  The dynamic localization of a two-level atom in a periodic potential under
the action of spin-orbit coupling and a weak harmonically-varying linear force
is studied. We consider optical and Zeeman potentials that are either in-phase
or out-of-phase in two spinor components, respectively. The expectation value
for the position of the atom after one oscillation period of the linear force
is recovered in authentic resonances or in pseudo-resonances. The frequencies
of the linear force corresponding to authentic resonances are determined by the
band structure of the periodic potential and are affected by the spin-orbit
coupling. The width/dispersion of the wavepacket in authentic resonances is
usually minimal. The frequencies corresponding to pseudo-resonances do not
depend on the type of potential and on the strength of the spin-orbit coupling,
while the evolution of excitations at the corresponding frequencies is usually
accompanied by significant dispersion. Pseudo-resonances are determined by the
initial phase of the linear force and by the quasi-momentum of the wavepacket.
Due to the spinor nature of the system, the motion of the atom is accompanied
by periodic, but not harmonic, spin oscillations. Under the action of
spin-orbit coupling the oscillations of the wavepacket can be nearly completely
suppressed in optical lattices. Dynamic localization in Zeeman lattices is
characterized by doubling of the resonant oscillation periods due to band
crossing at the boundary of the Brillouin zone. We also show that higher
harmonics in the Fourier expansion of the energy band lead to effective
dispersion, which can be strong enough to prevent dynamic localization of the
Bloch wavepacket.
