Quantum Movement Of Two Captive Ions

Ion traps have a wide range of applications in various areas of science and technology.Many quantum systems have been incorporated as the basic framework of quantum computer.One of the most feasible quantum system is ion trap, which plays an important role in the realization of qubits, quantum gate and quantum memory in quantum information processing. While the development of ion storage and laser cooling reach to the extent that trapped ions can be cooled to very low temperatures, which make the ion’s movement reach to the ground state of quantum mechanics, quantum theory is adapted to this system. Classical and quantum research of multiple-ion systems have made fruitful achievements, but the research on single or a few ions still plays an fundamental and important role in the further study of more complex systems. This paper focus on the study of quantum motion of two trapped ions.The main contents are as follows: The first chapter: the basic structure and principal of Paul trap, quantum motion of a single particle in a Paul trap and votex included in the third chapter are briefly introduced.The second chapter: the research focus on the quantum motion of two coulombrelated ions in a linear Paul trap, the main purpose of which is to reduce the applied frequency of relative motion of two trapped ions when being cooled to low quantum states. The method used here is the application of high frequency time-varying harmonic potential.A recombination frequency is obtained via the use of high frequency approximation, which has been reduced for about one order of magnitude when compared with the case of without high frequency time-varying potential. The expectation value of the distance between two ions has been calculated and we have discussed the relationship between expectation value and the relative quantum number, which provide some theoretical reference for the cooling of two trapped ions.The third chapter: we investigate the exact votex solution of a charged particle pair in a two dimensional Paul trap. Probability density plot of wave function of relation motion are plotted according to the exact votex solution which have already been obtained before and the nature of votex have been analyzed, which may enrich the theoretical study of the system to some extent.The forth chapter: we briefly summary the work we have done and give a outlook of the future research direction.