Theory of adiabatic quantum control in the presence of cavity-photon shot noise

Many areas of physics rely upon adiabatic state transfer protocols, allowing a quantum state to be moved between different physical systems for storage and retrieval or state manipulation. However, these state-transfer protocols suffer from dephasing and dissipation. In this thesis we go beyond the standard open-systems treatment of quantum dissipation allowing us to consider non-Markovian environments. We use adiabatic perturbation theory in order to give analytic descriptions for various quantum state-transfer protocols. The leading-order corrections will give rise to additional terms adding to the geometric phase preventing us from achieving a perfect fidelity. We obtain analytical descriptions for the effects of the geometric phase in non-Markovian regimes. The Markovian regime is usually treated by solving a standard Bloch-Redfield master equation, while in the non-Markovian regime, we perform a secular approximation allowing us to obtain a solution to the density matrix without solving master equations. This solution contains all the relevant phase information for our state-transfer protocol. After developing the general theoretical tools, we apply our methods to adiabatic state transfer between a four-level atom in a driven cavity. We explicitly consider dephasing effects due to unavoidable photon shot noise and give a protocol for performing a phase gate. These results will be useful to ongoing experiments in circuit quantum electrodynamics (QED) systems.