Unitary Control in Quantum Ensembles, Maximizing Signal Intensity in Coherent Spectroscopy", Science 280, 421-424 (1998) S. J. Glaser, T. Schulte-Herbrüggen, M. Sieveking, O. Schedletzky, N. C. Nielsen, O. W. Sørensen, C. Griesinger

**Abstract: **Experiments in coherent magnetic resonance, microwave and optical spectroscopy control quantum-mechanical ensembles by guiding them from initial 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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