Analysis of Multipolar Linear Paul Traps for Ion–Atom Ultracold Collision Experiments

M Niranjan,Anand Prakash,S A Rangwala

doi:10.3390/atoms9030038

Abstract

We evaluate the performance of multipole, linear Paul traps for the purpose of studying cold ion–atom collisions. A combination of numerical simulations and analysis based on the virial theorem is used to draw conclusions on the differences that result, by considering the trapping details of several multipole trap types. Starting with an analysis of how a low energy collision takes place between a fully compensated, ultracold trapped ion and an stationary atom, we show that a higher order multipole trap is, in principle, advantageous in terms of collisional heating. The virial analysis of multipole traps then follows, along with the computation of trapped ion trajectories in the quadrupole, hexapole, octopole and do-decapole radio frequency traps. A detailed analysis of the motion of trapped ions as a function of the amplitude, phase and stability of the ion’s motion is used to evaluate the experimental prospects for such traps. The present analysis has the virtue of providing definitive answers for the merits of the various configurations, using first principles.

Highlights

Linear multipole Paul trap configurations are emerging as a natural choice for a wide range of charged particle trapping experiments [1,2,3,4,5,6,7,8,9,10,11,12,13]
While the linear Paul trap can be used for a large number of experiments with different and ever expanding objectives, here we examine and evaluate different linear Paul trap electrode configurations, in an effort to decide which multipole rf linear electrode configuration is suitable for the study of ion–atom collisions at the coldest temperatures
We first observe that the agreement of the computed ion motion with the virial theorem holds well, for all the multipole traps considered here

Summary

Introduction

Linear multipole Paul trap configurations are emerging as a natural choice for a wide range of charged particle trapping experiments [1,2,3,4,5,6,7,8,9,10,11,12,13]. 2. Microscopic Detail of Ultracold Ion–Atom Collision For specificity, let us compare the scenarios of a single zero energy 40Ca+ ion at the center of a quadruple and an octupole trap colliding with a zero energy 40Ca atom placed proximate to the ion. Microscopic Detail of Ultracold Ion–Atom Collision For specificity, let us compare the scenarios of a single zero energy 40Ca+ ion at the center of a quadruple and an octupole trap colliding with a zero energy 40Ca atom placed proximate to the ion In this scenario, the mutual ion–atom interaction potential results in ion displacement from the compensated point and a collision initiates. The collision is complex enough so that there can be several sequential collisions between the ion–atom pair before they eventually separate

Pole Trap xion yion xatom yatom

Pole Trap 4 Pole Trap

Ion Trap Configurations

Virial Theorem for 2k-Pole Traps

Equivalence of Trajectory Calculations and Virial Results

Discussion and Conclusions