Senior Thesis Defense

Thursday, May 26, 2016, Wilder 104, 2:00 PM

Jonathan Vandermause, Department of Physics and Astronomy, Dartmouth College

Title:  Characterization and Control of Nuclear Spin Systems

Abstract: Liquid-state nuclear magnetic resonance (NMR) spectroscopy allows small quantum systems of coupled nuclear spins to be precisely controlled. This thesis examines three aspects of characterization and control of nuclear spins using liquid-state NMR. First, we present an efficient method for characterizing a sample's T1 relaxation time that improves the classic inversion recovery sequence by drawing on the powerful tools of convex optimization. We then consider two different methods available in NMR for steering an initial quantum state to a desired target state using shaped radiofrequency pulses. First, the GRAPE (gradient ascent pulse engineering) algorithm is used to design and implement gates that may be used in an NMR quantum computation. Second, Berry's superadiabatic formalism is used to speed up traditionally slow adiabatic pulses. The resulting pulses are shown to have many of the desirable features of traditional adiabatic pulses, including robustness to inhomogeneity in the external and control fields. First steps toward an experimental implementation of these superadiabatic pulses are discussed. Together, these techniques provide experimentally realizable and time-efficient ways to learn the properties of a quantum system and accurately control its evolution in time.