Dissertation Defense: Jared Rovny, Yale University, “New NMR Applications and Methods: Discrete Time Crystalline Signatures and Accelerated Acquisition using Iterated Maps”

This thesis describes two distinct research endeavors linked by nuclear magnetic resonance (NMR) experiments. One is related to the nascent study of discrete time crystals (DTCs) in driven quantum systems. In this thesis I describe the first NMR studies of DTC signatures in solids, characterizing the DTC signatures we observed in a crystal of ammonium dihydrogen phosphate, where we addressed nuclear spins of phosphorus 31P and hydrogen 1H. I also describe the methods we used to demonstrate quantum coherence in the resulting spin state, the lifetime of observables of the driven system, and the important experimental factors that play a recurrent role in the spin physics.
The other topic pertains to accelerating NMR experiments, by acquiring less data than usual and reconstructing the resulting data sets. The reconstruction is performed using variants of the Difference Map (DiffMap) algorithm, whose properties we study extensively. I also describe a new method that was created during this work, based on DiffMap and useful for data sets possessing correlations among parts of the data, called coDiffMap. I demonstrate how coDiffMap allows us to reconstruct a pseudo-3D NMR data set very quickly with high fidelity, and discuss various aspects of this new algorithm’s implementation.
Thesis Advisor: Sean Barrett (sean.barrett@yale.edu)