  As one of the most critical methods for optical super-resolved microscopy,
stimulated emission depletion (STED) microscopy has been widely applied in
biological and chemical fields, leading to the Nobel prize of 2014 in
chemistry. 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
two-dimensional snapshots of a single trapped ion beyond the optical
diffraction limit, by combining the main idea of STED with the quantum state
transition control in cold atoms. We achieve a spatial resolution up to 175 nm
and a time resolution up to 50 ns simultaneously using a NA=0.1 objective in
the experiment, which is improved over ten times compared to direct
fluorescence imaging. To show the potential of this method, we applied it to
record the motion of the trapped ion and observe one cycle of the secular
motion of the ion with a displacement detection sensitivity of 10 nm. Our
method provides a powerful tool for probing particles' positions, momenta and
correlations, as well as their dynamics in cold atomic systems.
