Phase-space study of surface-electrode Paul traps: Integrable, chaotic, and mixed motions

TL;DR

This paper provides a detailed phase-space analysis of ion motion in surface-electrode Paul traps, exploring integrable and chaotic dynamics, and proposes an experiment to observe trapping pockets and complex escape behaviors.

Contribution

It introduces a universal phase-space framework for surface-electrode Paul traps, rigorously derives the pseudopotential approximation, and proposes an experimental method to observe phase-space structures.

Findings

Identification of trapping pockets within mixed phase-space structures

Quantification of the pseudopotential approximation's validity

Prediction of experimental signatures of chaotic and regular ion dynamics

Abstract

We present a comprehensive phase-space treatment of the motion of charged particles in electrodynamic traps. Focusing on five-wire surface-electrode Paul traps, we study the details of integrable and chaotic motion of a single ion. We introduce appropriate phase-space measures and give a universal characterization of the trap effectiveness as a function of the parameters. We rigorously derive the commonly used (time-independent) pseudopotential approximation, quantify its regime of validity and analyze the mechanism of its breakdown within the time-dependent potential. The phase space approach that we develop gives a general framework for describing ion dynamics in a broad variety of surface Paul traps. To probe this framework experimentally, we propose and analyze, using numerical simulations, an experiment that can be realized with an existing four-wire trap. We predict a robust experimental signature of the existence of trapping pockets within a mixed regular and chaotic phase-space structure. Intricately rich escape dynamics suggest that surface traps give access to exploring microscopic Hamiltonian transport phenomena in phase space.