Chaotic dynamics of cold atoms in multidimensional optical lattices

Optical lattices, created by interfering laser beams, are efficient tools to manipulate cold atoms by adjusting the lattice geometry and parameters. A number of dynamical effects has been studied with cold atoms in one-dimensional optical lattices in classical, quantum, and semiclassical regimes. Recently, it has been shown that multi-dimensional optical lattices may lead to deeply different dynamics of non-interacting atoms allowing us to investigate the quantum–classical correspondence. We discuss the recent progress in studying classical, semiclassical, and quantum chaotic dynamics of cold atoms in two-dimensional and three-dimensional optical lattices with non-trivial geometry. The special attention is paid to classical versus quantum dynamics of atoms with the coupling between the internal and translational degrees of freedom. The dynamical mechanisms of transition to chaos and inhibition of the onset of chaos for atoms trapped inside wells of the optical potential and moving between different wells are discussed. We propose the experimental schemes that could distinguish between the regular and chaotic dynamics. The perspectives for observation of quantum chaos with cold atoms, that is the quantum regime of a system, whose classical dynamics is chaotic, are considered.