HOW LANDAU-ZENER TUNNELING TAKES TIME

We calculate the time evolution of Landau-Zener tunneling for atoms in an accelerating optical lattice. Analytical expressions are obtained that are in good agreement with a recent observation of nonexponential decay. We identify new experimental regimes that show a crossover fro m strong coherent oscillations to exponential decay in the temporal ev olution of the survival probability. We establish the time scale of th is crossover, and make connection to a tunneling time of Zener breakdo wn.