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 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 $N^{-0.51pm0.06}$. We independently determine the spatial frequency to be $1494pm 11,text{rad}^{-1}$, 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.