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

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.

Mathieu–Hill Equation Stability Analysis for Trapped Ions: Anharmonic Corrections for Nonlinear Electrodynamic Traps

“…These limitations superimpose weak multipole fields such as hexapole, octopole, decapole and higher-order electric fields [103,120,[166][167][168]. The superposition of higher multipole fields significantly alters ion dynamics with respect to the case of a pure quadrupole trap [169,170]. The equation that characterizes ion motion in an anharmonic, real trap [56,125,163], is the nonlinear Mathieu equation which has no analytical solutions [115,129].…”

“…Furthermore, electrode misalignment results in symmetry breaking and leads to extra local minima in the trapping potential [98,165]. Trapped ion trajectories in the quadrupole, hexapole, octopole and dodecapole RF traps are investigated in [170]. 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.…”

Ultracold ion-atom experiments: cooling, chemistry, and quantum effects

“…For multipole traps, reaching very low temperatures for the ion-atom collision energy is in principle easier compared to a Paul trap as the ion can be confined in a region with little micromotion. But on the other hand, this makes the ion more prone to stray electric fields that cause excess micromotion (Trimby et al, 2022;Niranjan et al, 2021). Multipole traps have been used for studying ion-atom collisions and buffer gas cooling at K-mK temperatures (Wester, 2009;Asvany and Schlemmer, 2009;Nötzold et al, 2020).…”