We found that the static passive PT symmetric system corresponds to the con-tinuous measurement model in quantum measurement,and the measured system of the pulsed measurement model is exactly a Floquet PT symmetric system.The mathemati-cal form of measurement frequency and measurement intensity is successfully defined in the pulse measurement model.Therefore,it is found that whether the PT symmetry of the measured system is broken is related to the measurement frequency and measurement intensity.When the measurement frequency and intensity reach a certain degree,the PT symmetry of the measured system will spontaneously break.This work not only improves researchers’understanding of quantum measurement and symmetry,but also may inspire further research on the relationship between quantum measurement and symmetry.the PT symmetric system successfully simulated in the trapped ion system lays a foundation for the basic physics research related to PT symmetry and can also help design and utilize unconventional ion-based devices.