Aharonov-Bohm interferometry with interacting quantum dots

This master’s thesis investigates an Aharonov-Bohm interferometer with two interacting quantum dots. The Aharonov-Bohm effect makes quantum coherences detectable. Quantum dots are used because they have discrete energy levels, among other things, which simplifies the calculations. This makes it possible to investigate the interplay of interaction and coherence. As measurement quantity the current is primarily used. It is calculated using first-order perturbation theory in the tunnelling strength, employing Feynman diagrams and quantum master equations. The implementation of this calculation in Mathematica, and specifically the automated creation and evaluation of the diagrams, are essential components of this master’s thesis. With this, transitions between existing results can be demonstrated for a finite interaction. Furthermore, areas are identified in which the interferometric visibility becomes negative. This causes the phase of the Aharonov-Bohm oscillations to shift. Furthermore, at the point where the visibility vanishes, the oscillations has twice the frequency. In addition, energy level-dependent interference patterns can be described that occur without an applied magnetic flux. It is shown that the methods implemented here make it possible to distinguish between single- and double-occupancy effects on the quantum dots. Finally, it is demonstrated that new effects can be made visible in the non-linear response regime.