On the $K+P$ Problem for a Three-level Quantum System: Optimality Implies Resonance

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dc.creatorBoscain, Ugo
dc.creatorChambrion, Thomas
dc.creatorGauthier, Jean-Paul
dc.date2002-04-18
dc.date.accessioned2026-07-07T04:47:47Z
dc.date.available2026-07-07T04:47:47Z
dc.descriptionWe 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 ``$\k\oplus\p$ 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''.
dc.description19 pages, 1 figure
dc.identifierhttps://arxiv.org/abs/math/0204233
dc.identifierhttp://arxiv.org/abs/math/0204233
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/63854
dc.subjectOptimization and Control
dc.subjectAnalysis of PDEs
dc.subject49j15; 81p68
dc.titleOn the $K+P$ Problem for a Three-level Quantum System: Optimality Implies Resonance
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