QUANTUM CONTROL OF MULTIDIMENSIONAL SYSTEMS - IMPLEMENTATION WITHIN THE TIME-DEPENDENT HARTREE APPROXIMATION

The exact formulation of quantum control is now well known and suffici ently general to describe multidimensional quantum systems. The implem entation of this formalism relies on the solution of the time-dependen t Schrodinger equation (TDSE) of the system under study, and thus far has been limited for computational reasons to simple quantum systems o f very small dimensionality. To study quantum control in larger system s, such as polyatomic molecules and condensed phases, we explore an im plementation of the control formalism in which the TDSE is solved appr oximately using the time-dependent Hartree (TDH) approximation. We dem onstrate formally that the TDH approximation greatly simplifies the im plementation of control in the weak response regime for multidimension al systems. We also present numerical examples to show that the TDH ap proximation for the weak response case is sufficiently accurate to pre dict the laser fields that best drive a quantum system to a desired go al at a desired time, in systems containing more than one degree of fr eedom, by considering a two-dimensional quantum system and comparing t he optimal fields obtained by solving the TDSE exactly to those obtain ed using the TDH approximation. (C) 1996 American Institute of Physics .