Ensemble control of bloch equations

IEEE Transactions on Automatic Control

Volumn 54, Issue 3, 2009, Pages 528-536

  Li, Jr Shin ^a   Khaneja, Navin ^b  

^a WASHINGTON UNIVERSITY IN ST LOUIS   (United States)

^b HARVARD UNIVERSITY   (United States)

Author keywords

Ensemble control; Ensemble controllability; Lie bracketing; Nuclear magnetic resonance (NMR); Polynomial approximation

Indexed keywords

ALGEBRA; CONTROLLABILITY; DATA PROCESSING; DYNAMICAL SYSTEMS; DYNAMICS; MOTIVATION; NUCLEAR MAGNETIC RESONANCE; NUCLEAR MAGNETIC RESONANCE SPECTROSCOPY; QUANTUM ELECTRONICS; QUANTUM OPTICS; RESONANCE; SPIN DYNAMICS; SYSTEM THEORY;

BLOCH EQUATIONS; CONTROL INPUTS; CONTROL PROBLEMS; CONTROL SIGNALS; ENSEMBLE CONTROL; ENSEMBLE CONTROLLABILITY; LIE BRACKETING; MATHEMATICAL STRUCTURES; NUCLEAR SPINS; PARAMETERS CHARACTERIZING; POINTS OF INTERESTS; QUANTUM SYSTEMS; QUANTUM-INFORMATION PROCESSING; RADIO FREQUENCY FIELDS; SYSTEM DYNAMICS; SYSTEMATIC STUDIES; VECTOR FIELDS;

POLYNOMIAL APPROXIMATION;

EID: 63449104585     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/TAC.2009.2012983     Document Type: Article

References (33)

