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

Abstract

Nuclear spins are promising candidates for quantum information processing because their good isolation from the environment precludes the rapid loss of quantum coherence. Many strategies have been developed to further extend their decoherence times. Some of them make use of decoupling techniques based on the Carr-Purcell and Carr-PurcellMeiboom-Gill pulse sequences. In many cases, when applied to inhomogeneous samples, they yield a magnetization decay much slower than that of the Hahn echo. However, we have proved that these decays cannot be associated with longer decoherence times, as coherences remain frozen. They result from coherences recovered after their storage as local polarization and thus they can be used as memories. We show here how this freezing of the coherent state, which can subsequently be recovered after times longer than the natural decoherence time of the system, can be generated in a controlled way with the use of field gradients. A similar behaviour of homogeneous samples in inhomogeneous fields is demonstrated. It is emphasized that the effects of inhomogeneities in solid-state nuclear magnetic resonance, independently of their origin, should not be disregarded, as they play a crucial role in multipulse sequences.

Long-lived selective spin echoes in dipolar solids under periodic and aperiodicπ-pulse trains

“…Finally, we will end by comparing the theory presented in this work to the Barrett [16][17][18] and Levstein [20][21][22][23] proposals. Like both proposals, our theory predicts that the CPMG(Y, Y ) and CPMG(X, −X) pulse trains can generate long-lived echoes from initial y-magnetization while the CPMG(X, X) and CPMG(Y, −Y ) pulse trains cannot.…”

“…Since stimulated echo pathways were considered as a potential source of the long-lived echoes [21][22][23] pulse trains in Fig. 11(A), the reduction in echo amplitude was not due to line narrowing, as can be seen from the spectra from the last echo in Fig.…”

“…The periodicity of the CPMG pulse train also ensures that all possible coherence pathways that begin and end with single-quantum coherence will refocus at the time of the echo, meaning that the long-lived echoes contain contributions from all possible coherence pathways 24,25 . As mentioned in the introduction, one proposal [20][21][22][23] for the long-lived echoes under the CPMG pulse train is that the echoes arise from stimulated echo 7 pathways. In a stimulated echo pathway, a portion of the single-quantum coherence is stored as zero-quantum coherence and/or longitudinal magnetization by an imperfect π−pulse, which can then be transferred back into single-quantum coherence from subsequent imperfect π−pulses.…”

“…Levstein argued that the contributions from the stimulated echoes therefore make the echo amplitudes appear to be "artificially" long-lived. Because it was demonstrated that stimulated echoes in C 60 were present after the application of a few π−pulses 21,23 , it was argued that stimulated echoes generated by magnetization coherence transfer pathways contributed at all echo times due to the periodicity of the CPMG pulse train 24,25 . In this work, we present an alternative theory for the long-lived echoes in dipolar solids observed under CPMG(φ 1 , φ 2 ) pulse trains under the conditions τ t p .…”

“…However, it was also observed that long-lived echoes could also be observed even when τ t p , where many of the AHT arguments used in the Barrett proposal [16][17][18] would break down since the contribution of H D during the pulse to the average Hamiltonian would appear to be negligible under these conditions. An alternative theory proposed by the Levstein group [20][21][22][23] , which will be referred to as the Levstein proposal in this paper, was advanced which argued that the long-lived echoes were not due to violations of the δ-pulse limit but were instead the consequence of imperfect π−rotations from field inhomogeneities within the sample along with the absence of spin diffusion during the CPMG sequence. In their proposal, the imperfect π−pulses could store some of the single-quantum coherence along the the direction of the large, static Zeeman field (taken to be along the z-direction) in the form of z-magnetization and/or zero-quantum coherences.…”