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Unitary Control in Quantum Ensembles: Maximizing Signal Intensity in Coherent Spectroscopy

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Science  17 Apr 1998:
Vol. 280, Issue 5362, pp. 421-424
DOI: 10.1126/science.280.5362.421

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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.

  • * To whom correspondence should be addressed. E-mail: sg{at}org.chemie.uni-frankfurt.de (S.J.G.) and cigr{at}org.chemie.uni-frankfurt.de (C.G.)

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