Quantum control of bound and continuum state dynamics

We review theoretical work in the field of “coherent control” (CC) of bound- and continuum-state dynamics. We explain the principles of bichromatic and polychromatic control and show that CC is made possible through the execution of a disentanglement transformation. We discuss limitations to control and show that controllability in continuum states is linked to a generalized Schwarz inequality of vector spaces. We illustrate the success of these techniques in controlling photo-current directionality in semiconductors using one- vs. two-photon interferences. We next turn our attention to CC using adiabatic passage (AP) processes, enabling the achievement of both selectivity and complete population transfer. We demonstrate controllability in bound state dynamics by the explicit construction of guiding fields which solve the “non-degenerate quantum control” problem. The CC + AP methodology is then extended to the control of manifolds composed entirely of degenerate bound states. We use AP techniques in the control of photoassociation and especially in the controlled recombination of ultracold atoms to form ultracold molecules. We next discuss the optical manipulation of interferences between overlapping, decaying resonances as a way of suppressing spontaneous emission, intramolecular vibrational redistribution, and internal conversion in molecules. Finally we discuss decoherence and the way material and radiative phase-instabilities diminish controllability. We show how to combat decoherence and how to use CC to construct “decoherence-free subspaces”.