Roger Brockett
Harvard University
On the Stochastic Control of Quantum Ensembles
Over the last 50 years quantum mechanics has come to be applied in very
sophisticated ways. Some of these applications involve the control and
observation of quantum
systems using subtle noncommutative effects. However only recently has
there been any
attempt to look at these from a control theory perspective. In this talk
we cast some of
the main ideas from Nuclear Magnetic Resonance (NMR) as applied to
imaging and spectroscopy in a
system theoretic framework. For example, NMR spectroscopy is taken to
be a system identification
problem. Many key aspects of high resolution NMR spectroscopy involve
manipulating and controlling
nuclear spins in such a way as to generate a suitable signal for
the identification problem. This active control of nuclear spin is
presented as a problem in the control of nonlinear systems. We will show
how the framework of control on Lie groups fits this problem in a
natural way and illustrate how its use leads to improvements over
standard techniques. This is based on Joint work with Navin Khaneja and
Steffen Glaser.
Abstract in Postscript
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