1. J.-S. Li and N. Khaneja, "Control of inhomogeneous quantum ensembles," Phys. Rev. A, vol. 73, p. 030302, 2006.
2. J.-S. Li, "Control of Inhomogeneous Ensembles," Ph.D. dissertation, Harvard University, Cambrdige, MA, 2006.
3. J.-S. Li and N. Khaneja, "Noncommuting vector fields, polynomial approximations and control of inhomogeneous quantum ensembles," Quant. Phys. 2005 [Online]. Available: http://arxiv.org/abs/ quant-ph/0510012
4. M. H. Levitt, "Composite pulses," Prog. NMR Spectrosc., vol. 18, pp. 61-122, 1986.
5. R. Tycko, "Broadband population inversion," Phys. Rev. Lett., vol. 51, pp. 775-777, 1983.
6. R. Tycko, N. M. Cho, E. Schneider, and A. Pines, "Composite pulses without phase distortion," J. Magn. Reson., vol. 61, pp. 90-101, 1985.
7. A. J. Shaka and R. Freeman, "Composite pulses with dual compensation," J. Magn. Reson., vol. 55, pp. 487-493, 1983.
8. M. Levitt and R. Freeman, "NMR population inversion using a composite pulse," J. Magn. Reson., vol. 33, p. 473, 1979.
9. M. Levitt and R. R. Ernst, "Composite pulses constructed by a recursive expansion procedure," J. Magn. Reson., vol. 55, p. 247, 1983.
10. M. Garwood and Y. Ke, "Symmetric pulses to induce arbitrary flip angles with compensation for rf inhomogeneity and resonance offsets," J. Magn. Reson., vol. 94, pp. 511-525, 1991.
11. T. E. Skinner, T. Reiss, B. Luy, N. Khaneja, and S. J. Glaser, "Application of optimal control theory to the design of broadband excitation pulses for high resolution NMR," J. Magn. Reson., vol. 163, pp. 8-15, 2003.
12. K. Kobzar, T. E. Skinner, N. Khaneja, S. J. Glaser, and B. Luy, "Exploring the limits of broadband excitation and inversion pulses," J. Magn. Reson., vol. 170, pp. 236-243, 2004.
13. K. Kobzar, B. Luy, N. Khaneja, and S. J. Glaser, "Pattern pulses: design of arbitrary excitation profiles as a function of pulse amplitude and offset," J. Magn. Reson., vol. 173, pp. 229-235, 2005.
14. G. C. Chingas, A. N. Garroway, R. D. Bertrand, and W. B. Moniz, "NMR J cross-polarization in liquids: A refocusing method," J. Magn. Reson. vol. 35, pp. 283-288, 1979.
15. M. S. Silver, R. I. Joseph, C.-N. Chen, V. J. Sank, and D. I. Hoult, "Selective population inversion in NMR," Nature, vol. 310, pp. 681-683, 1984.
16. D. E. Rourke, "Selective Pulses in NMR," Ph.D. dissertation, Cambridge University, Cambridge, U.K., 1992.
17. M. Shinnar and J. S. Leigh, "The application of spinors to pulse synthesis and analysis," Magn. Reson. Med., vol. 12, pp. 93-98, 1989.
18. P. Le Roux, "Exact synthesis of radio frequency waveforms," in Proc. 7th SMRM, 1988, p. 1049.
19. S. Conolly, D. Nishimura, and A. Macovski, "Optimal control to the magnetic resonance selective excitation problem," IEEE Trans. Med. Imag, vol. MI-5, no. 2, pp. 106-115, Jun. 1986.
20. J. Mao, T. H. Mareci, K. N. Scott, and E. R. Andrew, "Selective inversion radiofrequency pulses by optimal control," J. Magn. Reson. vol. 70, pp. 310-318, 1986.
21. D. Rosenfeld and Y. Zur, "Design of adiabatic selective pulses using optimal control theory," Magn. Reson. Mde., vol. 36, pp. 401-409, 1996.
22. S. Wimperis, "Broadband, narrowband, and passband composite pulses for use in advanced NMR experiments," J. Magn. Reson., vol. B 109, pp. 221-231, 1994.
23. J. Jones, "Robust ising gates for practical quantum computation," Phys. Rev. A, vol. 67, p. 012317, 2002.
24. K. R. Brown, A. W. Harrow, and I. L. Chuang, "Arbitrarily accurate composite pulse sequences," Phys. Rev. A, vol. 70, p. 052318, 2004.
25. I. Roos and K. Moelmer, "Quantum computing with an inhomogeneously broadened ensemble of ions: Suppression of errors from detuning variations by specially adapted pulses and coherent population trapping," Phys Rev. A, vol. 69, p. 022321, 2004.
26. M. Riebe, H. Häfner, C. F. Roos, W. Hänsel, J. Benhelm, G. P. T. Lancester, T. W. Körber, C. Bercher, F. Schmidt-Kaler, D. F. V. James, and R. Blatt, "Deterministic quantum teleportation with atoms," Nature, vol. 429, pp. 734-737, 2004.
27. M. D. Barrett, J. Chiaverini, T. Schaetz, J. Britton, W. M. Itano, J. D. Jost, E. Knill, C. Langer, D. Leibfried, R. Ozeri, and D. J. Wineland, "Deterministic quantum teleportation of atomic qubits," Nature, vol. 429, pp. 737-739, 2004.
28. A. Abragam, The Principles of Nuclear Magnetism. London, U.K.: Oxford University Press, 1961.
29. H. L. Royden, Real Analysis. New York: Macmillan, 1968.
30. R. Brockett, "System theory on group manifolds and coset spaces," SIAM J. Contr., vol. 10, pp. 265-284, 1972.
31. V. Jurdjevic and H. J. Sussmann, "Control systems on Lie Groups," J. Diff. Eqs., vol. 12, pp. 313-329, 1972.
32. M. D. Crisp, "Adiabatic following approximation," Phys. Rev. A, vol. 8, pp. 2128-2135, 1973.
33. S. Sastry, Nonlinear Systems: Analysis, Stability, and Control. New York: Springer, 1999.