A Simplified Approach to Optimally Controlled Quantum Dynamics

A new formalism for the optimal control of quantum mechanical physical observables is presented. This approach is based on an analogous classical control technique reported previously[J. Botina, H. Rabitz and N. Rahman, J. chem. Phys. Vol. 102, pag. 226 (1995)]. Quantum Lagrange multiplier functions are used to preserve a chosen subset of the observable dynamics of interest. As a result, a corresponding small set of Lagrange multipliers needs to be calculated and they are only a function of time. This is a considerable simplification over traditional quantum optimal control theory[S. shi and H. Rabitz, comp. Phys. Comm. Vol. 63, pag. 71 (1991)]. The success of the new approach is based on taking advantage of the multiplicity of solutions to virtually any problem of quantum control to meet a physical objective. A family of such simplified formulations is introduced and numerically tested. Results are presented for these algorithms and compared with previous reported work on a model problem for selective unimolecular reaction induced by an external optical electric field.Comment: Revtex, 29 pages (incl. figures

A New Approach to Molecular Classical Optimal Control: Application to the Reaction . . .

We present a new method for classical control theory of Hamiltonian systems. This approach is based on a special treatment of the adjoint or Lagrange multiplier equations of motion. The latter function is only asked to preserve the mean of the ensemble of molecular trajectories. In the present case only four such equations are involved greatly simplifying the field design process and making it faster and more stable. Good results are obtained for the selective photodissociation of HCN. The objective is to control the intramolecular reaction HCN ! HC + N (i.e., break the stronger bond). Hamilton's equations of motion are employed to model the HCN molecule, initially in its ground state. The control equations are integrated to obtain a high degree of selectivity in the unimolecular dissociation. The robustness of the results to changes in the initial conditions and pulse durations are investigated. An increase of the pulse duration beyond a certain point makes it more difficult to dissoc..