Anomalies in the NMR of Silicon: Unexpected Spin Echoes in a Dilute Dipolar Solid

NMR spin echo measurements of $^{29}$Si in Silicon powders have uncovered a variety of surprising phenomena that appear to be independent of doping. These surprises include long tails and even-odd asymmetry in Carr-Purcell-Meiboom-Gill (CPMG) echo trains, and anomalous stimulated echoes with several peculiar characteristics. Given the simplicity of this spin system, these results, which to date defy explanation, present a new and interesting puzzle in solid state NMR. In the broader context of quantum computation, these experiments suggest that similar surprises may be found in other systems with small, long-range, qubit-qubit interactions, particularly when ``bang-bang'' control is used.