Quantum Control of d-Dimensional Quantum Systems with Application to Alkali Atomic Spins

In this dissertation I analyze Hamiltonian control of $d$-dimensional quantum systems as realized in alkali atomic spins. Alkali atoms provide an ideal platform for studies of quantum control due to the extreme precision with which the control fields are characterized as well as their isolation from their environment. In chapter 2, I review some background material on open-loop quantum control theory. Chapter 3 provides a derivation of the Hamiltonians arising from electromagnetic fields that we use to control our alkali atomic spins. In chapter 4, I develop an algorithm for state preparation, that is mapping a fiducial state to some arbitrary target state, and show numerical and experimental implementations for making arbitrary superpositions of hyperfine states in $^{133}Cs. Finally, chapter 5 presents a protocol for generating full unitary maps efficiently by utilizing the ability to construct state mappings.