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

• DOI: 10.1126/science.280.5362.421
• Publication Date: 2002-07-27T09:35:26Z
• Authors: S. J. Glaser; T. Schulte-Herbru...; M. Sieveking; O. Schedletzky; N. C. Nielsen; O. W. Sørensen; C. Griesinger
• Keywords: 0209 industrial biotechnology; 02 engineering and technology

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.