Time optimal control in spin systems

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 63, Issue 3, 2001, Pages 1-13

  Khaneja, Navin ^a   Brockett, Roger ^b   Glaser, Steffen J ^c  

^a Dartmouth College   (United States)

^b HARVARD UNIVERSITY   (United States)

^c TECHNICAL UNIVERSITY OF MUNICH   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33646192786     PISSN: 10502947     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevA.63.032308     Document Type: Article

References (29)

1. S. Kobayashi and K. Nomizu, Foundations of Differential Geometry (Interscience, New York, 1969) Vols. 1 and 2.
2. S. Helgason, Differential Geometry, Lie Groups, and Symmetric Spaces (Academic, New York, 1978).
3. J. A. Wolf, Spaces of Constant Curvature (McGraw Hill, New York, 1967).
4. V. Jurdjevic and H. J. Sussmann, J. Diff. Eqns. 12, 313 (1972).
5. R. R. Ernst, G. Bodenhausen, and A. Wokaun, Principles of Nuclear Magnetic Resonance in One and Two Dimensions (Oxford University Press, Oxford, 1987).
6. S. J. Glaser, T. Schulte-Herbrüggen, M. Sieveking, O. Schedletzky, N. C. Nielsen, O. W. Sørensen, and C. Griesinger, Science 280, 421 (1998).
7. W. S. Warren, H. Rabitz, and M. Dahleh, Science 259, 1581 (1993).
8. N. A. Gershenfeld and I. L. Chuang, Science 275, 350 (1997); D. G. Cory, A. Fahmy, and T. Havel, Proc. Natl. Acad. Sci. U.S.A. 94, 1634 (1997).
9. N. A. Gershenfeld and I. L. Chuang, Science 275, 350 (1997); D. G. Cory, A. Fahmy, and T. Havel, Proc. Natl. Acad. Sci. U.S.A. 94, 1634 (1997).
10. T. Untidt, T. Schulte-Herbrüggen, B. Luy, S. J. Glaser, C. Griesinger, O. W. Sørensen, and N. C. Nielsen, Mol. Phys. 95, 787 (1998); T. Untidt, S. J. Glaser, C. Griesinger, and N. C. Nielsen, Mol. Phys. 96, 1739 (1999).
11. T. Untidt, T. Schulte-Herbrüggen, B. Luy, S. J. Glaser, C. Griesinger, O. W. Sørensen, and N. C. Nielsen, Mol. Phys. 95, 787 (1998); T. Untidt, S. J. Glaser, C. Griesinger, and N. C. Nielsen, Mol. Phys. 96, 1739 (1999).
12. J. Cavanagh, A. G. Palmer III, P. E. Wright, and M. Rance, J. Magn. Reson. 91, 429 (1991); A. G. Palmer III, J. Cavanagh, P. E. Wright, and M. Rance, ibid. 93, 151 (1991); L. E. Kay, J. Am. Chem. Soc. 115, 2055 (1993); J. Schleucher, M. Schwendinger, M. Sattler, P. Schmidt, O. Schedletzky, S. J. Glaser, O. W. Sørensen, and C. Griesinger, J. Biomol. NMR 4, 30 (1994).
13. J. Cavanagh, A. G. Palmer III, P. E. Wright, and M. Rance, J. Magn. Reson. 91, 429 (1991); A. G. Palmer III, J. Cavanagh, P. E. Wright, and M. Rance, ibid. 93, 151 (1991); L. E. Kay, J. Am. Chem. Soc. 115, 2055 (1993); J. Schleucher, M. Schwendinger, M. Sattler, P. Schmidt, O. Schedletzky, S. J. Glaser, O. W. Sørensen, and C. Griesinger, J. Biomol. NMR 4, 30 (1994).
