Electrostatics of surface-electrode ion traps

TL;DR

This paper develops analytical models for surface-electrode ion traps, deriving formulas for trap geometry, strength, and depth, and explores how control fields influence trap depth, aiding the design of scalable quantum computing devices.

Contribution

It introduces analytical methods for modeling SE traps, including formulas for geometry, strength, and depth, advancing trap design for quantum information processing.

Findings

Derived analytical expressions for trap geometry and strength.

Calculated trap depth without control fields.

Showed control fields can significantly affect trap depth.

Abstract

Surface-electrode (SE) rf traps are a promising approach to manufacturing complex ion-trap networks suitable for large-scale quantum information processing. In this paper we present analytical methods for modeling SE traps in the gapless plane approximation, and apply these methods to two particular classes of SE traps. For the SE ring trap we derive analytical expressions for the trap geometry and strength, and also calculate the depth in the absence of control fields. For translationally symmetric multipole configurations (analogs of the linear Paul trap), we derive analytical expressions for electrode geometry and strength. Further, we provide arbitrarily good approximations of the trap depth in the absence of static fields and identify the requirements for obtaining maximal depth. Lastly, we show that the depth of SE multipoles can be greatly influenced by control fields.