Control of quantum dynamics using external fields designed by optimal control theory, learning algorithms, and inverse control

The possibility of controlling quantum dynamics using external fields is explored. New applications of control theory are considered which include controlling unimolecular/dissociation processes with multiple laser fields in the collisional regime. Here the Bloch equations are employed to describe optical excitation and decay processes and optimal control theory is used to design amplitude modulated fields which produce the desired excited state products. Optimal control theory is also used to design fields to control curve-crossing dynamics of a model diatomic system between two dissociative electronic states through radiative coupling with a third bound state. Starting with an initial wavepacket on one the crossing surfaces, the radiative field either enhances or eliminates (at our choice) selectivity of one product channel over another.; An efficient optimization procedure for producing selective excitation of molecules undergoing stochastic dephasing collisions is presented. This procedure utilizes gradients of the perturbation-averaged physical objective with respect to the laser field parameters, and it is shown that this method is computationally efficient because large scale averaging of dynamical simulations is not necessary.; An iterative optimization algorithm for designing laser fields to control molecular motion which utilizes laboratory input (test fields) and output (resulting product yields) information is proposed. Laboratory uncertainties such as laser field noise and detector imprecision are included in the simulations of the experiments, and it is shown that this learning-based algorithm is a potentially feasible method of controlling chemical reactions.; Finally, quantum-mechanical control of molecules is studied using the inverse control method. Here a requisite external field is obtained to exactly track a prescribed molecular objective expectation value as a function of time. Results are presented for position and energy tracking for the hydrogen fluoride molecular system. The numerical results show that seemingly "benign" (or reasonable) objective tracks may give rise to unreasonable fields which may contain large D.C. and low frequency components and singularities. However, these undesirable characteristics do not present problems in the evolution of the dynamical quantities and instead provide useful hints for designing robust fields.