Licentiate Thesis Defense: Quantum properties of light and matter in one dimension

This licentiate thesis concerns topics in non-interacting and interacting quantum physics in one dimension. We present the notions of Wannier functions and tight-binding models.
Quantum walks are presented, quantum mechanical analogues to random walks. We demonstrate the ideas of Bloch oscillation and super-Bloch oscillation – revivals of quantum states for particles in a periodic lattice subject to a constant force. Next, the Rabi model of light-matter interaction is derived. The concept of quantum phase transitions is presented for the Dicke model of super-radiance. The idea of adiabatic elimination is used to highlight the connectedness of the Dicke model. Finally, we present a one-dimensional interacting system of resonators and artificial atoms that could be built as a superconducting circuit. Using adiabatic elimination as well as matrix product states, we find the phase diagram of this model.