  We analyze quantum phase transitions in a system of optical lattice bosons
coupled to an array of atomic quantum dots, or pseudospins-1/2. The system
parallels the Bose-Hubbard model with a single difference of the direct
tunneling between the lattice sites being replaced by an assisted tunneling via
coupling to the atomic quantum dots. We calculate the phase diagram of the
combined system, numerically within the Gutzwiller ansatz and analytically
using the mean-field decoupling approximation. The result of the assisted
Bose-Hubbard model is that the Mott-superfluid transition still takes place,
however, the Mott lobes strongly depend on the system parameters such as the
detuning. One can even reverse the usual hierarchy of the lobes with the first
lobe becoming the smallest. The phase transition in the bosonic subsystem is
accompanied by a magnetization rotation in the pseudospin subsystem with the
tilting angle being an effective order parameter. When direct tunneling is
taken into account, the Mott lobes can be made disappear and the bosonic
subsystem becomes superfluid throughout.
