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

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, spect...

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Bibliographic Details
Published in:Science (American Association for the Advancement of Science) 1998-04, Vol.280 (5362), p.421-424
Main Authors: Glaser, S. J., Schulte-Herbrüggen, T., Sieveking, M., Schedletzky, O., Nielsen, N. C., Sørensen, O. W., Griesinger, C.
Format: Article
Language:English
Subjects:
Algorithms
Axes of rotation
Eigenvalues
Exact sciences and technology
Geometric planes
Infrared, submillimeter wave, microwave and radiowave instruments, equipment and techniques
Instruments, apparatus, components and techniques common to several branches of physics and astronomy
Mathematical functions
Mathematical transformations
Mathematics
Methods
Nuclear magnetic resonance
Nuclear spin
Physics
Quantum chemistry
Spectroscopy
Spectrum analysis
Statistical Data
Time-resolved optical spectroscopies and other ultrafast optical measurements in condensed matter
Trajectories
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Summary: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.
ISSN:0036-8075
1095-9203
DOI:10.1126/science.280.5362.421