We present a theory for controlling the dynamics of a dissipative, quantum system with a laser field optimized locally in time. The theory is applicable to both weak and strong field control of the quantum dynamics. The theoretical groundwork is based on the equation of motion of the density matrix in Liouville space. Interactions between the molecules and the heat bath are taken into account within a Markov approximation. The derivation of the locally optimized laser field in a feedback form is based on the local optimization theory in the Hilbert space, proposed in a previous paper [M. Sugawara and Y. Fujimura, J. Chem. Phys. 100, 5646 (1994)]. The theory is applied to a simple, two-level quantum system with a dephasing constant. We present both the calculated time evolution of the off-diagonal density matrix element and that of the population of the states in the optimized laser field. These calculations show that the control of the system by the laser field is sufficient to avoid the dephasing effects. We discuss how the dephasing dynamics affects the optimization of the laser field.
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