The "Quantum Control" problem can be phrased as finding ways of inducing complete transfer of population from an arbitrary initial wave packet of quantum states to a desired target wave packet of quantum states. This objective can be achieved by employing a (polychromatic) set of mutually coherent light fields, or equivalently, a set of tailor-made shaped laser pulses.
In recent years Quantum Control has been realized by using a number of strategies, such as, Coherent Control [1], which achieves final state selectivity using laser-controlled interference between two or more quantum pathways, by tuning the phases and other parameters of the light fields; Optimal Control [2], which is a general procedure for optimizing laser pulses using pulse-shaping techniques to achieve a desired outcome, and Adiabatic Passage [3], which is a way of affecting complete population transfer between selected states and, also their coherent superposition.
The merging of Coherent Control and Adiabatic Passage has been recently achieved resulting in the Coherently Controlled Adiabatic Passage methodology [4], which allows for both selectivity and completeness. The Coherently Controlled Adiabatic Passage [4] has been applied to various problems in physics and chemistry: How to completely transfer population from an initial wave packet of arbitrary shape, composed of a set of non-degenerate energy eigenstates, to a final arbitrary wave packet, also composed of non-degenerate states, as well as complete population transfer in systems with degenerate states. Such generic approaches have been further generalized to situations with many initial, intermediate, and final states and applied to quantum coding and decoding problems. The Coherently Controlled Adiabatic Passage has been also used to control cyclic population transfer, induced by coupling three states of a system with broken inversion-symmetry in a cyclic fashion, 1->2->3->1. Interference between two adiabatic pathways in such a cyclic coupled system allows for complete population transfer, combined with multi-channel selectivity, by virtue of its phase sensitivity. Such a process can be used to show the purification of mixtures of right-handed and left-handed chiral molecules. Finally, the quantum-field Coherent Control has been also introduced after extending the Coherently Controlled Adiabatic Passage method to the use of non-classical light. This emerging field can be used to generate new types of entangled radiation-matter states.
Complete Control of Population Transfer between Clusters of Degenerate States, I. Thanopulos, P. Kral, and M. Shapiro,Phys. Rev. Lett. 92, 113003 (2004). Left: (Upper panel) Population in a space-localized wave packet |1>_loc, composed of n degenerate eigenstates is transferred to a single state |0>, by a two-photon adiabatic passage via n non-degenerate intermediate states. (Lower panel) Population transfer by a time reversed process with different laser pulses from |0> to the target wave packet |2>_loc', composed also of a set of degenerate eigenstates. Right: Control of population transfer between clusters of degenerate states has been applied in the three Jahn-Teller minimum configurations of the Al3O molecule, with the XY_3 symmetry, shown together with the three intermediate saddle point structures. In the center, we present the potential along the coordinates for the molecular isomerization
(s direction) and the motion of the X unit out of the Y_3 plane (z direction).
[1] M. Shapiro and P. Brumer, Principles of the Quantum Control of Molecular Processes , Wiley-Interscience, New York, 2003. [2] S.A. Rice and M. Zhao, Optical Control of Molecular Dynamics, Wiley, New York, 2000. [3] N.V. Vitanov, M. Fleischauer, B.W. Shore, and K. Bergmann, Adv. At. Mol. Opt. Phys. 46, 55 (2001). [4] P. Kral, I. Thanopulos, and M. Shapiro, Rev. Mod. Phys. 79, 53 (2007).