14. J. Cavanagh, A. G. Palmer III, P. E. Wright, and M. Rance, J. Magn. Reson. 91, 429 (1991); A. G. Palmer III, J. Cavanagh, P. E. Wright, and M. Rance, ibid. 93, 151 (1991); L. E. Kay, J. Am. Chem. Soc. 115, 2055 (1993); J. Schleucher, M. Schwendinger, M. Sattler, P. Schmidt, O. Schedletzky, S. J. Glaser, O. W. Sørensen, and C. Griesinger, J. Biomol. NMR 4, 30 (1994).
15. J. Cavanagh, A. G. Palmer III, P. E. Wright, and M. Rance, J. Magn. Reson. 91, 429 (1991); A. G. Palmer III, J. Cavanagh, P. E. Wright, and M. Rance, ibid. 93, 151 (1991); L. E. Kay, J. Am. Chem. Soc. 115, 2055 (1993); J. Schleucher, M. Schwendinger, M. Sattler, P. Schmidt, O. Schedletzky, S. J. Glaser, O. W. Sørensen, and C. Griesinger, J. Biomol. NMR 4, 30 (1994).
16. M. Sattler, P. Schmidt, J. Schleucher, O. Schedletzky, S. J. Glaser, and C. Griesinger, J. Magn. Reson., Ser. B 108, 235 (1995).
17. D. P. Weitekamp, J. R. Garbow, and A. Pines, J. Chem. Phys. 77, 2870 (1982); 80, 1372 (1984); P. Caravatti, L. Braunschweiler, and R. R. Ernst, Chem. Phys. Lett. 100, 305 (1983); S. J. Glaser and J. J. Quant, in Advances in Magnetic and Optical Resonance, edited by W. S. Warren (Academic Press, New York, 1996), Vol. 19, pp. 59-252.
18. D. P. Weitekamp, J. R. Garbow, and A. Pines, J. Chem. Phys. 77, 2870 (1982); 80, 1372 (1984); P. Caravatti, L. Braunschweiler, and R. R. Ernst, Chem. Phys. Lett. 100, 305 (1983); S. J. Glaser and J. J. Quant, in Advances in Magnetic and Optical Resonance, edited by W. S. Warren (Academic Press, New York, 1996), Vol. 19, pp. 59-252.
19. D. P. Weitekamp, J. R. Garbow, and A. Pines, J. Chem. Phys. 77, 2870 (1982); 80, 1372 (1984); P. Caravatti, L. Braunschweiler, and R. R. Ernst, Chem. Phys. Lett. 100, 305 (1983); S. J. Glaser and J. J. Quant, in Advances in Magnetic and Optical Resonance, edited by W. S. Warren (Academic Press, New York, 1996), Vol. 19, pp. 59-252.
20. D. P. Weitekamp, J. R. Garbow, and A. Pines, J. Chem. Phys. 77, 2870 (1982); 80, 1372 (1984); P. Caravatti, L. Braunschweiler, and R. R. Ernst, Chem. Phys. Lett. 100, 305 (1983); S. J. Glaser and J. J. Quant, in Advances in Magnetic and Optical Resonance, edited by W. S. Warren (Academic Press, New York, 1996), Vol. 19, pp. 59-252.
21. R. S. Judson, K. K. Lehmann, H. Rabitz, and W. S. Warren, J. Mol. Struct. 223, 425 (1990).
22. T. Schulte-Herbrüggen, Aspects and Prospects of High-Resolution NMR, Ph.D. thesis, ETH Zurich, 1998.
23. R. W. Brockett and Navin Khaneja, System Theory: Modeling, Analysis and Control (Kluwer Academic, New York, 1999).
24. Navin Khaneja, Ph.D. thesis, Harvard University, 2000.
25. O. W. Sørensen, G. W. Eich, M. H. Levitt, G. Bodenhausen, and R. R. Ernst, Progr. NMR Spectrosc. 16, 163 (1983).
26. Robert Gilmore, Lie Groups, Lie Algebras and Some of Their Applications (Wiley-Interscience, New York, 1974).
27. Roger W. Brockett, in Proceedings of the 1999 CDC Conference, Phoenix, AZ, 1999, pp. 13-16 (unpublished).
28. B. Kostant, Ann. Sci. Ecole Norm. Sup. 6, 413 (1973).
29. G. W. Haynes and H. Hermes, SIAM J. Control Optim. 8, 450 (1970).