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Title: Minimal time trajectories for two-level quantum systems with two bounded controls

In this paper we consider the minimum time population transfer problem for a two level quantum system driven by two external fields with bounded amplitude. The controls are modeled as real functions and we do not use the Rotating Wave Approximation. After projection on the Bloch sphere, we treat the time-optimal control problem with techniques of optimal synthesis on 2D manifolds. Based on the Pontryagin Maximum Principle, we characterize a restricted set of candidate optimal trajectories. Properties on this set, crucial for complete optimal synthesis, are illustrated by numerical simulations. Furthermore, when the two controls have the same bound and this bound is small with respect to the difference of the two energy levels, we get a complete optimal synthesis up to a small neighborhood of the antipodal point of the initial condition.
Authors:
 [1] ;  [2] ;  [3] ;  [4]
  1. CNRS, CMAP Ecole Polytechnique, France and Team GECO, INRIA Saclay (France)
  2. Department of Physics, Royal Institute of Technology (KTH) (Sweden)
  3. General Motors of Canada, 1908 Colonel Sam Drive, Oshawa (Canada)
  4. Department of Chemistry, Princeton University, Princeton, New Jersey 08544-1009 (United States)
Publication Date:
OSTI Identifier:
22306183
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Mathematical Physics; Journal Volume: 55; Journal Issue: 6; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; APPROXIMATIONS; COMPUTERIZED SIMULATION; ENERGY LEVELS; HILBERT SPACE; MATHEMATICAL MANIFOLDS; OPTIMAL CONTROL; QUANTUM MECHANICS; TRAJECTORIES