Hahn Spin Echo Research Articles

Pore structure and fractal dimension analysis of ancient city wall bricks in China

Comprehensive quantitative characterization of the pore structures of ancient city wall bricks is important for predicting the durability of historical masonry buildings. However, in most previous studies, only one or two methods were used to analyse the pore structures of fired clay bricks. In this study, mercury intrusion porosimetry (MIP), low-temperature nitrogen adsorption (LTNA), and low-field nuclear magnetic resonance (LF-NMR) were used to characterize the pore structure and fractal dimension of nine different ancient city wall bricks. The results show that the surface relaxivity of ancient bricks measured via the Hahn spin echo (HSE) in LF-NMR ranged from 1.55 to 1.75 μm/s. Furthermore, the porosity of the blue bricks measured via LF-NMR were much lower than that obtained via the gravimetric method owing to a higher number of paramagnetic iron mineral phases. LTNA was not suitable for describing pore size distribution of ancient bricks as the pore diameters were mainly concentrated in the range of 100–1000 nm. The pore structures of ancient bricks in dried and water-saturated states were different, the pore size of the white bricks obtained via LF-NMR was smaller than the MIP-derived pore-throat size by a factor of approximately 2.

Analysis and information content of quadrupolar NMR in glasses: 25Mg NMR in vitreous MgSiO3 and CaMgSi2O6

The static wideline and high-resolution magic angle spinning (MAS) 25Mg NMR lineshapes measured for isotopically enriched enstatite and diopside glasses indicate a wide distribution of the electric-field gradient (EFG) components at the 25Mg position caused by disorder. The correct characterization of this distribution requires simulations with special attention paid to the experimental parameters. Here, both the static spectra obtained by wideband excitation and the MAS-NMR spectra obtained via rotor-synchronized Hahn spin echo acquisition were successfully simulated with the Czjzek distribution model, using one consistent set of parameters. Average nuclear electric quadrupole coupling constants near 8 MHz and a distribution width around 4 MHz were obtained for both materials, which suggests that earlier results on these glasses need to be re-examined. The results of this study outline a general strategy for characterizing the local environments of strongly coupled quadrupolar nuclei in amorphous and glassy materials. Despite the discrepancies between the interaction parameters extracted from our data and those published in earlier NMR work, the best fit to the data indicate an average isotropic chemical shift near 13 ppm (vs. aqueous MgCl2 solution) for both the enstatite and diopside glasses. Assuming the applicability of the current database relating the 25Mg chemical shifts with coordination numbers in crystalline compounds, this value suggests that the Mg2+ ions are six-coordinated. This conclusion, however, is based on the simplifying assumption that the 25Mg spectrum comprises a Czjzek distribution centered at a single isotropic chemical shift value and stands in contrast to the results of recent isotope-selective neutron diffraction studies which give an average Mg-O coordination number of 4.4–4.5 for both glasses. However, reasonable fits to the MAS-NMR spectra can also be obtained when constraining the average isotropic chemical shift to 50 ppm, a value typical of four-coordinated Mg. We conclude that multiple Mg sites with different coordination numbers may well be present and that, in the present glasses, 25Mg NMR at typically used spinning rates and magnetic field strengths (20 kHz, 14.1 T) is not capable of resolving them due to excessive broadening by quadrupolar interactions.

The decay of the refocused Hahn echo in double electron-electron resonance (DEER) experiments.

Double electron-electron resonance (DEER) is a pulse electron paramagnetic resonance (EPR) technique that measures distances between paramagnetic centres. It utilizes a four-pulse sequence based on the refocused Hahn spin echo. The echo decays with increasing pulse sequence length , where and are the two time delays. In DEER, the value of is determined by the longest inter-spin distance that needs to be resolved, and is adjusted to maximize the echo amplitude and, thus, sensitivity. We show experimentally that, for typical spin centres (nitroxyl, trityl, and Gd(III)) diluted in frozen protonated solvents, the largest refocused echo amplitude for a given is obtained neither at very short (which minimizes the pulse sequence length) nor at (which maximizes dynamic decoupling for a given total sequence length) but rather at values smaller than . Large-scale spin dynamics simulations based on the coupled cluster expansion (CCE), including the electron spin and several hundred neighbouring protons, reproduce the experimentally observed behaviour almost quantitatively. They show that electron spin dephasing is driven by solvent protons via the flip-flop coupling among themselves and their hyperfine couplings to the electron spin.

