  Improved control of the motional and internal quantum states of ultracold
neutral atoms and ions has opened intriguing possibilities for quantum
simulation and quantum computation. Many-body effects have been explored with
hundreds of thousands of quantum-degenerate neutral atoms and coherent
light-matter interfaces have been built. Systems of single or a few trapped
ions have been used to demonstrate universal quantum computing algorithms and
to detect variations of fundamental constants in precision atomic clocks. Until
now, atomic quantum gases and single trapped ions have been treated separately
in experiments. Here we investigate whether they can be advantageously combined
into one hybrid system, by exploring the immersion of a single trapped ion into
a Bose-Einstein condensate of neutral atoms. We demonstrate independent control
over the two components within the hybrid system, study the fundamental
interaction processes and observe sympathetic cooling of the single ion by the
condensate. Our experiment calls for further research into the possibility of
using this technique for the continuous cooling of quantum computers. We also
anticipate that it will lead to explorations of entanglement in hybrid quantum
systems and to fundamental studies of the decoherence of a single, locally
controlled impurity particle coupled to a quantum environment.
