Abstract
The exact formulation of quantum control is now well known and sufficiently general to describe multidimensional quantum systems. The implementation of this formalism relies on the solution of the time-dependent Schrödinger equation (TDSE) of the system under study, and thus far has been limited for computational reasons to simple quantum systems of very small dimensionality. To study quantum control in larger systems, such as polyatomic molecules and condensed phases, we explore an implementation of the control formalism in which the TDSE is solved approximately using the time-dependent Hartree (TDH) approximation. We demonstrate formally that the TDH approximation greatly simplifies the implementation of control in the weak response regime for multidimensional systems. We also present numerical examples to show that the TDH approximation for the weak response case is sufficiently accurate to predict the laser fields that best drive a quantum system to a desired goal at a desired time, in systems containing more than one degree of freedom, by considering a two-dimensional quantum system and comparing the optimal fields obtained by solving the TDSE exactly to those obtained using the TDH approximation.
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