Quantum Control of Hole Transition Dynamics between Valence Bands

The problem of optimal quantum control of radiative transitions of a free charge carrier between energy bands in semiconductors is considered. Results on simulation of optimal intervalence transitions induced by an ultrashort radiation pulse are presented. Two methods of solving the problem are described. In the first method one assumes a fixed overall shape of an ultrashort optical electric field pulse characterized by a number of free parameters, and then finds an optimal set that maximizes the transition probability. In the second, more general method, the problem of finding an optimal radiation pulse is treated as a constrained minimization problem. A simple example of hole transitions between valence bands is used to illustrate both methods.