NMR Relaxation by Redfield equation in a spin system I=7/2.

The Redfield master equation was solved analytically for a nuclear system with spin I=7/2. Using the irreducible tensor operator basis, the solutions of each density matrix element were computed. The experimental setup consisted of the 133Cs nuclei of the cesium-pentadecafluorooctanoate molecule in a lyotropic liquid crystal sample in the nematic phase at room temperature. Experimental longitudinal and transverse magnetization dynamics of the 133Cs nuclei were monitored, and the theoretical approach was used to generate valuable mathematical expressions with the highest accuracy through numerical procedures. This methodology can be extended to other nuclei with minimal difficulties.

Direct NMR T1 distribution measurement without using ill-posed fitting methods.

The usual Nuclear Magnetic Resonance (NMR) experiments for measuring spin-lattice relaxation time (T1) distributions are Inversion-Recovery (IR) and Saturation-Recovery (SR), followed by data processing based on ill-posed multi-exponential curve fitting methods. Recently, a new method combining SR and IR, called Saturation-Inversion-Recovery (SIR), has been proposed to obtain sharper T1-dependences than IR and SR. In this article, we propose an appropriate combination of SIR signals to directly obtain T1 distributions without using any multi-exponential fitting methods.

Saturation-recovery as a T1-filter for T2-T2 exchange NMR.

The Inversion-Recovery (IR) technique has already been proposed to be used as a T1-filter for T2-T2 Exchange experiments. However, when the Exchange experiments are employed for studying samples that show T1 distributions, where the pools are defined by broad relaxation time distributions, e.g. porous media, IR might be difficult to be used as a filter. This paper presents the difficulties found when using IR and proposes the use of Saturation-Recovery (SR) technique as an alternative to T1-filter.

Spin squeezing in a quadrupolar nuclei NMR system.

We have produced and characterized spin-squeezed states at a temperature of 26 °C in a nuclear magnetic resonance quadrupolar system. The experiment was carried out on 133Cs nuclei of spin I=7/2 in a sample of lyotropic liquid crystal. The source of spin squeezing was identified as the interaction between the quadrupole moment of the nuclei and the electric field gradients present within the molecules. We use the spin angular momentum representation to describe formally the nonlinear operators that produce the spin squeezing on a Hilbert space of dimension 2I+1=8. The quantitative and qualitative characterization of this spin-squeezing phenomenon is expressed by a squeezing parameter and squeezing angle developed for the two-mode Bose-Einstein condensate system, as well as by the Wigner quasiprobability distribution function. The generality of the present experimental scheme points to potential applications in solid-state physics.

Measuring bipartite quantum correlations of an unknown state.

We report the experimental measurement of bipartite quantum correlations of an unknown two-qubit state. Using a liquid state Nuclear Magnetic Resonance setup and employing geometric discord, we evaluate the quantum correlations of a state without resorting to prior knowledge of its density matrix. The method is applicable to any 2 ⊗ d system and provides, in terms of number of measurements required, an advantage over full state tomography scaling with the dimension d of the unmeasured subsystem. The negativity of quantumness is measured as well for reference. We also observe the phenomenon of sudden transition of quantum correlations when local phase and amplitude damping channels are applied to the state.

Environment-induced sudden transition in quantum discord dynamics.

Nonclassical correlations play a crucial role in the development of quantum information science. The recent discovery that nonclassical correlations can be present even in separable (nonentangled) states has broadened this scenario. This generalized quantum correlation has been increasing in relevance in several fields, among them quantum communication, quantum computation, quantum phase transitions, and biological systems. We demonstrate here the occurrence of the sudden-change phenomenon and immunity against some sources of noise for the quantum discord and its classical counterpart, in a room temperature nuclear magnetic resonance setup. The experiment is performed in a decohering environment causing loss of phase relations among the energy eigenstates and exchange of energy between system and environment, resulting in relaxation to the Gibbs ensemble.

