Analytic controllability of time-dependent quantum control systems

Journal of Mathematical Physics

Volumn 46, Issue 5, 2005, Pages

  Lan, Chunhua ^a   Tarn, Tzyh Jong ^a   Chi, Quo Shin ^b   Clark, John W ^b  

^a WASHINGTON UNIVERSITY IN ST LOUIS   (United States)

^b WASHINGTON UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 18844409135     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.1867979     Document Type: Article

References (75)

1. A. Kuriksha, Quantum Optics and Optical Location (Sovetskoe Radio, 1973).
2. D. J. Bradley, J. Russ. Soc. Arts, Nov, 3 (1977).
3. A. G. Butkovskiy and Y. I. Samoilenko, Autom. Remote Control (Engl. Transl.) 40, 485 (1979).
4. A. G. Butkovskiy and Y. I. Samoilenko, Autom. Remote Control (Engl. Transl.) 40, 629 (1979).
5. G. M. Huang, T. J. Tarn, and J. W. Clark, J. Math. Phys. 24, 2608 (1983).
6. A. Blaquiere, Proceedings of the 4th International Seminar on Mathematical Theory of Dynamical Systems and Microphysics, Udine, 1985.
7. A. Blaquiere, Proceedings of the Bellman Continuum Workshop, Sophia Antipolis, 1988.
8. A. G. Butkovskiy and Y. I. Samoilenko, Control of Quantum Mechanical Processes and Systems (Kluwer, Dordrecht, 1990).
9. H. Ezawa and Y. Murayama, Proceedings of the ISQM Satellite Workshop ARL, Hitachi, 1992.
10. R. Gordon and S. A. Rice, Annu. Rev. Phys. Chem. 48, 601 (1997).
11. H. Rabitz, R. de Vivie-Riedle, M. Motzkus, and K. Kompa, Science 288, 824 (2000).
12. S. Lloyd, Phys. Rev. A 62, 022108 (2000).
13. S. Lloyd and S. L. Braunstein, Phys. Rev. Lett. 82, 1784 (1999).
14. R. W. Brockett, Proc. IEEE 64, 61 (1976).
15. C. P. Slichter, Principles of Magnetic Resonance, 3rd ed. (Springer-Verlag, New York, 1990).
16. C. P. Ernst, G. Bodenhausen, and A. Wokaun, Principles of Nuclear Magnetic Resonance in One and Two Dimensions (Oxford University Press, Oxford, 1987).
17. L. Elmsley and A. Pines, Proceedings of the International School of Physics "Enrico Fermi," 2nd ed., Varenna, 1994.
18. S. Lloyd, Phys. Rev. Lett. 75, 346 (1995).
19. D. Deutsch, A. Barenco, and A. Ekert, Proc. R. Soc. London, Ser. A 449, 669 (1995).
20. V. M. Akulin, V. Gershkovich, and G. Harel, Phys. Rev. A 64, 012308 (2001).
21. J. W. Clark, Condens. Matter Theor. 11, 3 (1996).
22. V. Ramakrishna, M. V. Salapaka, M. Dahleh, H. Rabitz, and A. Peirce, Phys. Rev. A 51, 960 (1995).
23. V. Ramakrishna and H. Rabitz, Phys. Rev. A 54, 1715 (1996).
24. H. J. Sussmann and V. Jurdjevic, J. Diff. Eqns. 12, 95 (1972).
25. V. Jurdjevic and H. J. Sussmann, J. Diff. Eqns. 12, 313 (1972).
26. S. Lloyd and J. J. E. Slotine, Phys. Rev. Lett. 80, 4088 (1998).
27. S. L. Braunstein, Phys. Rev. Lett. 80, 4084 (1998).
28. S. L. Braunstein, Nature (London) 394, 47 (1998).
29. S. L. Braunstein and H. J. Kimble, Phys. Rev. Lett. 80, 869 (1998).
30. A. Furusawa, Science 282, 706 (1998).
31. G. M. Huang, Doctoral dissertation, Washington University, 1980.
32. E. Nelson, Ann. Math. 70, 572 (1959).
33. Y. Sakawa, SIAM J. Control Optim. 21, 667 (1983).
