  Dynamics of non-interacting ultracold atoms with artificial spin-orbit
coupling is considered. Spin-orbit coupling is created using two moving optical
lattices with orthogonal polarizations. Our main goal is to study influence of
lattice noise on Rabi oscillations. Special attention is paid to the phenomenon
of the Zitterbewegung being trembling motion caused by Rabi transitions between
states with different velocities. Phase and amplitude fluctuations of lattices
are modelled by means of the two-dimensional stochastic Ornstein-Uhlenbeck
process, also known as harmonic noise. In the the noiseless case the problem is
solved analytically in terms of the momentum representation. It is shown that
lattice noise significantly extends duration of the Zitterbewegung as compared
to the noiseless case. This effect originates from noise-induced decoherence of
Rabi oscillations.
