Dipole and Bloch oscillations of cold atoms in a parabolic lattice

The paper studies the dynamics of a Bose-Einstein condensate loaded in a 1D parabolic optical lattice and excited by a sudden shifting of the lattice center. Depending on the initial shift, this dynamics is either the dipole or Bloch oscillations of the atoms. The effects of the dephasing and atom-atom interactions on the above atomic oscillations are discussed.