Control of Nuclear Spin Systems

In this talk I will describe applications of control theory to problems that arise in manipulation of spin dynamics in nuclear magnetic resonance (NMR) spectroscopy using radio frequency pulses. In control and manipulation of quantum systems, the system of interest is rarely isolated but interacts with its environment. This leads to relaxation which in practice results in signal loss and limits the range of applications.

I will present our work on optimal design of rf pulse sequences for minimizing relaxation losses and improving the sensitivity of experiments. I will motivate the study of class of optimal control problems ranging from time optimal control of dynamical systems evolving on compact Lie Groups to computing the reachable sets of dissipative control systems.

Applications of these optimal control methods to quantum information processing and NMR spectroscopy of biomolecules will be discussed. These experiments involve steering an ensemble of quantum systems, which show dispersion in the parameters that govern their dynamics. This gives rise to interesting control problems of steering a continuum of dynamical systems with different dynamics using the same control signal that can compensate for the various dispersions. I will discuss our work on controllability of quantum ensembles.

Navin Khaneja, Harvard University

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