  We study the motion of a cold atom in a frequency-modulated standing laser
wave. If the detuning between the atomic electronic transition and the field is
large, the atom moves in a modulated optical potential demonstrating known
classical nonlinear effects such as chaos and nonlinear resonances. If the
atom-field detuning is small, then two optical potentials emerge in the system,
and the atom performs Landau-Zener (LZ) tunnelings between them. It is a
radically non-classical behavior. However, we show that classical nonlinear
structures in system's phase space (KAM-tori and chaotic layers) survive.
Quantum effect of LZ tunnelings only induces small random jumps of trajectories
between these structures (dynamical tunneling).
