Ion counting and temperature determination of Coulomb-crystallized laser-cooled ions in traps using convolutional neural networks

Coulomb crystals---ordered structures of cold ions confined in ion traps---have applications in a variety of research fields. The number and temperature of the ions forming the Coulomb crystals are two key attributes of interest in many trapped-ion experiments. Here, we present a fast and accurate approach to determining these attributes from fluorescence images of the ions based on convolutional neural networks (CNNs). In this approach, we first generate a large number of images of Coulomb crystals with different numbers of ions at different temperatures using molecular-dynamics simulations and then train CNN models on these images to classify the desired attributes. The classification performance of several common pretrained CNN models is compared in example tasks. We find that for crystals with numbers of ions in the range 100--299 and secular temperatures of 5--15 mK, the best-performing model can discern variations of a single ion with an accuracy of 93% and temperature changes of 1 mK with an accuracy of 92%. Since the trained models can be directly integrated into experiments, in situ determination of these attributes can be realized in a noninvasive fashion. This has the potential to greatly enhance the analysis and control of trapped ions in real time.