Limit points the monotonic schemes for quantum control

Many numerical simulations in quantum (bilinear) control use the monotonically convergent algorithms of Krotov (introduced by Tannor in [12]), Zhu & Rabitz ([11]) or the general form of Maday & Turinici ([13]). This paper presents an analysis of the limit set of controls provided by these algorithms and a proof of convergence in a particular case.

[1]  David J. Tannor,et al.  Control of Photochemical Branching: Novel Procedures for Finding Optimal Pulses and Global Upper Bounds , 1992 .

[2]  Gerber,et al.  Control of chemical reactions by feedback-optimized phase-shaped femtosecond laser pulses , 1998, Science.

[3]  H. Rabitz Shaped Laser Pulses as Reagents , 2003, Science.

[4]  Gustav Gerber,et al.  Controlling the Femtochemistry of Fe(CO)5 , 1999 .

[5]  B. Bamieh,et al.  Iterative algorithms for optimal control of quantum systems , 2002, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..

[6]  Gabriel Turinici,et al.  Control of quantum dynamics: Concepts, procedures and future prospects , 2003 .

[7]  P. Bucksbaum,et al.  Controlling the shape of a quantum wavefunction , 1999, Nature.

[8]  H. Rabitz,et al.  Teaching lasers to control molecules. , 1992, Physical review letters.

[9]  John A. Hildebrand,et al.  Selective Bond Dissociation and Rearrangement with Optimally Tailored , Strong-Field Laser Pulses , .

[10]  Vladislav V. Yakovlev,et al.  Feedback quantum control of molecular electronic population transfer , 1997 .

[11]  J. Salomon,et al.  Control of Molecular orientation and alignement by monotonic schemes , 2005 .

[12]  Jerrold E. Marsden,et al.  Controllability for Distributed Bilinear Systems , 1982 .

[13]  Vladislav V. Yakovlev,et al.  Quantum Control of Population Transfer in Green Fluorescent Protein by Using Chirped Femtosecond Pulses , 1998 .

[14]  Herschel Rabitz,et al.  A RAPID MONOTONICALLY CONVERGENT ITERATION ALGORITHM FOR QUANTUM OPTIMAL CONTROL OVER THE EXPECTATION VALUE OF A POSITIVE DEFINITE OPERATOR , 1998 .

[15]  Yvon Maday,et al.  New formulations of monotonically convergent quantum control algorithms , 2003 .

[16]  H. Rabitz,et al.  Optimal control of selective vibrational excitation in harmonic linear chain molecules , 1988 .

[17]  R. Vivie-Riedle,et al.  Adapting optimal control theory and using learning loops to provide experimentally feasible shaping mask patterns , 2001 .