Dale Li

This doctoral dissertation is a detailed examination of the effects of strong π pulses applied to a large system of spin-½ nuclei. Nuclear magnetic resonance experiments in a variety of dipolar solids are shown to defy conventional expectations set by the delta-function pulse approximation. Observed effects include multiple π-pulse echo trains with measurable coherence well beyond the expected T₂ for short delays between pulses, an even-odd asymmetry in the echo amplitudes where even-numbered echoes are larger than odd-numbered echoes for long delays between pulses, a fingerprint pattern in the echo train for intermediate delays between pulses, and a strong dependence of the echo train decay rate on the π pulse phase.

Many advanced pulse sequences and proposed quantum algorithms frequently rely on the delta-function pulse approximation to describe how a spin system evolves under the action of many pulses. In particular, it is assumed that π pulses do not refocus the dipolar coupling. However, the action of the system’s internal Hamiltonian during a real finite pulse opens new coherence transfer pathways that lead to the observed effects. Visualization of the entire density matrix shows a unique flow of quantum coherence from non-observable to observable cells when applying repeated π pulses. This work uses Average Hamiltonian theory, combined with exact quantum calculations, to show that the pulse power required to approximate a real pulse as a delta-function pulse appears to be arbitrarily large and depends on the system size, spin-spin coupling strength, rapidity of applied pulses, and the spread of local magnetic fields.