Experimentally witnessing the quantumness of correlations.

The quantification of quantum correlations (other than entanglement) usually entails labored numerical optimization procedures also demanding quantum state tomographic methods. Thus it is interesting to have a laboratory friendly witness for the nature of correlations. In this Letter we report a direct experimental implementation of such a witness in a room temperature nuclear magnetic resonance system. In our experiment the nature of correlations is revealed by performing only few local magnetization measurements. We also compared the witness results with those for the symmetric quantum discord and we obtained a fairly good agreement.

Multi-quantum echoes in GdAl2 zero-field high-resolution NMR.

In this paper we present a series of high-resolution zero-field NMR spectra of the polycrystalline intermetallic compound GdAl(2). The spectra were obtained with the sample at 4.2K in the ordered magnetic state and in the absence of an external static magnetic field. Using a sequence composed of two RF pulses, we obtained up to five multi-quantum echoes for the (27)Al nuclei, which were used to construct the zero-field NMR spectra. The spectra obtained from the FID observed after the second pulse and the even echoes exhibited higher resolution than the odd ones. In order to explain such behavior, we propose a model in which there are two regions inside the sample with different inhomogeneous spectral-line broadenings. Moreover, with the enhanced resolution from the FID signal, we were able to determine quadrupolar couplings with great precision directly from the respective spectra. These results were compared with those obtained from the quadrupolar oscillations of the echo signals, and showed good agreement. Similar data were also obtained from (155)Gd and (157)Gd nuclei.

Characterization of organic matter in sediment cores of the Todos os Santos Bay, Bahia, Brazil, by elemental analysis and 13C NMR.

The impact of human activity on the sediments of Todos os Santos Bay in Brazil was evaluated by elemental analysis and 13C Nuclear Magnetic Resonance (13C NMR). This article reports a study of six sediment cores collected at different depths and regions of Todos os Santos Bay. The elemental profiles of cores collected on the eastern side of Frades Island suggest an abrupt change in the sedimentation regime. Autoregressive Integrated Moving Average (ARIMA) analysis corroborates this result. The range of depths of the cores corresponds to about 50 years ago, coinciding with the implantation of major onshore industrial projects in the region. Principal Component Analysis of the 13C NMR spectra clearly differentiates sediment samples closer to the Subaé estuary, which have high contents of terrestrial organic matter, from those closer to a local oil refinery. The results presented in this article illustrate several important aspects of environmental impact of human activity on this bay.

The effects of anticalcification treatments and hydration on the molecular dynamics of bovine pericardium collagen as revealed by 13C solid-state NMR.

This article describes a solid-state NMR (SSNMR) investigation of the influence of hydration and chemical cross-linking on the molecular dynamics of the constituents of the bovine pericardium (BP) tissues and its relation to the mechanical properties of the tissue. Samples of natural phenethylamine-diepoxide (DE)- and glutaraldehyde (GL)-fixed BP were investigated by (13)C cross-polarization SSNMR to probe the dynamics of the collagen, and the results were correlated to the mechanical properties of the tissues, probed by dynamical mechanical analysis. For samples of natural BP, the NMR results show that the higher the hydration level the more pronounced the molecular dynamics of the collagen backbone and sidechains, decreasing the tissue's elastic modulus. In contrast, in DE- and GL-treated samples, the collagen molecules are more rigid, and the hydration seems to be less effective in increasing the collagen molecular dynamics and reducing the mechanical strength of the samples. This is mostly attributed to the presence of cross-links between the collagen plates, which renders the collagen mobility less dependent on the water absorption in chemically treated samples.

NMR quadrupolar system described as Bose-Einstein-condensate-like system.

