  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.
