  We study the effect of a one dimensional optical lattice in a cavity field
with quantum properties on the superfluid dynamics of a Bose-Einstein
condensate(BEC). In the cavity the influence of atomic backaction and the
external driving pump become important and strongly modify the optical
potential. Due to the strong coupling between the condensate wavefunction and
the cavity modes, the cavity light field develops a band structure. This study
reveals that the pump and the cavity emerges as a new handle to control the
superfluid properties of the BEC.