The decay of the refocused Hahn echo in DEER experiments

Abstract. Double electron–electron resonance (DEER) is a pulse electron paramagnetic resonance (EPR) technique that measures distances between paramagnetic centres. It utilizes a four-pulse sequence based on the refocused Hahn spin echo. The echo decays with increasing pulse sequence length 2(τ1 + τ2), where τ1 and τ2 are the two time delays. In DEER, the value of τ2 is determined by the longest inter-spin distance that needs to be resolved, and τ1 is adjusted to maximize the echo amplitude and thus sensitivity. We show experimentally that for typical spin centres (nitroxyl, trityl, Gd(III)) diluted in frozen protonated solvents, the largest refocused echo amplitude for a given τ2 is obtained neither at very short τ1 (which minimizes the pulse sequence length) nor at τ1 = τ2 (which maximizes dynamic decoupling for a given total sequence length), but rather at τ1 values smaller than τ2. Large-scale spin dynamics simulations including the electron spin and several hundred neighbouring protons reproduce the experimentally observed behaviour almost quantitatively. They show that electron spin dephasing is driven by solvent protons via the flip-flop coupling among themselves and their hyperfine couplings to the electron spin.

Coherent surface spin manipulation

Spin Physics Spin-based quantum information processing requires coherent spin manipulation. Yang et al. demonstrate coherent control of surface titanium and iron atom spins on a magnesium oxide surface with a magnetic scanning tunneling microscope tip. Arbitrary sequences of fast electrical pulses delivered to the top induced large electric fields. These fields drove metal-atom movement, which then modulated the tip-atom exchange interaction to create an oscillating effective magnetic field. Advanced spin-control protocols such as Ramsey fringes and Hahn spin echoes revealed quantum dynamics, such as coherent oscillations in a titanium atom dimer assembled on the surface with the tip. Science , this issue p. [509][1] [1]: /lookup/doi/10.1126/science.aay6779

Rabi oscillations as a tool to detect strong coupling of paramagnetic center with the nuclear spin bath

We show that strong coupling with the nuclear spin ensemble leaves an imprint on the nutation dynamics of the electron spin in the form of forced oscillations. The frequency of these oscillations equals Larmor precession frequency of the nuclear spins. This effect is evidenced by our experimental data on Rabi oscillations of paramagnetic nitroxyl radical TEMPO ((2,2,6,6-tetramethylpiperidin-1-yl)oxidanyl) dispersed in glassy and crystalline ethanol. The data are interpreted in terms of a simple model that represents an impact of the proton spin bath as random local field with certain probability distribution. The electron spin coherence times of TEMPO in ethanol obtained by means of Hahn spin echo and Carr-Purcell-Meiboom-Gill sequences are compared with the calculations based on a spin diffusion model.

Quantum time mirrors for general two-band systems

Methods that are devised to achieve reversal of quantum dynamics in time have been named "quatum time mirrors". Such a time mirror can be considered as a generalization of Hahn's spin echo to systems with continuous degrees of freedom. We extend the quantum time mirror protocol originally proposed for Dirac dispersions to arbitrary two-band systems and establish the general requirements for its efficient implementation. We further discuss its sensitivity to various non- homogeneous perturbations including disorder potentials and the effect of external static magnetic and electric fields. Our general statements are verified for a number of exemplary Hamiltonians, whose phase-coherent dynamics are studied both analytically and numerically. The Hamiltonians considered can be used to describe the low-energy properties of systems as diverse as cold atom- optics setups, direct band gap semiconductors or (mono- or bilayer) graphene. We discuss the consequences of many-body effects at a qualitative level, and consider the protocol feasibility in state-of-the-art experimental setups.

