Abstract
In this thesis we theoretically investigate the quantum simulation of lattice gauge theories for cold atom experiments. We give an explicit proposal to study a (1+1) - dimensional U(1) lattice gauge theory. Starting with a bosonic and a fermionic atomic gas we tune the geometry and engineer the interactions such that we end up with a one-dimensional system obeying the principle of local gauge invariance. A further important aspect of this proposal is the explicit use of highly occupied bosonic states in order to make the investigation of strong field quantum electrodynamics feasible. In addition, we present an approach based on the functional integral in order to theoretically treat U(1) and SU(N) gauge fields interacting with matter out of equilibrium. We show that under specific conditions the quantum theory can be accurately mapped onto a classical statistical ensemble. Further, exploiting this possibility, we study the prospect to observe intricate high energy phenomena like Schwinger pair-production and string breaking in such future cold atom experiments.
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