Optimal Control Functions of Photon Fock States in a Cavity

The ability to control quantum mechanical states is an essential requirement for many experiments in fundamental quantum mechanics and applications in quantum information systems.~ Controllability for an atom in a cavity has been shown, and experimental techniques for controlling Fock states in a cavity have been displayed.~ However, a classical control theoretic treatment of an atom in a cavity has not been developed.~ From methods in quantum control theory, we develop optimal control functions for an atom in a cavity for different constraints and cost functions.~~