This paper presents a description of nuclear magnetic resonance (NMR) of quadrupolar systems using the Holstein-Primakoff (HP) formalism and its analogy with a Bose-Einstein condensate (BEC) system. Two nuclear spin systems constituted of quadrupolar nuclei I=3/2 ((23)Na) and I=7/2 ((133)Cs) in lyotropic liquid crystals were used for experimental demonstrations. Specifically, we derived the conditions necessary for accomplishing the analogy, executed the proper experiments, and compared with quantum mechanical prediction for a Bose system. The NMR description in the HP representation could be applied in the future as a workbench for BEC-like systems, where the statistical properties may be obtained using the intermediate statistic, first established by Gentile. The description can be applied for any quadrupolar systems, including new developed solid-state NMR GaAS nanodevices.

A study of the relaxation dynamics in a quadrupolar NMR system using Quantum State Tomography.

This article reports a relaxation study in an oriented system containing spin 3/2 nuclei using quantum state tomography (QST). The use of QST allowed evaluating the time evolution of all density matrix elements starting from several initial states. Using an appropriated treatment based on the Redfield theory, the relaxation rate of each density matrix element was measured and the reduced spectral densities that describe the system relaxation were determined. All the experimental data could be well described assuming pure quadrupolar relaxation and reduced spectral densities corresponding to a superposition of slow and fast motions. The data were also analyzed in the context of Quantum Information Processing, where the coherence loss of each qubit of the system was determined using the partial trace operation.

Quantum state tomography for quadrupolar nuclei using global rotations of the spin system.

In this paper, we describe a quantum state tomography method based on global rotations of the spin system which, together with a coherence selection scheme, enables the complete density matrix reconstruction. The main advantage of this technique, in respect to previous proposals, is the use of much shorter rf pulses, which decreases significantly the time necessary for algorithm quantum state tomography. In this case, under adequate experimental conditions, the rf pulses correspond to simple spatial rotations of the spin states, and its analytical description is conveniently given in the irreducible tensor formalism. Simulated results show the feasibility of the method for a single spin 72 nucleus. As an experimental result, we exemplify the application of this method by tomographing the steps during the implementation of the Deutsch algorithm. The algorithm was implemented in a (23)Na quadrupole nucleus using the strongly modulated pulses technique. We also extended the tomography method for a 3-coupled homonuclear spin 12 system, where an additional evolution under the internal Hamiltonian is necessary for zero order coherences evaluation.

Quantum logical operations for spin 3/2 quadrupolar nuclei monitored by quantum state tomography.

This article presents the realization of many self-reversible quantum logic gates using two-qubit quadrupolar spin 3/2 systems. Such operations are theoretically described using propagation matrices for the RF pulses that include the effect of the quadrupolar evolution during the pulses. Experimental demonstrations are performed using a generalized form of the recently developed method for quantum state tomography in spin 3/2 systems. By doing so, the possibility of controlling relative phases of superimposed pseudo-pure states is demonstrated. In addition, many aspects of the effect of the quadrupolar evolution, occurring during the RF pulses, on the quantum operations performance are discussed. Most of the procedures presented can be easily adapted to describe selective pulses of higher spin systems (>3/2) and for spin 1/2 under J couplings.

Analysis of one-dimensional pure-exchange NMR experiments for studying dynamics with broad distributions of correlation times.

One-dimensional (1D) exchange NMR experiments can elucidate the geometry, time scale, memory, and heterogeneity of slow molecular motions (1 ms-1 s) in solids. The one-dimensional version of pure-exchange (PUREX) solid-state exchange NMR, which is applied to static samples and uses the chemical shift anisotropy as a probe for molecular motion, is particularly promising and convenient in applications where site resolution is not a problem, i.e., in systems with few chemical sites. In this work, some important aspects of the 1D PUREX experiment applied to systems with complex molecular motions are analyzed. The influence of intermediate-regime (10 micros-1 ms) motions and of the distribution of reorientation angles on the pure-exchange intensity are discussed, together with a simple method for estimating the activation energy of motions occurring with a single correlation time. In addition, it is demonstrated that detailed information on the motional geometry can be obtained from 1D PUREX spectral line shapes. Experiments on a molecular crystal, dimethyl sulfone, confirm the analysis quantitatively. In two amorphous polymers, atactic polypropylene (aPP) and polyisobutylene (PIB), which differ only by one methyl group in the repeat unit, the height of the normalized exchange intensity clearly reveals a striking difference in the width of the distribution of correlation times slightly above the glass transition. The aPP shows the broad distribution and Williams-Landel-Ferry temperature dependence of correlation times typical of polymers and other "fragile" glass formers. In contrast, the dynamics in PIB occur essentially with a single correlation time and exhibits Arrhenius behavior, which is more typical of "strong" glass formers; this is somewhat surprising given the weak intermolecular forces in PIB.

