This project will study quantum transport of ultra-cold atoms in optical lattices. One dimensional-standing waves will be combined to form periodic and quasi-periodic optical lattices in one, two, and three spatial dimensions, and time- dependent amplitudes and phases will be imposed. Fundamental problems will be addressed which play important roles in atomic physics, condensed matter physics, and nonlinear dynamics. These include the role of dimensionally on dynamical localization, destruction of dynamical delocalization by decoherence, effects of quantum tunneling and scars, resonant tunneling between energy levels in different potential wells, spatial spread of atoms and transport of a cold beam of atoms, and topological quantum numbers.
