  We report the trapping of ultracold neutral $ \text{Rb}$ atoms and $
\text{Ba}^+ $ ions in a common optical potential in absence of any
radiofrequency (RF) fields. We prepare $ \text{Ba}^+ $ at $ 370 ~ \mu K $ and
demonstrate efficient sympathetic cooling by $100 ~ \mu K $ after one
collision. Our approach is currently limited by the $ \text{Rb}$ density and
related three-body losses, but it overcomes the fundamental limitation in RF
traps set by RF-driven, micromotion-induced heating. It is applicable to a wide
range of ion-atom species, and may enable novel ultracold chemistry experiments
and complex many-body dynamics.
