Simplified Approach to Optimally Controlled Quantum Dynamics

摘要

A new fomalism for the optimal control of quantum mechanical physical observablesis presented. This approach is based on an analogous classical control technique reported previously J. Botina, H. Rabitz, and N. Rahman, J. Chem. Phys. 102, 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. 63, 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.