A complicated Duffing oscillator in the surface-electrode ion trap

TL;DR

This paper investigates nonlinear oscillation effects in a surface-electrode ion trap, modeling them with a coupled Duffing equation, and demonstrates how understanding these effects can improve quantum information stability.

Contribution

It introduces a detailed model of nonlinear coupling in a surface-electrode ion trap using a coupled Duffing equation and validates it with experimental data.

Findings

Coupled nonlinear oscillations observed in the ion trap.

The model accurately fits experimental oscillation data.

Insights for suppressing qubit instability in quantum computing.

Abstract

The oscillation coupling and different nonlinear effects are observed in a single trapped $^{40}Ca^{+}$ ion confined in our home-built surface-electrode trap (SET). The coupling and the nonlinearity are originated from the high-order multipole potentials due to different layouts and the fabrication asymmetry of the SET. We solve a complicated Duffing equation with coupled oscillation terms by the multiple scale method, which fits the experimental values very well. Our investigation in the SET helps for exploring nonlinearity using currently available techniques and for suppressing instability of qubits in quantum information processing with trapped ions.