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Applied Magnetic Resonance

Decoherence-Induced Stabilization of the Multiple-Quantum NMR-Spectrum Width

A. A. Lundin, V. E. Zobov

Published Feb 20, 2016• 10 citations
Publisher
DOI
10.1007/s00723-016-0770-z

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As opposed to traditional methods of multiple-quantum NMR spectroscopy authors of the article [G.A. Alvarez, D. Suter, Phys. Rev. A 84, 012320 (2011)] generated the effective double-quantum Hamiltonian, with the slight adding usual secular dipole-dipole Hamiltonian to the first one at the stage of the correlations preparing (so the perturbation appeared). At this framework the width of MQ spectra reveals tending to any constant amount with the growing up of the time. Also there were shown that the spectral width decreases with increasing perturbation strength. The growing up of the cluster size as it was supposed by G.A. Alvarez and D. Suter was restricted by mentioned perturbation. We are assuming an alternative explanation. The growing up of cluster size still goes on but the width of MQ spectrum becomes stable because of different decay rate of MQ-spectral components in dependence on theirs location in spectrum. Here we are calculating the widths of MQ spectra in dependence on the time of "preparation" for different values of the perturbation strength and by this way we get the dependence of stabilized amount of MQ-spectrum width on mentioned strength. So, the excellent compliance obtains with the analogues experimental relation observed in Ref. [Phys. Rev. A 84, 012320 (2011)].
Abstract On the basis of the earlier developed statistical theory of the growth of the effective size of correlated clusters (the number of correlated spins), an expression for the shape of the multiple-quantum (MQ) NMR spectrum is obtained that takes into account the loss of coherence in a spin system due, for example, to the controlled intervention of the experimenter. It is shown that the scrambling and decoherence processes in the MQ spectrum of the multiparticle system of a solid are not separated, unlike the corresponding spectra of some large isolated molecules [27] in a solution. The relations obtained allow one to extract the necessary information about the above processes (scrambling and decoherence) from the dependence of the MQ spectra on experimental parameters.
Decoherence induced by coupling a system with an environment may display universal features. We demonstrate that when the coupling to the system drives a quantum phase transition in the environment, the decay of quantum coherences in the system is Gaussian with a width independent of the system-environment coupling strength. We obtain analytical results for a class of solvable models, and present numerical evidence supporting the validity of our results in more general cases. This effect opens the way for a quantum simulation algorithm, where a single qubit is used to detect a quantum phase transition. We discuss possible implementations of such an algorithm and relate our results to available data on universal decoherence in NMR echo experiments.