  We demonstrate full quantum state control of two species of single atoms
using optical tweezers and assemble the atoms into a molecule. Our
demonstration includes 3D ground-state cooling of a single atom (Cs) in an
optical tweezer, transport by several microns with minimal heating, and merging
with a single Na atom. Subsequently, both atoms occupy the simultaneous
motional ground state with 61(4)\% probability. This realizes a sample of
exactly two co-trapped atoms near the phase-space-density limit of one, and
allows for efficient stimulated-Raman transfer of a pair of atoms into a
molecular bound state of the triplet electronic ground potential $a^3\Sigma^+$.
The results are key steps toward coherent creation of single ultracold
molecules, for future exploration of quantum simulation and quantum information
processing.
