  We study the quantum phase transitions between superfluid and Mott insulator
states for ultracold bosons occupying two bands of an optical lattice. The two
atomic states are resonantly coupled by a single cavity mode which mediates
transitions between the two bosonic particle modes via absorption or emission
of a cavity photon. This coupling between the bands shifts the appearance of
the Mott insulator phase towards deeper optical lattice potentials and stronger
on-site interaction strength, as atomic coherence can build up via photon
assisted tunneling in both bands. Varying the intra and interband on-site
interactions leads to several different atomic phase configurations. There are
even parameter regions where a mean field approach predicts concurrence of a
Mott insulator state in one band, while atoms in the second band stay
superfluid.
