1. Control of Inhomogeneous Spin Ensembles

2. Robust Control of Inhomogeneous Spin Ensembles M x y M

3. Compensation and Composite Pulses z x y

4. Robust Control of Inhomogeneous Spin Ensembles M x y M

7. The problem of manipulating quantum systems with uncertainities or inhomogeneities in parameters govering the system dynamics is ubiquitous in spectroscopy and information processing. a) Understanding what aspect of system dynamics makes compensation possible. b) What kind of inhomogeneities or errors can or cannot be corrected. Typical settings include a) Resonance offsets b) Inhomogeneities in the strength of excitation field (systematic errors) c) Time dependent noise (nonsystematic errors) d) Addressing errors or cross talk Widespread use of composite pulse sequences and pulse shaping first to correct for errors or compensate for inhomogeneties

8. Broadband Control

9. Lie Algebras and Polynomial Approximations

10. Choosesuch that it is approx. constant for Using as generators

11. Lie Algebras and Polynomial Approximations and Ensemble Controllability Create Unitary Evolution as a function of inhomogeneity to desired level of accuracy

12. Basic Mathematical Structure: Non commutativity of generators and an underlying semi-simple Lie-algebra Repeated Lie brackets (commutators) will raise the dispersion parameter to higher powers. The various powers of can be combined to form polynomials that approximate any desired evolution with continuous dependency on

13. Ensemble Controllability of Bloch Equations

14. Larmor Dispersion and Strong Fields

15. Larmor Dispersion and Bounded Controls Adiabatic Passage Adiabatic Passage is Robust to rf-inhomogeneity

16. Ensemble Controllability of Bloch Equations

18. Some Negative Results Nil-Potent Systems Cannot be Compensated x y

19. Some Negative Results Linear systems cannot be compensated for field inhomogeneities

20. Some Negative Results Phase Dispersions Cannot be Compensated

21. Ensemble Controllability of Coupled Spins with Inhomogeneous Couplings

23. I S NOE M x y M H

25. One dimensional spectrum

27. Relaxation Optimized Coherent Spectroscopy Singular Optimal Control Problems Anisotropy Compensated Experiments in Solid state NMR Theory of Broadband Control

28. Inhomogeneous Broadening due to Dipolar Coupling Dispersion B0B0    S

29. Broadband control in biological solid- state NMR DCP OC DCP OC HORROR HORROR J. Am. Chem. Soc., 126 (2005) Chem. Phys. Letter (2005)

30. Time Optimal control of inhomogeneous quantum ensembles Find the shortest pulse sequence (shape) that produces a coherent excitation over

35. Optimal control of inhomogeneous quantum ensembles Create desired excitation profile as a function of

36. Minimum energy pulses for desired excitations (SLR algorithm)

37. Constructive Controllability

38. Applications in NMR and MRI Time optimal selective excitation, inversion and saturation pulses. Imaging and Spectroscopy in inhomogeneous fields.

39. Phase correcting pulses for NMR in Inhomogeneous Static Fields X Y

40. NMR in Inhomogeneous Static Fields

42. Relaxation Specific Excitation

43. Collaborators Steffen Glaser Burkhard Luy Frank Kramer Timo Reiss Kyryl Kobzar Andreas Spoerl Bjoern Heitmann Gerhard Wagner Dominique Frueh Takuhiro Ito Niels Nielsen Astrid Sivertsen Cindie Kehlet Morten Bjerring Technische Universitaet Muenchen Harvard Medical School University of Aarhus

44. NSF Career, NSF Qubic, Sloan, DARPA, AFRL, ONR, AFOSR, Humboldt Haidong Yuan Dionisis Stefanatos Brent Pryor Dan Iancu Andrew Johnson Navin Khaneja Jr-Shin Li