Unitary control in quantum ensembles: maximizing signal intensity in coherent spectroscopy |
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Authors: | SJ Glaser T Schulte-Herbruggen M Sieveking O Schedletzky NC Nielsen OW Sorensen C Griesinger |
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Affiliation: | S. J. Glaser, O. Schedletzky, C. Griesinger, Institut fur Organische Chemie, J. W. Goethe-Universitat, Marie-Curie-Strasse 11, D-60439 Frankfurt, Germany. T. Schulte-Herbruggen, Laboratorium fur Physikalische Chemie, ETH Zentrum, CH-809. |
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Abstract: | Experiments in coherent magnetic resonance, microwave, and optical spectroscopy control quantum-mechanical ensembles by guiding them from initial states toward target states by unitary transformation. Often, the coherences detected as signals are represented by a non-Hermitian operator. Hence, spectroscopic experiments, such as those used in nuclear magnetic resonance, correspond to unitary transformations between operators that in general are not Hermitian. A gradient-based systematic procedure for optimizing these transformations is described that finds the largest projection of a transformed initial operator onto the target operator and, thus, the maximum spectroscopic signal. This method can also be used in applied mathematics and control theory. |
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