  The motion of atoms and nanoparticles in a trap formed by sequences of
counter-propagating light pulses has been analyzed. The atomic state is
described by a wave function constructed with the use of the Monte Carlo
method, whereas the atomic motion is considered in the framework of classical
mechanics. The effects of the momentum diffusion associated with the
spontaneous radiation emission by excited atoms and the pulsed character of the
atom-to-field interaction on the motion of a trapped atom or nanoparticle are
estimated. The motion of a trapped atom is shown to be slowed down for properly
chosen parameters of the atom-to-field interaction, so that the atom oscillates
around the antinodes of a non-stationary standing wave formed by
counter-propagating light pulses at the point where they "collide".
