Lyapunov control of Schrödinger equations: Beyond the dipole approximation

Proceedings of the IASTED International Conference on Modelling, Identification, and Control, MIC

Volumn , Issue , 2009, Pages 119-123

  Grigoriu, Andreea ^a   Lefter, Cǎtǎlin ^b   Turinici, Gabriel ^a  

^a UNIVERSITÉ PARIS DAUPHINE   (France)

^b ALEXANDRU IOAN CUZA UNIVERSITY OF IASI   (Romania)

Author keywords

Control Lyapunov function; Numerical simulations; Quantum control; Stabilization

Indexed keywords

COMPUTER SIMULATION; LYAPUNOV FUNCTIONS; STABILIZATION;

CONTROL LYAPUNOV FUNCTION; CONVERGENCE RESULTS; DIPOLE APPROXIMATION; LYAPUNOV CONTROL; NUMERICAL APPROACHES; QUANTUM CONTROL; SECOND-ORDER COUPLING; TRAJECTORY TRACKING;

MICROWAVE INTEGRATED CIRCUITS;

EID: 72049124513     PISSN: 10258973     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (20)

1. C. Altafini. Controllability of quantum mechanical systems by root space decomposition of su(n). J. Math. Phys., 43(5):2051-2062, 2002.
2. R. Brockett. Lie theory and control systems defined on spheres. SIAM J. Appl. Math., 25(2):213-225, 1973.
3. Y. Chen, P. Gross, V. Ramakrishna, H. Rabitz, and K. Mease. Competitive tracking of molecular objectives described by quantum mechanics. J. Chem. Phys., 102:8001-8010, 1995.
4. T. Constantinescu and V. Ramakrishna. Parametrizing quantum states and channels. Quantum Information Processing, 2:221-248, 2003.
5. A. Ferrante, M. Pavon, and G. Raccanelli. Control of quantum systems using model-based feedback strategies. In Proc. of the International Symposium MTNS'2002, 2002.
6. S. Grivopoulos and B. Bamieh. Lyapunov-based control of quantum systems. In Proceedings of the 42nd IEEE Conference on Decision and Control, 2003.
7. P. Gross, H. Singh, H. Rabit, K. Mease, and G.M. Huang. Inverse quantum-mechanical control: A means for design and a test of intuition. Phys. Rev. A, 47:4593, 1993.
8. V. Jurdjevic and J.P. Quinn. Controllability and stability. J. of Diff. Eq., 28:381-389, 1978.
9. H.K. Khalil. Nonlinear Systems. MacMillan, 1992.
10. R. Kosloff, S.A. Rice, P. Gaspard, Tersigni S., and D.J. Tannor. Wavepacket dancing: Achieving chemical selectivity by shaping light pulses. Chem. Phys., 139:201-220, 1989.
11. Y. Maday and G. Turinici. New formulations of monotonically convergent quantum control algorithms. J. Chem. Phys, 118(18), 2003.
12. M. Mirrahimi, P. Rouchon, and G.Turinici. Lyapunov control of bilinear Schrödinger equations. Automatica, 41:1987 1994, 2005.
13. H. Rabitz. and W. Zhu. Quantum control design via adaptive tracking. J. Chem. Phys., 119(7), 2003.
14. V. Ramakrishna, R.J. Ober, K.L. Flores, and H. Rabitz. Control of a coupled two-spin system without hard pulses. Phys. Rev. A, 65:063405-1-9, 2002.
15. S. Shi, A. Woody, and H. Rabitz. Optimal control of selective vibrational excitation in harmonic linear chain molecules. J. Chem. Phys., 88(11):6870-6883, 1988.
16. M. Sugawara. General formulation of locally designed coherent control theory for quantum systems. J. Chem. Phys., 118(15):6784-6800, 2003.
17. H.J. Sussmann and V. Jurdjevic. Controllability of nonlinear systems. J. Diff. Eq, 12:95-116, 1972.
18. G. Turinici. Beyond bilinear controllability: applications to quantum control. In Proceedings of the Workshop on Optimal Control of Coupled Systems of PDE, april 2005.
19. U. Vaidya, D. DAlessandro, and I. Mezic. Control of heisenberg spin systems; lie algebraic decompositions and action-angle variables. In Proceedings of the 42nd IEEE Conference on Decision and Control, 2003.
20. P. Vettori. On the convergence of a feedback control strategy for multilevel quantum systems. In Proc. of the International Symposium MTNS'2002, 2002.