  A Bose-Einstein condensate is dispersively coupled to a single mode of an
ultra-high finesse optical cavity. The system is governed by strong
interactions between the atomic motion and the light field even at the level of
single quanta. While coherently pumping the cavity mode the condensate is
subject to the cavity optical lattice potential whose depth depends nonlinearly
on the atomic density distribution. We observe bistability already below the
single photon level and strong back-action dynamics which tunes the system
periodically out of resonance.
