Quantum-Mechanical Behavior Of Two Paul-Trapped Ions

Ion trap has been widely used in various fields of scientific and technical researches. Recently, as the development of laser-cooling technology, the ion trap has become an extensive experimental tool for making new material, observing new phenomenon and obtaining new knowledge. Esecilly, the technology of ion trap supplied experimental support for quantum compution and quantum communication theories, which imply important applications of high technology. When the trapped ions are cooled to near quantum-mechanical ground state, the system is governed by the quantum-mechanical principle and the quantum method is necessitated for invetstigating the system thereby. Although some classical and quantum dynamical characters of multi-ion systems have been investigated in the previous works, it is necessary to further study the Coulomb-correlated two-ion system, becaue of its importance.In this dissertation, two Coulomb-correlated Paul-trapped ions are treated deeply and the main results are concentrated as the following:In the first chapter, the basic principle of the Paul trap is briefly introduced, and the history, progress and development for the research of two trapped ions are presented.In the second chapter, the harmonically confined two ions in a linear trap are considered. Taking account of the Coulomb correlation between the ions and based on the known exact solutions of Schrodinger equation of the system, we establish a numerical program to calculate the expansion coffi-cients and energy eigenvalues contained in the exact solutions. By analysing the quantum-mechanical behavior of two ions, we obtain the exact quantum states with parameters in the experimental region. The results supply theoretical suggestions for the quantum logical operotions and quantum apparatus designs.In the third chapter, we extend the above-mentioned results to a planar two-ion system under the pseudopotential approximation of Paul trap. It iswell-known that the two ions can be trapped on x — y plane for the suitable parameters. We construct the exact solution of Schrodinger equation for the coplanarity two-ion system. Based on the exact solution, we show some interesting quantum phenomenons of the system, including the quantum level and state and so on. The exact solution does't depend on the other assumption and approximation, except the pseudopotential approximation. Therefore, it can describe the quantum-mechanical behavior of the Paul-trapped ion system accurately.In the last chapter, some conclusions on the work are drawed and the outlook on the quantum behavior of trapped ions are given.In the dissertation, the main works are included in chapter two and three.