Manifestations of the absence of spin diffusion in multipulse NMR experiments on diluted dipolar solids

Abstract

Puzzling anomalies previously observed in multipulse NMR experiments in natural abundance 29 Si [A.E. Dementyev, D. Li, K. MacLean, and S.E. Barrett, Phys. Rev. B 68, 153302 (2003)] such as long-lived spin echoes and even-odd asymmetries, are also found in polycrystalline C60. Further experiments controlling the phases and tilting angles of the pulse trains, as well as analytical and numerical calculations allowed us to explain the origin of these anomalies. We prove that the observation of long magnetization tails requires two conditions: i) an rf field inhomogeneity able to produce different tilting angles in different sites of the sample and ii) the absence of spin diffusion (non-effective flip-flop interactions). The last requirement is easily satisfied in diluted dipolar solids, where the frequency differences between sites, caused by disorder or other sources, are usually at least one order of magnitude larger than the dipolar couplings. Both conditions lead to the generation of stimulated echoes in Carr-Purcell (CP) and Carr-Purcell-Meiboom-Gill (CPMG) pulse trains. We show, both experimentally and theoretically, that the stimulated echoes interfere constructively or destructively with the normal (Hahn) echoes depending on the alternation or not of the π pulse phases in the CP and the CPMG sequences. Constructive interferences occur for the CP and CPMG sequences with and without phase alternation respectively, which are the cases where long magnetization tails are observed. Sequences with two, three and four π pulses after the π/2 pulse allow us to disentangle the contributions of the different echoes and show how the stimulated echoes originate the even-odd asymmetry observed in both 29 Si and C60 polycrystalline samples.During the last years, the control of quantum coherence has become of great importance for quantum information processing and for the development of new nanotechnologies. In the nanoscale, many quantum phenomena become evident and can be exploited. However, interaction with various degrees of freedom of the environment degrades the quantum coherence. As a consequence, it is necessary to understand in detail the mechanisms that produce decoherence and their timescales. Many suggestions to implement quantum computations involve nuclear or electron spins.1,2 In particular, as silicon has been an essential component of one of the main proposals, 3 a group of researchers carried out a series of nuclear magnetic resonance (NMR) measurements to study the spin-spin "decoherence" time (T 2 ) in 29 Si (4.67% natural abundance, spin 1 2 ) doped with different concentrations of donors or acceptors.4 Their results were completely unexpected and defied explanation to date.They performed T 2 measurements with different pulse sequences commonly used with this purpose. They found that it is possible to detect 29 Si NMR signals up to much longer times (more than two orders of magnitude) by applying the Carr-Purcell-Meiboom-Gill sequence as compared with the characteristic decay time obtained from ...

Storage of quantum coherences as phase-labelled local polarization in solid-state nuclear magnetic resonance

“…Similar situations were observed in all the systems that manifest long decay times when CPMG-like sequences are applied [12,43,44].…”

“…It can be observed that the stimulated echoes appear 1 ms after the last pulse (remember that they should not be formed with perfect p pulses) and they show a phase that coincides with or is opposite to that of the Hahn echo, which appears at t 1 − t = 14 ms, for the CPMG1 STE and CPMG2 STE , respectively. A phenomenological explanation for the long magnetization tails based on the constructive or destructive interference between the stimulated and normal echoes was reported by us in a previous paper [43] and later on verified through hole burning experiments [44]. Thus, although disappointing for the experimentalists of the quantum information community, we concluded that the observed long tails in the magnetization decays are a signature not of long decoherence times but of the recovery of coherences saved as polarization.…”

“…It is straightforward to see that whether the second and third pulses in figure 5 are p pulses, a stimulated echo will not be created [43,61]. Nevertheless, if a spatial distribution of flip angles is present in the sample, stimulated echoes will be created owing to the deviations from p pulses, as shown elsewhere [43,60].…”

“…As reviewed in §3 and in figures 1-4, we analysed [43] two different sequences derived from Carr-Purcell [35] and Carr-Purcell-Meiboom-Gill [36], which produce long decay times compared with the Hahn echo in inhomogeneous samples, namely CP2 and CPMG1 (figure 1). In this section, the evolution of the magnetization during these sequences is studied upon variations of external field gradients and inter-pulse spacing.…”

“…We summarize our own findings on anomalous long-lived echo signals [12,[41][42][43][44]. In particular, we emphasize the use of a simple stimulated echo sequence to discern whether one is in the presence of true long decoherence times or if the coherences are being saved as polarization and then recovered.…”