Gaussian Laser-manipulating Quantum States Of A Trapped Ion

With the development and mature of ion trap technology,ion trap technol-ogy has important applications in the preparation of quantum states,quantum information and quantum computing,proteomics analysis and drug metabolism and mass spectrometry technology and so on.Since people are not content with the study of the control problem of the center of mass of the trapped particles,they begin to make use of the interaction between the ions and the light field to precisely manipulate the internal electronic states and vibration quantum states of trapped ions,so as to realize the relevant tasks of quantum information processing.The development of laser-shaping technology and the research on the effectiveness of ultrashort laser pulses controlling the microscopic system make the manipula-tion of the ions possible.At present,many literatures have studied the spin and topological states of the quantum states in the semiconductor by using the ultra short and ultra fast laser pulses.Especially in recent years,the development of technologies of laser cooling and laser trapping atoms have been more mature and widely used in various fields of science and technology studies.Since people have shown a keen interest in the manipulation of quantum states,in this paper we try to apply the Gauss laser pulses to the trapped ion system,hoping to find the effective parameters of ion manipulation to realize the transfer of ionic state.This paper consists of four chapters.The first chapter is the introduction in which we briefly introduce the basic principle of Paul trap and the review of the trapped ion system.Then,the Gaussian laser simulation method of Delta potential is introduced.In chapter two,we consider the situation of stationary state and concretely study the dynamics of the single ions trapped in the ion trap under the action of Gauss laser pulse.By using the quantum perturbation,we obtain the exact solution of the perturbation Schrodinger equation under the Gauss laser,and the first order correction of the energy and wave function of the harmonic oscillator are given.It is found that the spatial positions of Gauss laser beams have some effects on energy and wave functions,and different laser positions correspond to different quantum states.In chapter three,we consider the situation of adding Gauss laser pulse within a certain time interval T and by regulating the spatial location of the Gauss laser pulse,we calculate the size of transition probabilities.We can find that when Gauss laser is aligned with different spatial positions,the transition probabilities of particle between various energy levels are different.In a particular region,the transition probability of ions from the ground state to the second excited state is much bigger than that of the transition from ground state to the first excited state.We spread the results to another condition.When the position of laser pulse is fixed,the transition probabilities vary periodically with the time of laser action,meanwhile the periods of transition probabilities are different between ground state and different excited states,and the higher energy level of the excited state is,the smaller period is.It is also interesting to find that the spatial positions of the maximum probability of transition does not change with the length of laser action time.In chapter four,a brief induction and summary of our research work and fu-ture perspective about the dynamics of laser manipulating ions are given.