We present a theoretical treatment of the surprisingly large damping observed
recently in one-dimensional Bose-Einstein atomic condensates in optical
lattices. We show that time-dependent Hartree-Fock-Bogoliubov (HFB)
calculations can describe qualitatively the main features of the damping
observed over a range of lattice depths. We also derive a formula of the
fluctuation-dissipation type for the damping, based on a picture in which the
coherent motion of the condensate atoms is disrupted as they try to flow
through the random local potential created by the irregular motion of
noncondensate atoms. We expect this irregular motion to result from the
well-known dynamical instability exhibited by the mean-field theory for these
systems. When parameters for the characteristic strength and correlation times
of the fluctuations, obtained from the HFB calculations, are substituted in the
damping formula, we find very good agreement with the experimentally-observed
damping, as long as the lattice is shallow enough for the fraction of atoms in
the Mott insulator phase to be negligible. We also include, for completeness,
the results of other calculations based on the Gutzwiller ansatz, which appear
to work better for the deeper lattices.
