  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.
