Journal
JOURNAL OF DYNAMICAL AND CONTROL SYSTEMS
Volume 8, Issue 4, Pages 547-572Publisher
SPRINGER/PLENUM PUBLISHERS
DOI: 10.1023/A:1020767419671
Keywords
subriemannian geometry; Lie groups; quantum control
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We apply techniques of subriemannian geometry on Lie groups to laser-induced population transfer in a three-level quantum system. The aim is to induce transitions by two laser pulses, of arbitrary shape and frequency, minimizing the pulse energy. We prove that the Hamiltonian system given by the Pontryagin maximum principle is completely integrable, since this problem can be stated as a k + p problem on a simple Lie group. Optimal trajectories and controls are exhausted. The main result is that optimal controls correspond to lasers that are in resonance.
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