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

The effect of Landau-Zener tunnelings on the nonlinear dynamics of cold atoms in a modulated laser field