Weak Chaos with Cold Atoms in a 2D Optical Lattice with Orthogonal Polarizations of Laser Beams

We study theoretically coherent dynamics of cold atoms in the near-resonant 2D optical lattice with orthogonal polarizations, taking into account a coupling between the atomic internal (electronic) and external (translational) degrees of freedom. We show that in the semiclassical approximation this dynamics may be regular or chaotic in dependence on the values of the detuning between the electric-dipole transition and the laser field frequencies. Chaos manifests itself both in the Rabi oscillations and in the translational motion at comparatively small absolute values of the detuning. The center-of-mass motion in the chaotic regime resembles the random walk of atoms in a 2D lattice which is an absolutely rigid one. Chaos is quantified by the values of the maximal Lyapunov exponent and is shown to be weaker as compared with the case of cold atoms in a 1D lattice. In fact, chaos appears at the time moments when the atom crosses 1D or 2D nodes of the lattice potential when its induced electric dipole moment changes suddenly in a random-like manner.