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Physics
Boundary of quantum evolution under decoherence
Division of Applied Sciences, Harvard University, Cambridge, MA 02138; and ¶Institute for Organic Chemistry and Biochemistry, Technische Universität München, 85747 Garching, Germany
Edited by Alfred G. Redfield, Brandeis University, Waltham, MA and approved August 13, 2003 (received for review June 28, 2003)
Relaxation effects impose fundamental limitations on our ability to coherently control quantum mechanical phenomena. In this article, we use principles of optimal control theory to establish physical limits on how closely a quantum mechanical system can be steered to a desired target state in the presence of relaxation. In particular, we explicitly compute the maximum amplitude of coherence or polarization that can be transferred between coupled heteronuclear spins in large molecules at high magnetic fields in the presence of relaxation. Very general decoherence mechanisms that include cross-correlated relaxation have been included in our analysis. We give analytical characterization for the pulse sequences (control laws) that achieve these physical limits and provide supporting experimental evidence. Exploitation of cross-correlation effects has recently led to the development of powerful methods in NMR spectroscopy to study very large biomolecules in solution. For two heteronuclear spins, we demonstrate with experiments that cross-correlated relaxation optimized pulse (CROP) sequences provide significant gains over the state-of-the-art methods. It is shown that despite large relaxation rates, coherence can be transferred between coupled spins without any loss in special cases where cross-correlated relaxation rates can be tuned to autocorrelated relaxation rates.
Abbreviations: CSA, chemical shift anisotropy; DD, dipole-dipole; CROP, cross-correlated relaxation optimized pulse.
To whom correspondence should be addressed. E-mail: navin{at}hrl.harvard.edu.
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  N. Khaneja, J.-S. Li, C. Kehlet, B. Luy, and S. J. Glaser Broadband relaxation-optimized polarization transfer in magnetic resonance PNAS, October 12, 2004; 101(41): 14742 - 14747. [Abstract] [Full Text] [PDF]
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