  In cold atomic systems, fast and high-resolution microscopy of individual
atoms is crucial, since it can provide direct information on the dynamics and
correlations of the system. Here, we demonstrate nanosecond-scale
two-dimensional stroboscopic pictures of a single trapped ion beyond the
optical diffraction limit, by combining the main idea of ground-state depletion
microscopy with quantum state transition control in cold atoms. We achieve a
spatial resolution up to 175~nm using an NA = 0.1 objective in the experiment,
which represents a more than tenfold improvement compared with direct
fluorescence imaging. To show the potential of this method, we apply it to
observe the secular motion of the trapped ion, we demonstrate a temporal
resolution up to 50~ns with a displacement detection sensitivity of 10~nm. Our
method provides a powerful tool for probing particle positions, momenta, and
correlations, as well as their dynamics in cold atomic systems.
