  We describe the ground state of a gas of bosonic atoms with two coherently
coupled internal levels in a deep optical lattice in a one dimensional
geometry. In the single-band approximation this system is described by a
Bose-Hubbard Hamiltonian. The system has a superfluid and a Mott insulating
phase which can be either paramagnetic or ferromagnetic. We characterize the
quantum phase transitions at unit filling by means of a density matrix
renormalization group technique and compare it with a mean-field approach. The
presence of the ferromagnetic Ising-like transition modifies the Mott lobes. In
the Mott insulating region the system maps to the ferromagnetic spin-1/2 XXZ
model in a transverse field and the numerical results compare very well with
the analytical results obtained from the spin model. In the superfluid regime
quantum fluctuations strongly modify the phase transition with respect to the
well established mean-field three dimensional classical bifurcation.
