Imaging Trapped Ion Structures via Fluorescence Cross-Correlation Detection

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 spatial frequency, thus distance, as well alignment ions. For case two ions we obtain cross-correlations frequency ${f}_{\text{spatial}}=1490\ifmmode\pm\else\textpm\fi{}{2}_{\mathrm{stat}}\ifmmode\pm\else\textpm\fi{}{8}_{\mathrm{syst}}\text{ }\text{ }{\mathrm{rad}}^{\ensuremath{-}1}$, where statistical uncertainty improves with integrated number correlation events ${N}^{\ensuremath{-}0.51\ifmmode\pm\else\textpm\fi{}0.06}$. We independently determine to be $1494\ifmmode\pm\else\textpm\fi{}11\text{ proving excellent agreement. Expanding our method three ions, demonstrate its functionality two-dimensional arrays emitters indistinguishable photons, serving model system yield structural information direct imaging techniques fail.