In this chapter, we describe our experiments with ultra cold atoms in optical potentials and show how we can address fundamental issues of time in quantum mechanics. The high degree of experimental control and the conceptual simplicity are the main advantages of our system. We start with an overview of the basic interaction of atoms and light and make the connection between atoms in optical lattices and solid state physics. While this latter connection has evolved into a major theme in physics over the past decade, at the time of this work it was still new and unexplored. After introduction of the theoretical model and the basic equations, we introduce the experimental apparatus. We then review our experiments to observe the Wannier–Stark ladder in an accelerating lattice. This system was used to study quantum tunneling where short-time non-exponential decay was first observed for an