Dynamics Of A Single Trapped Ion Interacting With Laser

Ion traps have been widely used in researches of science and technology. Especially, in recent years, as a powerful method, ion traps get an extensive application in the quantum logic operation , quantum calculation, quantum information and the preparation of quantum states, which leads to more and more attention focused on the dynamics of trapped ions. However, the motion of trapped ions sensitively depends on the system parameters and initial conditions. Very small variations of them can lead to large deviation of the trajectories of the ions and even force the ions into chaotic motion, which makes the motion of the ions uncontrollable. So, in this thesis, the chaotic dynamics of a single trapped ion and the corresponding quantum-mechanical treatment are investigated more extensively. The main contents is presented as follows:In the first chapter, the basic principle of the paul trap is briefly introduced , and the history and progress on the researches of single trapped ions is presented.In the second chapter, we study the secular motion of a single ion stored in a Paul trap and subjected to a sequence of standing laser pulses. Through theoretical analyses and numerical calculations, we obtain an exact solution of the classical motion equation that describes time evolution of the system. By using the exact solution we investigate regular and chaotic motion of the system. For a weakly trapped ion with small confining frequency, a critical condition under which the system going into global chaos is found. The loss of stability caused by the resonance is shown and a method for controlling the instability is established. In the third chapter, the system of the trapped ion is studied quantum-mechanically. Theoretical analyses and numerical calculations show that, in the first-order approximation, the classically chaotic character disappears; and that there exist a rule for the transition between different motional states of the traaped ion. It is also revealed that, by regulating the phase parameter, the transition probability can be controlled. The time-evolution of an initial motional state just over one period is also studied in detail. In the fourth chapter, some conclusive remarks on the work presented in this thesis and the outlook on the prospect for the dynamics of trapped ions...