34. B. Keulen, SIAM J. Control Optim. 32, 261 (1994).
35. K. A. Morris, Syst. Control Lett. 44, 211 (2001).
36. K. A. Morris, J. Math. Syst. Est. Control 4, 1 (1994).
37. O. L. V. Costa and C. S. Kubrusly, J. Math. Syst. Est. Control 6, 1 (1996).
38. G. Weiss and R. Rebarber, SIAM J. Control Optim. 39, 1204 (2000).
39. J. T. Wen, Syst. Control Lett. 13, 445 (1989).
40. C. Corduneanu, Integral Equations and Stability of Feedback Systems (Academic, New York, 1973).
41. G. A. Leonov, D. V. Ponomarenko, and V. B. Smirnova, Frequency-Domain Methods for Nonlinear Analysis (World Scientific, Singapore, 1996).
42. H. Logemann, Automatica 27, 677 (1991).
43. D. Wexler, SIAM J. Math. Anal. 11, 969 (1980).
44. R. Rebarber and H. Zwart, Math. Control, Signals, Syst. 11, 129 (1998).
45. F. M. Callier and J. Winkin, Int. J. Control 52, 55 (1990).
46. F. M. Callier and J. Winkin, Automatica 28, 757 (1992).
47. O. J. Staffans, Eur. J. Control 5, 167 (1999).
48. M. Weiss and G. Weiss, Math. Control, Signals, Syst. 10, 287 (1997).
49. L. Viola, E. Knill, and S. Lloyd, Phys. Rev. Lett. 82, 2417 (1999).
50. M. Thorwart, P. Reimann, and P. Hänggi, Theoretische Physik I, 1999, p. 142.
51. R. K. Colegrave and M. S. Abdalla, Opt. Acta 28, 495 (1981).
52. R. K. Colegrave and M. S. Abdalla, J. Phys. A 15, 1549 (1982).
53. B. Remaud and E. S. Hernandez, J. Phys. A 13, 2013 (1980).
54. H. Kunita, Proceedings of the International Symposium on SDE, 1976, p. 163.
55. R. M. Santilli, Foundations of Theoretical Mechanics I, The Inverse Problem in Newtonian Mechanics (Springer-Verlag, New York, 1978).
56. T. J. Tarn, G. M. Huang, and J. W. Clark, Mathematical Modelling 1, 109 (1980).
57. A. O. Barut and R. Raczka, Theory of Group Representations and Applications (World Scientific, Singapore, 2000).
58. H. Kunita, Appl. Math. Optim. 5, 89 (1979).
59. A. Isidori, Nonlinear Control Systems, 3rd ed. (Springer, New York, 1995).
60. J. W. Clark, T. J. Tarn, and D. G. Lucarelli, Proceedings of PhysCon 2003, St. Petersburg, Russia, 2003, p. 20.
61. J. W. Clark, D. G. Lucarelli, and T. J. Tarn, Int. J. Mod. Phys. B 6, 411 (2002).
62. W. L. Chow, Math. Ann. 117, 98 (1939).
63. G. Hochschild, The Structure of Lie Groups (Holden-Day, San Francisco, 1965).
64. K. Ichihara and H. Kunita, Z. Wahrscheinlichkeitstheor. Verwandte Geb. 30, 235 (1974).
65. K. Ichihara and H. Kunita, Z. Wahrscheinlichkeitstheor. Verwandte Geb. 39, 81 (1977).
66. C. Lan, Doctoral dissertation, Washington University, 2003.
67. D. F. Walls and G. J. Milburn, Quantum Optics (Springer-Verlag, Berlin, 1995).
68. C. Brif, A. Vourdas, and A. Mann, J. Phys. A 29, 5873 (1996).
69. C. C. Gerry, Phys. Rev. A 35, 2146 (1987).
70. C. C. Gerry, J. Opt. Soc. Am. B 8, 685 (1991).
71. L. Zhang, G. Yang, and D. Cao, Phys. Lett. A 308, 235 (2003).
72. C. P. Boyer, E. G. Kalnins, and W. Miller, J. Math. Phys. 16, 499 (1975).
73. S. Zhang and F. Li, J. Phys. A 29, 6143 (1996).
74. J. Ĺvy-Leblond, Phys. Rev. A 52, 1845 (1995).
75. L. Chetouani, L. Dekar, and T. F. Hammann, Phys. Rev. A 52, 82 (1995).