  Sympathetic cooling is the process of energy exchange between a system and a
colder bath. We investigate this fundamental process in an atom-ion experiment
where the system is composed of a single ion, trapped in a radio-frequency Paul
trap, and prepared in a coherent state of ~200 K and the bath is an ultracold
cloud of atoms at {\mu}K temperature. We directly observe the sympathetic
cooling dynamics with single-shot energy measurements during one, to several,
collisions in two distinct regimes. In one, collisions predominantly cool the
system with very efficient momentum transfer leading to cooling in only a few
collisions. In the other, collisions can both cool and heat the system due to
the non-equilibrium dynamics of the atom-ion collisions in the presence of the
ion-trap's oscillating electric fields. While the bulk of our observations
agree well with a molecular dynamics simulation of hard-sphere (Langevin)
collisions, a measurement of the scattering angle distribution reveals
forward-scattering (glancing) collisions which are beyond the Langevin model.
This work paves the way for further non-equilibrium and collision dynamics
studies using the well-controlled atom-ion system.
