Ultracold quantum gases in three-dimensional optical lattice potentials

In this thesis I report on experiments that enter a new regime in
the many body physics of ultracold atomic gases. A Bose-Einstein
condensate is loaded into a three-dimensional optical lattice
potential formed by a standing wave laser light field. In this
novel quantum system we have been able to both realize a quantum
phase transition from a superfluid to a Mott insulator, and to
observe the collapse and revival of a macroscopic matter wave
field. Quantum phase transitions are driven by quantum fluctuations
and occur, even at zero temperature, as the relative strength of
two competing energy terms in the underlying Hamiltonian is varied
across a critical value. In the first part of this work I report on
the observation of such a quantum phase transition in a
Bose-Einstein condensate with repulsive interactions, held in a
three-dimensional optical lattice potential. In the superfluid
ground state, each atom is spread-out over the entire lattice,
whereas in the Mott insulating state, exact numbers of atoms are
localized at individual lattice sites. We observed the reversible
transition between those states and detected the gap in the
excitation spectrum of the Mott insulator. A Bose-Einstein
condensate is usually described by a macroscopic matter wave field.
However, a quantized field underlies such a "classical" matter wave
field of a Bose-Einstein condensate. The striking behavior of
ultracold matter due to the field quantization and the nonlinear
interactions between the atoms is the focus of the second part of
this work. The matter wave field of a Bose-Einstein condensate is
observed to undergo a series of collapses and revivals as time
evolves. Furthermore, we show that the collisions between
individual pairs of atoms lead to a fully coherent collisional
phase shift in the corresponding many-particle state, which is a
crucial cornerstone of proposed novel quantum computation schemes
with neutral atoms. With these experiments we enter a new field of
physics with ultracold quantum gases. In this strongly correlated
regime, interactions between atoms dominate the behavior of the
many-body system such that it can no longer be described by the
usual theories for weakly interacting Bose gases. This novel
quantum system offers the unique possibility to experimentally
address fundamental questions of modern solid state physics, atomic
physics, quantum optics, and quantum information.