The Intrinsic Origin of Spin Echoes in Dipolar Solids Generated by Strong Pi Pulses

Abstract

In spectroscopy, it is conventional to treat pulses much stronger than the linewidth as delta-functions. In NMR, this assumption leads to the prediction that pi pulses do not refocus the dipolar coupling. However, NMR spin echo measurements in dipolar solids defy these conventional expectations when more than one pi pulse is used. Observed effects include a long tail in the CPMG echo train for short delays between pi pulses, an even-odd asymmetry in the echo amplitudes for long delays, an unusual fingerprint pattern for intermediate delays, and a strong sensitivity to pi-pulse phase. Experiments that set limits on possible extrinsic causes for the phenomena are reported. We find that the action of the system's internal Hamiltonian during any real pulse is sufficient to cause the effects. Exact numerical calculations, combined with average Hamiltonian theory, identify novel terms that are sensitive to parameters such as pulse phase, dipolar coupling, and system size. Visualization of the entire density matrix shows a unique flow of quantum coherence from non-observable to observable channels when applying repeated pi pulses.

24 pages, 27 figures. Revised from helpful referee comments. Added new Table IV, new paragraphs on pages 3 and 19

References in corpus (6)

• Tackling Systematic Errors in Quantum Logic Gates with Composite Rotations
• Coherence Time of a Solid-State Nuclear Qubit
• Multi-spin dynamics of the solid-state NMR Free Induction Decay
• Principles of Control for Decoherence-Free Subsystems
• Generating Unexpected Spin Echoes in Dipolar Solids with Pi Pulses
• Controlling coherence using the internal structure of hard pi pulses

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