The study of systems formed from ultracold atomic gases has emerged to become
one of the most active research elds within the condensed matter landscape. These
highly controllable macroscopic systems amalgamate ideas from many sub disciplines
of physics, including the study of low temperatures, quantum optics and quantum
information theory as well as the seemingly disparate eld of high energy physics.
The central concept of this thesis is gauge theories as applied to systems of bosonic
atoms, which at temperatures close to absolute zero form Bose-Einstein condensates.
To simulate the mathematical structure of a gauge theory, the geometric (Berry)
phase formalism is adopted. This is in turn accomplished by considering the adiabatic
following of the eigenstates of the light-matter coupling for an ensemble of
atoms forming a Bose-Einstein condensate. These concepts are then applied to show
how one can generate a spin-orbit coupling in a one-dimensional condensate, which
additionally features a random mass term that allows us to study the physics of Anderson
localization in an intriguing \quasi" relativistic regime. One of the features
of light induced gauge potentials is that they are static; in the sense that there is no
feedback between the light-matter interaction and the matter eld. In the second
part of this thesis it is demonstrated how such a feedback mechanism can be induced
by the appropriate modi cation of the light-matter interaction. The consequences
this has for the condensate are then described at the mean- eld level, including
the expected experimental signatures of the resulting `interacting' gauge theory, in
terms of the expansion of the condensate and also the structure of the solitons of this
nonlinear system. Finally, this nonlinear model is applied to a double well system,
from which the associated Bose-Hubbard model is derived and analysed; and the
nonlinear Josephson problem studied
