Robust Manipulation and Computation for Inhomogeneous Quantum Ensembles.

摘要

This project focused on the development of a novel control-theoretic framework with a set of tractable computational methods for robust manipulation of inhomogeneous quantum ensembles. Engineering the time evolution of quantum ensembles in a desired manner by using electromagnetic pulses of appropriate shape and frequency is an indispensable step that enables many applications in quantum control, such as nuclear magnetic resonance (NMR) spectroscopy and imaging, laser cooling, solid state physics, and quantum computation. This project carried out a fundamental investigation of ensemble control systems. New methods were established to analyze controllability of quantum ensembles through polynomial approximations, which inspired the development of a unified computational method based on pseudospectral approximations for solving optimal ensemble control problems. This newly developed computational method has been used to design optimal pulses for protein NMR spectroscopy, which have been experimentally implemented yielding a significant sensitivity enhancement over the conventional pulses. The scope of this project was extended beyond the control of quantum ensembles to general ensemble systems, where controllability characterization for linear and nonlinear ensemble systems was provided, and efficient optimization-free computational methods for optimal control synthesis for such systems were developed.