CAREER: Optimal Control of Quantum Systems

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0133673KhanejaOver the past fifty years, there has been a steady increase in man's ability to manipulate and control quantum mechanical phenomena. Today we are surrounded with technology that owes its existence directly or indirectly to quantum mechanical effects. From transistors, lasers, compact disc players, optical fibre communications, magnetic resonance imaging to scanning tunneling microscopes, the quantum technology has effected every aspect of our life. These days the quantum technologists can trap and experiment with individual atoms, bounce atoms up and down on carefully sculpted electromagnetic fields, and image the structure of a crystal, atom by atom. Emergence of the science of quantum information in the last decade has added a new dimension to the applications of control of quantum mechanical phenomena. There is now an increasing emphasis on harnessing quantum dynamics for the purposes of computing, communication, and information storage. All these technologies involve exercising control over quantum mechanical phenomena. A central challenge in the control of quantum dynamics is the loss of coherence (decoherence) in system dynamics, due to unwanted couplings to the environment. This issue of decoherence arises in almost all potential implementations of quantum information devices and control of quantum systems in general. In this project the PI will develop methods inspired by geometric control theory for optimal control of quantum systems. He will compute fundamental bounds on the minimum time it takes to produce a desired evolution in a quantum system and design time optimal control laws which achieve these bounds. These geometric control ideas will be applied to design of time optimal pulse sequences for coherence transfer experiments in high resolution liquid state nuclear magnetic resonance (NMR) spectroscopy, with applications to structural biology and NMR quantum computing. Minimization of time is important as it reduces the effects of decoherence and increases the sensitivity of experiments in NMR spectroscopy. There is a great need for such work in the growing field of structural biology, because time optimal pulse sequences will significantly reduce the spectrometer time (by days in some experiments) leading the way to high-throughput determination of protein structures. Time optimal pulses will also help to scale NMR methods for processing of larger proteins by minimizing decoherence effects. This effort is broad in its scope and applicable to a wide variety of applications involving control of quantum systems.