Tracking the extensive three-dimensional motion of single ions by an engineered point-spread function

Three-dimensional (3D) imaging of individual atoms is a critical tool for discovering new physical phenomena and developing new technologies in microscopic systems. However, the current single-atom-resolved 3D imaging methods are limited to static circumstances or a shallow detection range. Here, we demonstrate a generic dynamic 3D imaging method to track the extensive motion of single ions by exploiting the engineered point-spread function (PSF). We show that the image of a single ion can be engineered into a helical PSF, thus enabling single-snapshot acquisition of the position information of the ion in the trap. A preliminary application of this technique is demonstrated by recording the 3D motion trajectory of a single trapped ion and reconstructing the 3D dynamical configuration transition between the zig and zag structures of a 5-ion crystal. This work opens the path for studies on single-atom-resolved dynamics in both trapped-ion and neutral-atom systems.