Optimal control in an open quantum system : selecting DNP pathways in an electron-nuclear system

Abstract

There is much interest in improving quantum control techniques for the purposes of quantum information processing. High fidelity control is necessary for the future of quantum computing. Optimal control theory has been used successfully to numerically optimize control sequences for spin-based systems. Previous control pulse finding efforts have primarily optimized pulses to a desired unitary control. Non-unitary dynamics are unavoidable in quantum systems, and, to improve current control techniques, interactions with the environment and stochastic noise processes must be incorporated into pulse design. We present here a method of pulse optimization that includes decoherence. This thesis discusses a particular example of engineering control for an open quantum system: selecting transfer pathways in dynamic nuclear polarization. Dynamic nuclear polarization (DNP) is a method of increasing the nuclear spin magnetization in a nuclear magnetic resonance experiment. DNP works by transferring polarization from a coupled electron spin. In solid state systems, however, there are multiple pathways through which polarization can be transferred. Excitation of more than one pathway can prevent the nuclear spin from achieving the maximum possible polarization. It is demonstrated in this thesis that optimal control theory (OCT) can be used to design pulses which will select one pathway and suppress the others. The pulses were found considering the open quantum system dynamics. This work includes an algorithm for generating noise realizations from a spectral density function. Future efforts to engineer high-fidelity control could use this method to incorporate stochastic noise in the pulse finding process.