Optimal Control of Large Spin-Atomic Systems with Coherent Electromagnetic Fields*

Cold atomic systems provide an excellent testing ground for quantum control protocols due to the isolation of these systems from their environment and the availability of high precision fields from the ``quantum optics toolbox''. In this talk, we look at controlling the sixteen dimensional ground state hyperfine manifold of $^{133}$Cs through microwaves and rf-magnetic fields. These controls allow for essentially coherent manipulation of a system that is large enough to exhibit non-trivial dynamics. In particular, we analyze the controllability of this system under different combinations of applied electromagnetic fields. Also, we present a scheme for performing state preparation, which is the mapping a fiducial state to an arbitrary target state, and show simulations that examine the performance of these state preparation protocols.~~~~~