Laser Controlling The Exact Quantum States Of Few Trapped Ions

Ion traps have been widely used in researches of science and technology. Especially, in recent years, as a powerful method, ion traps get many extensive applications in the quantum logic operation, quantum calculation, quantum information, and the preparation of quantum states, which leads to more and more attentions focused on the dynamics of trapped ions. However, the motions of trapped ions sensitively depend on the system parameters and initial conditions. Very small variations of them can lead to large deviations of the trajectories of the ions and even force the ions into loss of the stability, which makes the motions of the ions uncontrollable. So, in this thesis, the dynamics of trapped ions 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 few trapped ions is presented.In the second chapter, we have studied the quantum and classical motions of a single ion stored in a Paul trap with a time-dependent frequency and subjected to a periodic laser field. By using test-function method, we construct n exact solutions of quantum dynamics that describes space-time evolutions of the system whose probability density behaves like the Gaussian wave-packets. By adjusting the laser intensity and frequency, we can well control the motions of the center of the wavepacket trains. We also discuss the expectation energy, which contains both the quantum and classical parts, and derive the resonance conditions from the center orbit of wavepacket train, that propose the criterionfor avoiding the resonance loss of stability.In the third chapter, we have studied the relative motion and the center-of-mass motion of two. trapped ions stored in a Paul trap and interacting with a temporal-periodic laser field. We find that the relative motion is independent of the laser field, but the center-of-mass is closely related to the laser field. By adjusting the laser intensity and frequency, we can well control the motion of the center of mass of the two trapped ion system. We still discuss that the widths and the heights of the probability wavepackets of center-of-mass and some other physical properties such as the expectation value of the energy and the transition probabilities between the quantum states of center-of-mass.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 are given.