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Title: Topology of classical molecular optimal control landscapes for multi-target objectives

This paper considers laser-driven optimal control of an ensemble of non-interacting molecules whose dynamics lie in classical phase space. The molecules evolve independently under control to distinct final states. We consider a control landscape defined in terms of multi-target (MT) molecular states and analyze the landscape as a functional of the control field. The topology of the MT control landscape is assessed through its gradient and Hessian with respect to the control. Under particular assumptions, the MT control landscape is found to be free of traps that could hinder reaching the objective. The Hessian associated with an optimal control field is shown to have finite rank, indicating an inherent degree of robustness to control noise. Both the absence of traps and rank of the Hessian are shown to be analogous to the situation of specifying multiple targets for an ensemble of quantum states. Numerical simulations are presented to illustrate the classical landscape principles and further characterize the system behavior as the control field is optimized.
Authors:
 [1] ; ;  [2] ;  [3]
  1. Program in Applied and Computational Mathematics, Princeton University, Princeton, New Jersey 08544-1000 (United States)
  2. Department of Chemistry, Princeton University, Princeton, New Jersey 08544-1009 (United States)
  3. Department of Automation, Tsinghua University, Beijing (China)
Publication Date:
OSTI Identifier:
22415665
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Chemical Physics; Journal Volume: 142; Journal Issue: 15; Other Information: (c) 2015 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; COMPUTERIZED SIMULATION; MOLECULES; NOISE; PHASE SPACE; QUANTUM STATES; TOPOLOGY; TRAPS