Reduced-space analyses of the coherent control of quantum many-body dynamics

This thesis describes the results of an investigation into methods of coherent control of molecular dynamics in reduced spaces. A control strategy using the Reaction Path Hamiltonian is described. The optimal field required to maximize the populations of target eigenstates in the isomerization of HCN using the zero-curvature Reaction Path Hamiltonian is calculated. The intermediary dynamics are restricted to the ground state by using infrared pulses. Using trial fields of two time-delayed Gaussian pulses, the control algorithm proposed separately optimized the field parameters consistent with the Gaussian paradigm and the field amplitude at each point in time. In both cases it is found that the control field can generate complete isomerization using pulses that traverse the states of the system in single and multiple photon transitions. If the description of the system dynamics includes vibrational motions perpendicular to the one-dimensional reaction path and both the interactions between those vibrations and between them and the reaction path, one finds that the complexity of the power spectra of optimal control fields do not provide a simple description of the control mechanism as found by the simulations using the zero-curvature Reaction Path Hamiltonian. The effect of the inclusion of degrees of freedom orthogonal to the reaction path upon the dynamical control of HCN isomerization is discussed. The formalism of optimal control theory is also applied to the simulation of the dynamics of the selective transfer of population from an initial state into one of two degenerate states embedded within a larger manifold of states of an atom or molecule. In a model system with four states, it is found that complete population transfer is possible depending upon the arrangement of values of the transition dipole moments between the states. Comparisons with other coherent methods of population transfer are made. The existence of symmetries are seen to place limits on the controllability of quantum systems with degeneracies which may be accurately quantified.