  We address Bloch oscillations of a spin-orbit coupled atom in periodic
potentials of two types: Optical and Zeeman lattices. We show that in optical
lattices the spin-orbit coupling allows controlling the direction of atomic
motion and may lead to complete suppression of the oscillations at specific
values of the coupling strength. In Zeeman lattices the energy bands are found
to cross each other at the boundaries of the Brillouin zone, resulting in
period-doubling of the oscillations. In all cases, the oscillations are
accompanied by rotation of the pseudo-spin, with a dynamics that is determined
by the strength of the spin-orbit coupling. The predicted effects are discussed
also in terms of a Wannier-Stark ladder, which in optical lattices consist of
two mutually-shifted equidistant sub-ladders.

Quantum Gases;Quantum Physics