Physics – Quantum Physics
Scientific paper
2011-11-04
Physics
Quantum Physics
24 pages, 8 figures
Scientific paper
The broad theoretical and experimental success of optimally controlling quantum systems with external laser fields has been attributed to the favorable topology of the underlying quantum control landscape. Since a "trap-free" landscape topology can be proven only when no significant limitations are placed on the control resources, the effects of constrained controls on the landscape topology are of central importance in practice. This work addresses the consequences of employing a constrained control field on the topology and structure of the control landscape for selective population transfer. The control field is parameterized as a Fourier series of fixed frequencies, with the phases of the Fourier components acting as a finite set of controls. Optimization results reveal that analytical conclusions about the structure of the gradient vector and Hessian matrix specify the minimum number of such carefully chosen controls necessary to guarantee achievement of a high yield in the target state. The control field fluence is found to pose an additional constraint if it is fixed at a sufficiently small value. Further detailed examination of the second-order structure of critical regions on the landscape reveals the presence of suboptimal saddle regions as well as isolated trapping points. The analytically expected topology of optimal regions is confirmed, with connected optimal level sets observed when a sufficient number of controls is employed.
Moore Katharine W.
Rabitz Herschel
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