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

Superfluid properties of a Bose-Einstein condensate in an optical lattice confined in a cavity