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Journal of Experimental and Theoretical Physics Letters

Dynamics and relaxation of multiple quantum NMR coherences in a quasi-one-dimensional chain of nuclear spins 19F in calcium fluorapatite

Serge I. Doronin, Sergey G. Vasil’ev, A. A. Samoĭlenko, Edward B. Fel’dman, B. A. Shumm

Published May 1, 2015• 9 citations
Publisher

Abstract

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.

DOI
10.1134/s0021364015090076

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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.
The 19F^{19}\text{F}19F spins in a crystal of fluorapatite have often been used to experimentally approximate a one-dimensional spin system. Under suitable multipulse control, the nuclear-spin dynamics may be modeled to first approximation by a double-quantum one-dimensional Hamiltonian, which is analytically solvable for nearest-neighbor couplings. Here, we use solid-state nuclear magnetic resonance techniques to investigate the multiple quantum coherence dynamics of fluorapatite, with an emphasis on understanding the region of validity for such a simplified picture. Using experimental, numerical, and analytical methods, we explore the effects of long-range intrachain couplings, cross-chain couplings, as well as couplings to a spin environment, all of which tend to damp the oscillations of the multiple quantum coherence signal at sufficiently long times. Our analysis characterizes the extent to which fluorapatite can faithfully simulate a one-dimensional quantum wire.
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 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.
We investigate analytically and numerically the multiple-quantum (MQ) NMR dynamics in systems of nuclear spins 1∕21∕21∕2 coupled by the dipole-dipole interactions in the case of the dipolar ordered initial state. We suggest two different methods of MQ NMR. One of them is based on the measurement of the dipolar temperature in the quasiequilibrium state which is established after the time of order ${\ensuremath{\omega}}_{\mathit{loc}}^{\ensuremath{-}1}$ (${\ensuremath{\omega}}_{\mathit{loc}}$ is the dipolar local field) after the MQ NMR experiment. The other method uses an additional resonance ${(\ensuremath{\pi}∕4)}_{y}$ pulse after the preparation period of the standard MQ NMR experiment in solids. Many-spin clusters and 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.
Multiple quantum (MQ) nuclear magnetic resonance (NMR) spin dynamics are investigated analytically in infinite one-dimensional (1D) chains of spins 1/2. The representation of spin 1/2 operators with fermion field operators allows to calculate exactly the spin density operator, and hence NMR observables, under a variety of different conditions for 1D spin systems. The exact expressions are valid for all times and for a macroscopic number of coupled spins. The calculations for a 1D spin system initially at thermal equilibrium, and evolving under a 2-quantum/2-spin average dipolar Hamiltonian, in the presence of nearest-neighbor dipolar interactions yield MQ NMR spectra with 0- and 2-quantum coherences only. For a nonequilibrium initial condition with transverse magnetization, the analogous spin dynamics calculations produce MQ NMR spectra with all possible coherences of odd orders. Calculations at the level of perturbation theory, which include next-nearest-neighbor dipolar interactions, generate MQ spectra with higher even order coherences for equilibrium initial condition and evolution under a 2-quantum/2-spin propagator. Consideration of multiple spin correlations, 0-quantum coherences, and rf pulse imperfections are also presented. The relevance and implications of these theoretical results for comparison with the recent MQ NMR experiments of Yesinowski et al. on materials with quasi-one-dimensional distributions of spins, and for MQ NMR of solids in general are discussed.
We study the decay of multiple quantum (MQ) NMR coherences in systems with the large number of equivalent spins. As being created on the preparation period of the MQ NMR experiment, they decay due to the dipole-dipole interactions (DDI) on the evolution period of this experiment. It is shown that the relaxation time decreases with the increase in MQ coherence order (according to the known results) and in the number of spins. We also consider the modified preparation period of the MQ NMR experiment [G. A. Alvarez and D. Suter, Phys. Rev. Lett. 104, 230403 (2010)] concatenating the short evolution periods under the secular DDI Hamiltonian (the perturbation) with the evolution period under the nonsecular averaged two-spin/two-quantum Hamiltonian. The influence of the perturbation on the decoherence rate is investigated for the systems consisting of 200-600 equivalent spins.