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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 wearXiv:0906.4790v1 fatcat:5mniozqbhfebvjz2licg2hsoam