  We have prepared two ultracold fermionic atoms in an isolated double-well
potential and obtained full control over the quantum state of this system. In
particular, we can independently control the interaction strength between the
particles, their tunneling rate between the wells and the tilt of the
potential. By introducing repulsive (attractive) interparticle interactions we
have realized the two-particle analog of a Mott-insulating
(charge-density-wave) state. We have also spectroscopically observed how
second-order tunneling affects the energy of the system. This work realizes the
first step of a bottom-up approach to deterministically create a single-site
addressable realization of a ground-state Fermi-Hubbard system.
