| We experimentally study the quantum dynamics of several simple systems by observing the center-of-mass motion of cold atoms in time-dependent optical potentials. One of the most interesting types of quantum systems is one where the motion in the classical limit is chaotic. Chaotic motion in such a system is inhibited through dynamical localization. Quantum and classical motion in the system exhibit distinctly different overall behavior. One prototypical classically chaotic system is the quantum kicked rotor, which is a system that we can study with our experiments. We have used our setup to observe several phenomena related to dynamical localization, including the dependence of the diffusion rate on short-term correlations. A second topic of study is the effects of noise upon this system. Dynamical localization is a coherent quantum effect that can be destroyed by the introduction of noise, which is an interaction with the external environment. It has been suggested that such coherence-breaking interactions may be necessary for fundamentally quantum systems to exhibit classical dynamics. When we add high enough levels of noise to our experiments, we have found that certain features of the system behavior become indistinguishable from that of a classical system. Beyond the experiments with the kicked rotor, we have studied quantum transport in mixed phase space. We report the first direct observation of chaos-assisted tunneling, where quantum tunneling between two islands in phase space is accelerated by a region of chaotic dynamics that separates them. These experiments required the development of new methods of quantum state preparation, which we describe here. Finally, we have demonstrated a new method of spatially focusing atoms that has applications in atom lithography. |
