Imaging trapped ion structures via fluorescence cross-correlation detection

TL;DR

This paper introduces a fluorescence cross-correlation detection method to determine the spatial arrangement of trapped ion structures, providing a non-imaging approach for analyzing multi-ion arrays with high precision.

Contribution

The study presents a novel fluorescence cross-correlation technique to accurately reveal ion positions and arrangements, especially useful for complex arrays where direct imaging is challenging.

Findings

Achieved precise measurement of ion spatial frequency with high statistical confidence.

Validated the method by independently confirming the spatial frequency measurement.

Demonstrated applicability to two-dimensional ion arrays of indistinguishable photons.

Abstract

Cross-correlation signals are recorded from fluorescence photons scattered in free space off a trapped ion structure. The analysis of the signal allows for unambiguously revealing the spatial frequency, thus the distance, as well as the spatial alignment of the ions. For the case of two ions we obtain from the cross-correlations a spatial frequency $f_\text{spatial}=1490 \pm 2_{stat.}\pm 8_{syst.}\,\text{rad}^{-1}$, where the statistical uncertainty improves with the integrated number of correlation events as $N^{-0.51\pm0.06}$. We independently determine the spatial frequency to be $1494\pm 11\,\text{rad}^{-1}$, proving excellent agreement. Expanding our method to the case of three ions, we demonstrate its functionality for two-dimensional arrays of emitters of indistinguishable photons, serving as a model system to yield structural information where direct imaging techniques fail.