CAREER: Ensemble Control with Applications to Spectroscopy, Imaging, and Computation

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This CAREER proposal proposes a fundamental investigation of a new class of control problems, Ensemble Control, which involves controlling a large number of dynamical systems with the same control signal. State-of-the-art quantum technology can trap and experiment with individual atoms, image brains as well as generate structural and dynamical information of biological macromolecules. Numerous applications arising from such emerging techniques involve controlling a large quantum ensemble, e.g., on the order of Avogadro number (6X1023), by use of the same control field. In many cases, the elements of the ensemble show variations in the values of the parameters characterizing the system dynamics. For example, in magnetic resonance experiments, nuclear spins of an ensemble may have a dispersion in their natural frequencies, so that the spins of an ensemble may have a dispersion in their natural frequencies, so that spins with different excitations (pulse sequences) that can steer such an ensemble of systems with different dynamics from an initial state of desired final state. The challenge is to simultaneously steer a continuum of systems between points of interest with the same control signal. We plan to provide controllability conditions and optimal control techniques for such under-actuated systems. The resulting methodology, via a systematic study of ensemble control problems, can be directly applied to the design of optimal pulse sequences in Nuclear Magnetic Resonance (NMR) spectroscopy and imaging (MRI). The proposed work will advance stat-of ?the-art methods of mathematical control theory and has broad applications including medical imaging, structural biology, as well as quantum information processing. The PI proposes not only to make best use of engineering expertise in above areas of biology and quantum mechanics, but also to help make methods and problems in these fields more accessible to engineers. The proposed CAREER plan provides educational activities and research opportunities for both undergraduates and graduate students to work on multidisciplinary projects. They will work in close collaboration with scientists in other disciplines and will work on solving real world problems. For example, students will design optimal pulse sequences for MRI systems and will implement them onto the real MRI machines.