Formulation and numerical solution of finite-level quantum optimal control problems

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:216

Article

Borzi, A.¹  Salomon, J.²  Volkwein, S.¹ 

[1] Karl Franzens Univ Graz, Inst Math & Wissensch Rechnen, A-8010 Graz, Austria

[2] Univ Paris 09, CEREMADE, F-75775 Paris 16, France

关键词: quantum systems;    optimal control theory;    optimality conditions;    monotonic schemes;    cascadic acceleration;    non-linear conjugate gradient method;   

DOI  :  10.1016/j.cam.2007.04.029

来源: Elsevier

【 摘 要 】

Optimal control of finite-level quantum systems is investigated, and iterative solution schemes for the optimization of a control representing laser pulses are developed. The purpose of this external field is to channel the system's wavefunction between given states in its most efficient way. Physically motivated constraints, such as limited laser resources or population suppression of certain states, are accounted for through an appropriately chosen cost functional. First-order necessary optimality conditions and second-order sufficient optimality conditions are investigated. For solving the optimal control problems, a cascadic non-linear conjugate gradient scheme and a monotonic scheme are discussed. Results of numerical experiments with a representative finite-level quantum system demonstrate the effectiveness of the optimal control formulation and efficiency and robustness of the proposed approaches. (C) 2007 Elsevier B.V. All rights reserved.

【 授权许可】

Free