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 unstable
quantum system. We then describe our experiments to observe the quantum Zeno
and anti-Zeno effects for an unstable system that is repeatedly interrogated. We
conclude this chapter with a brief outlook into the future.