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Hu'nan Shifan Daxue xuebao. Ziran kexue ban

Local Motion of an Ion Manipulated by Laser in a Double-rf Paul Trap

Shuanwen Jia

Published Jan 1, 2013• 0 citations
OpenAlex

Abstract

An exact solution of the Schrodinger equation for the system is constructed.It is found that when the ratio of the driving frequency to the radio frequency is equal to certain discrete values,the double-rf Paul trap exists stable spatially localized states.This phenomenon is similar to the dynamic localization of a particle on a discrete lattice reported by Dunlap and Kenkre in 1986.However,the conditions for the latter case deal with the ratio of the field magnitude to the field frequency.The results of our calculations demonstrate a new category concerning the dynamic localization.

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An exact solution of the Schrodinger equation for the system is constructed.It is found that when the ratio of the driving frequency to the radio frequency is equal to certain discrete values,the double-rf Paul trap exists stable spatially localized states.This phenomenon is similar to the dynamic localization of a particle on a discrete lattice reported by Dunlap and Kenkre in 1986.However,the conditions for the latter case deal with the ratio of the field magnitude to the field frequency.The results of our calculations demonstrate a new category concerning the dynamic localization.
Due to an infinite series solution of the classical Mathieu equation, using single-radio-frequency (rf) driving makes it difficult to manipulate motional states of a Paul-trapped ion. Here, we apply double-rf driving consisting of two external fields to generate the squeezed coherent states of simple forms. Stability parameter regions of the system are found in which both the first and second rf fields may be very strong but only the latter can be weak. Based on exact solutions, we investigate the time evolutions of expectation energies and controllable transitions between not only two stationary states, but also two nonstationary states. Such a quantum-control scenario may be tested experimentally.
We consider the stability of systems subjected to periodic parametric driving such that their equations of motion are ordinary differential equations with periodic coefficients and carry out a detailed analysis of important aspects of such systems in the context of the confinement of ions by oscillating electric fields. We show how they can be understood in terms of a pseudopotential approximation and resonances arising from the parametric excitation and investigate the properties of a novel linear Paul trap configuration operating with two radio-frequencies to simultaneously confine two species with extremely different charge-to-mass ratios. The theoretical calculations have been verified by molecular dynamics simulations and normal modes analysis.
We present a theoretical study of trapping an electron in a two-frequency Paul trap, motivated by future hybrid architecture consisting of a doubly charged calcium ion (Ca2+^{2+}2+) and an electron. By isolating the electron from ionic-electron interactions, we formulate the equations of motion for the electron in the time-dependent trap potentials and cast them in the Hill form. Stability and dynamics are then analysed in terms of the dimensionless q-parameters, which encode the applied voltages, drive frequencies, trap geometry, and the particle's charge-to-mass ratio. Under the combined action of the two radio-frequency fields, the trapped electron's classical motion is shown to be approximated well by a slow secular oscillation modulated by two distinct motion sidebands originating from the low- and high-frequency RF drives. The approximation method presented here enables a quick evaluation of the relation between the device-design q-parameters and the electron motion. It offers a crucial foundation for developing physical models of electron-ion interactions in electron-ion traps.