Multi-input Schrodinger equation: Controllability, tracking, and application to the quantum angular momentum

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:256

Article

Boscain, Ugo¹  Caponigro, Marco²  Sigalotti, Mario³ 

[1] Ecole Polytech, CNRS, CMAP, F-91128 Palaiseau, France

[2] Conservatoire Natl Arts & Metiers, Equipe M2N, Paris, France

[3] Ecole Polytech, CMAP, Palaiseau, France

关键词: Quantum control;    Bilinear Schrodinger equation;    Galerkin approximations;    Quantum angular momentum;   

DOI  :  10.1016/j.jde.2014.02.004

来源: Elsevier

【 摘 要 】

We present a sufficient condition for approximate controllability of the bilinear discrete-spectrum Schrodinger equation in the multi-input case. The controllability result extends to simultaneous controllability, approximate controllability in Hs, and tracking in modulus. The sufficient condition is more general than those present in the literature even in the single-input case and allows the spectrum of the uncontrolled operator to be very degenerate (e.g. to have multiple eigenvalues or equal gaps among different pairs of eigenvalues). We apply the general result to a rotating polar linear molecule, driven by three orthogonal external fields. A remarkable property of this model is the presence of infinitely many degeneracies and resonances in the spectrum. (c) 2014 Elsevier Inc. All rights reserved.

【 授权许可】

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