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arXiv:0811.0716 · Journal of Physics Condensed Matter

Multiple quantum NMR dynamics in pseudopure states

G. B. Furman

Published Dec 9, 2008• 4 citations
arXivHTMLPDF

Abstract

We investigate numerically the multiple quantum (MQ) NMR dynamics in systems of nuclear spins 1/2 coupled by dipole-dipole interactions in the case of the pseudopure initial state. Simulations of the MQ NMR with real molecular structures such as six dipolar-coupled proton spins of benzene, hydroxyl proton chains in calcium hydroxyapatite, and fluorine chains in calcium fluorapatite open the way to experimental NMR testing of the obtained results. It was found that multiple-spin correlations are created faster in such experiments than in the usual MQ NMR experiments and can be used for the investigation of many-spin dynamics of nuclear spins in solids.

DOI
10.1088/0953-8984/21/2/026008

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Multiple quantum experiments on nuclear magnetic resonance on spins of 19 F in calcium fluorapatite have been performed. It has been shown that more than 97% of the observed signal refers to the multiple quantum coherences of the zeroth and plus/minus second orders. The dependences of the intensities of these coherences on the time of the preparation period of the multiple quantum NMR experiment have been obtained. The dipole relaxation of multiple quantum coherences on the evolution period of the multiple quantum nuclear magnetic resonance experiment has been studied. A probe providing short radio-frequency pulses with the duration up to 0.3 μs has been developed for experiments. The experimental results show that the studied system can be used for the transmission of quantum information and the study of the decoherence process in strongly correlated multispin clusters.
Multiple quantum (MQ) NMR methods1 are applied to the analysis of various problems of quantum information processing. It is shown that the two-spin/two-quantum Hamiltonian1 describing MQ NMR dynamics is related to the flip-flop Hamiltonian of a one-dimensional spin system in the approximation of the nearest neighbor interactions. As a result, it is possible to organize quantum state transfer along a linear chain. MQ NMR experiments are performed on quasi-one-dimensional chains of 19F nuclei in calcium fluorapatite Ca5(PO4)3F. Relaxation of the MQ NMR coherences is considered as the simplest model of decoherence processes. A theory of the dipolar relaxation of the MQ NMR coherences in one-dimensional systems is developed. A good agreement of the theoretical predictions and the experimental data is obtained.
We investigated dynamics of entangled states on the basis of multiple-quantum (MQ) NMR methods. A time evolution of MQ coherences of nuclear spins coupled by the dipole-dipole interactions (DDI) in solids is simply connected with dynamics of quantum entangled states. We studied analytically dynamics of the entangled states for two- and three-spin systems. In this case dynamics of the quantum entanglement is uniquely determined by the time evolution of MQ coherences of the second order. The real part of the density matrix describing MQ dynamics in solids is responsible for MQ coherences of the zeroth order while its imaginary part is responsible for the second order. Thus, one can conclude that dynamics of the entanglement is connected with transitions from the real part of the density matrix to the imaginary one and vice versa.