Wave-packet dynamics of an atomic ion in a Paul trap: approximations and stability

TL;DR

This study uses numerical simulations of the Schrödinger equation to analyze the quantum dynamics of an atomic ion in a Paul trap, confirming classical stability criteria apply to quantum motion.

Contribution

It provides a full quantum analysis of ion dynamics in a Paul trap, comparing quantum and classical trajectories and examining wave packet stability near the trap's stability boundary.

Findings

Quantum center-of-mass motion follows classical trajectories.

Wave packet width remains bounded within the stability region.

Classical trapping criteria are valid for quantum motion.

Abstract

Using numerical simulations of the time-dependent Schr\"odinger equation, we study the full quantum dynamics of the motion of an atomic ion in a linear Paul trap. Such a trap is based on a time-varying, periodic electric field, and hence corresponds to a time-dependent potential for the ion, which we model exactly. We compare the center of mass motion with that obtained from classical equations of motion, as well as to results based on a time-independent effective potential. We also study the oscillations of the width of the ion's wave packet, including close to the border between stable (bounded) and unstable (unbounded) trajectories. Our results confirm that the center-of-mass motion always follow the classical trajectory, that the width of the wave packet is bounded for trapping within the stability region, and therefore that the classical trapping criterion are fully applicable to quantum motion.