Time-dependent perturbation theory approach to the quantum motion of a particle in a Paul trap.

Abstract

The main objective of this study is to investigate the quantum mechanical lifetime of a trapped ion in a Paul trap. The motivation for this research is that there are several applications of trapped ion devices such as mass spectrometers, atomic clocks, and quantum computers. Active research is presently ongoing in the subject of an ion trapping by electric and magnetic fields. There are many classical studies of the characteristics of trapped ions, however there have been relatively few done quantum mechanically. It might be expected that purely quantum effects could play an important role in describing the trapped ions. So, those are the main factors behind the research on this topic. Time-dependent perturbation theory was used in this study which is to find the quantum mechanical lifetime of trapped ion in a Paul trap because time-dependent perturbation theory allows describing the complex system with the help of a simple system that can be calculated easily. It is shown that the lifetime of a trapped ion depends on its transition frequency and the transition between two allowed quantum states of the ion. The transition frequency of an ion has to be very close to the applied frequency of alternating current (AC). The results show that the lifetime of a trapped ion can be adjusted as desired for experimentation.