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.
Matrix Inequalities in Science and Engineering: Topics