  We study the problem of designing an artificial Mott insulator in a
correlated oxide heterostructure. We consider the extreme limit of quantum
confinement based on ionic discontinuity doping, and argue that a unique dimer
Mott insulator can be achieved for the case of a single SrO layer in a
GdTiO$_3$ matrix. In the dimer Mott insulator, electrons are localized not to
individual atoms but to bonding orbitals on molecular dimers formed across a
bilayer of two TiO$_2$ planes, and is analogous to the Mott insulating state of
Hubbard ladders, studied in the 1990s. We verify the existence of the dimer
Mott insulator through both ab initio and model Hamiltonian studies, and find
for reasonable values of Hubbard $U$ that it is stable and ferromagnetic with a
clear bonding/anti-bonding splitting of order 0.65eV, and a significant smaller
Mott gap whose size depends upon $U$. The combined effects of polar
discontinuity, strong structural relaxation and electron correlations all
contribute to the realization of this unique ground state.
