Observation of chaos-assisted tunneling between islands of stability.

We report the direct observation of quantum dynamical tunneling of atoms between separated momentum regions in phase space. We study how the tunneling oscillations are affected as a quantum symmetry is broken and as the initial atomic state is changed. We also provide evidence that the tunneling rate is greatly enhanced by the presence of chaos in the classical dynamics. This tunneling phenomenon represents a dramatic manifestation of underlying classical chaos in a quantum system.

Shape of the quantum diffusion front.

We show that quantum diffusion has well-defined front shape. After an initial transient, the wave packet front (tails) is described by a stretched exponential P(x,t) = A(t)exp(-absolute value of [x/w](gamma)), with 1 < gamma < infinity, where w(t) is the spreading width which scales as w(t) approximately t(beta), with 0 < beta < or = 1. The two exponents satisfy the universal relation gamma = 1/(1-beta). We demonstrate these results through numerical work on one-dimensional quasiperiodic systems and the three-dimensional Anderson model of disorder. We provide an analytical derivation of these relations by using the memory function formalism of quantum dynamics. Furthermore, we present an application to experimental results for the quantum kicked rotor.

Recovery of classically chaotic behavior in a noise-driven quantum system.

The quantum kicked rotor is studied in a regime of high amplitude noise. A transition to diffusive behavior is observed as dynamical localization, characterized by suppressed diffusion and exponential momentum distributions, is completely destroyed by noise. With increasing noise amplitude, further transition to classical behavior is shown through an accurate quantitative analysis, which demonstrates that both the energy growth and the momentum distributions are reaching their classical limits. The importance of short-time correlations in the recovery of classically chaotic behavior is discussed.