Exact solution for the motion of a particle in a Paul trap

I. A. Pedrosa

Fuli Li

A numerical method to solve the Schr\"odinger equation for a charged particle in a Paul trap is suggested. The quantum secular motion approximation is examined by comparing the exact numerical solution with the approximate result. The stability of quantum motion of the particle is discussed.

Lajos Diósi

Hai Kuo

Interaction between an external detecting field and an ion-cloud in an actual Paul trap is described by the Duffing equation.In this paper,we reported an exactly periodical solution,which reveals the dependence of the trap parameters and external field on the ion-cloud's periodical motion.The result shows that under the periodicity condition the frequency of ion's motion is one third of the frequency of detecting field,the motion amplitude is positively correlated to the frequency and amplitude of the detecting field and the trap frequency respectively,and is negatively correlated with the anharmonic parameters of the Paul trap.

Wu Yun-Wen, Hai Wen-Hua, 湖南吉首大学物理系，吉首 416000;湖南师范大学物理系，长沙 410081

We investigate the exact quantum motions of two ions in a two-dimensional Paul trap. When the Coulomb-correlation of the system is considered, we obtain a set of exact solutions of the system and the corresponding perturbed solutions, containing the exact discrete eigenstates and eigenenergies, and the approximate piecewise continuous spectra and the band structure. Taking several quantum states with lower quantum numbers as examples, we compute the average distances between two ions and give the plots of probability distribution of the two ions.

Jiaju Yin