Precise Experimental Investigation of Eigenmodes in a Planar Ion Crystal

TL;DR

This study combines experimental and theoretical methods to accurately characterize eigenmodes and eigenfrequencies of 2D ion crystals, crucial for their application in quantum simulation, revealing limitations of pseudopotential theory and validating full Coulomb models.

Contribution

It provides a comprehensive comparison between pseudopotential and full Coulomb theories for 2D ion crystals, highlighting the importance of advanced models for precise eigenfrequency predictions.

Findings

Pseudopotential theory accurately predicts ion positions and structural transitions.

Full Coulomb theory matches experimental eigenfrequency data within 2.5 x 10^(-3).

Results advance the use of ion crystals for quantum simulation.

Abstract

The accurate characterization of eigenmodes and eigenfrequencies of two-dimensional ion crystals provides the foundation for the use of such structures for quantum simulation purposes. We present a combined experimental and theoretical study of two-dimensional ion crystals. We demonstrate that standard pseudopotential theory accurately predicts the positions of the ions and the location of structural transitions between different crystal configurations. However, pseudopotential theory is insufficient to determine eigenfrequencies of the two-dimensional ion crystals accurately but shows significant deviations from the experimental data obtained from resolved sideband spectroscopy. Agreement at the level of 2.5 x 10^(-3) is found with the full time-dependent Coulomb theory using the Floquet-Lyapunov approach and the effect is understood from the dynamics of two-dimensional ion crystals in the Paul trap. The results represent initial steps towards an exploitation of these structures for quantum simulation schemes.