Magnetic susceptibility effects on 13C MAS NMR spectra of carbon materials and graphite.

13C high-resolution solid-state nuclear magnetic resonance (NMR) was employed to study carbon materials prepared through the thermal decomposition of four different organic precursors (rice hulls, endocarp of babassu coconut, peat, and PVC). For heat treatment temperatures (HTTs) above about 600 C, all materials presented 13C NMR spectra composed of a unique resonance line associated with carbon atoms in aromatic planes. With increasing HTT a continuous broadening of this resonance and a diamagnetic shift in its central frequency were verified for all samples. The evolution of the magnitude and anisotropy of the magnetic susceptibility of the heat-treated carbon samples with HTT explains well these findings. It is shown that these results are better understood when a comparison is made with the features of the 13C NMR spectrum of polycrystalline graphite, for which the magnetic susceptibility effect is also present and is much more pronounced.

Slow-down of 13C spin diffusion in organic solids by fast MAS: a CODEX NMR Study.

One- and two-dimensional 13C exchange nuclear magnetic resonance experiments under magic-angle spinning (MAS) can provide detailed information on slow segmental reorientations and chemical exchange in organic solids, including polymers and proteins. However, observations of dynamics on the time scale of seconds or longer are hampered by the competing process of dipolar 13C spin exchange (spin diffusion). In this Communication, we show that fast MAS can significantly slow down the dipolar spin exchange effect for unprotonated carbon sites. The exchange is measured quantitatively using the centerband-only detection of exchange technique, which enables the detection of exchange at any spinning speed, even in the absence of changes of isotropic chemical shifts. For chemically equivalent unprotonated 13C sites, the dipolar spin exchange rate is found to decrease slightly less than proportionally with the sample-rotation frequency, between 8 and 28 kHz. In the same range, the dipolar spin exchange rate for a glassy polymer with an inhomogeneously broadened MAS line decreases by a factor of 10. For methylene groups, no or only a minor slow-down of the exchange rate is found.

Pure-exchange solid-state NMR.

Three exchange nuclear magnetic resonance (NMR) techniques are presented that yield (13)C NMR spectra exclusively of slowly reorienting segments, suppressing the often dominant signals of immobile components. The first technique eliminates the diagonal ridge that usually dominates two-dimensional (2D) exchange NMR spectra and that makes it hard to detect the broad and low off-diagonal exchange patterns. A modulation of the 2D exchange spectrum by the sine-square of a factor which is proportional to the difference between evolution and detection frequencies is generated by fixed additional evolution and detection periods of duration tau, yielding a 2D pure-exchange (PUREX) spectrum. Smooth off-diagonal intensity is obtained by systematically incrementing tau and summing up the resulting spectra. The related second technique yields a static one-dimensional (1D) spectrum selectively of the exchanging site(s), which can thus be identified. Efficient detection of previously almost unobservable slow motions in a semicrystalline polymer is demonstrated. The third approach, a 1D pure-exchange experiment under magic-angle spinning, is an extension of the exchange-induced sideband (EIS) method. A TOSS (total suppression of sidebands) spectrum obtained after the same number of pulses and delays, with a simple swap of z periods, is subtracted from the EIS spectrum, leaving only the exchange-induced sidebands and a strong, easily detected centerband of the mobile site(s).