General solution to inhomogeneous dephasing and smooth pulse dynamical decoupling

In order to achieve the high-fidelity quantum control needed for a broad range of quantum information technologies, reducing the effects of noise and system inhomogeneities is an essential task. It is well known that a system can be decoupled from noise or made insensitive to inhomogeneous dephasing dynamically by using carefully designed pulse sequences based on square or delta-function waveforms such as Hahn spin echo or CPMG. However, such ideal pulses are often challenging to implement experimentally with high fidelity. Here, we uncover a new geometrical framework for visualizing all possible driving fields, which enables one to generate an unlimited number of smooth, experimentally feasible pulses that perform dynamical decoupling or dynamically corrected gates to arbitrarily high order. We demonstrate that this scheme can significantly enhance the fidelity of single-qubit operations in the presence of noise and when realistic limitations on pulse rise times and amplitudes are taken into account.

Composite-pulse and partially dipolar dephased multiCP for improved quantitative solid-state 13C NMR

Improved multiple cross polarization (multiCP) pulse sequences for quickly acquiring quantitative 13C NMR spectra of organic solids are presented. Loss of 13C magnetization due to imperfect read-out and storage pulses in multiCP has been identified as a significant mechanism limiting polarization enhancement for 13C sites with weak couplings to 1H. This problem can be greatly reduced by composite 90° pulses with non-orthogonal phases that flip the magnetization onto the spin-lock field and back to the longitudinal direction for the 1H repolarization period; the observed loss is <3% for over ±10 kHz resonance offset and up to 20% flip-angle error. This composite-pulse multiCP (ComPmultiCP) sequence consistently provides performance superior to that of conventional multiCP, without any trade-off. The longer total CP time enabled by the composite pulses allows for a wider amplitude ramp during CP, which decreases the sensitivity to Hartmann-Hahn mismatch by a factor of two, with a <7% root-mean-square deviation within a 1-dB range for Boc-alanine. In samples with very short T1ρ, under-polarization of non-protonated carbons can be compensated by slight dipolar dephasing of CHn signals resulting from relatively weak decoupling during the Hahn spin echo period before detection. Quantitative spectra have been obtained by ComPmultiCP for low-crystallinity branched polyethylene at 4.5 kHz MAS, and in combination with partial dipolar dephasing for soil organic matter at 14 kHz MAS.

Attenuation of the NMR signal in a field gradient due to stochastic dynamics with memory

The attenuation function S(t) for an ensemble of spins in a magnetic-field gradient is calculated by accumulation of the phase shifts in the rotating frame resulting from the displacements of spin-bearing particles. The found S(t), expressed through the particle mean square displacement, is applicable for any kind of stationary stochastic motion of spins, including their non-markovian dynamics with memory. The known expressions valid for normal and anomalous diffusion are obtained as special cases in the long time approximation. The method is also applicable to the NMR pulse sequences based on the refocusing principle. This is demonstrated by describing the Hahn spin echo experiment. The attenuation of the NMR signal is also evaluated providing that the random motion of particle is modeled by the generalized Langevin equation with the memory kernel exponentially decaying in time. The models considered in our paper assume massive particles driven by much smaller particles.

(Industrial Electrochemistry & Electrochemical Engineering Division Student Achievement Award) Anhydrous High-Proton Conductor Based on Ionic Nanopeapods

Here we describe, significant improvement in electrochemical performance of proton exchange membrane fuel cells (PEMFCs) via incorporation of superacid-filled single wall carbon nanotubes (CNTs), called ionic nanopeapod. It has been shown that capillary filling of carbon nanotubes is an effective method to alter their physical characteristics. Here and for the first time, we describe that there is a lot of room for development through modification of the interior space of CNT by tuning its ionic nature to boost the proton transport inside the CNT with or without the presence of water molecules. High-resolution transmission electron microscopy (HRTEM) images confirm the successful modification of the interior space of CNTs. The molecular dynamic simulations revealed that anisotropic alignment of ions/water molecules inside the carbon nanotubes makes wire-like proton chains that can facilitate ionic conductivitions with very low humidity dependency. The experimental results confirm these simulation observations by showing a very high-proton conductivity (>0.2 S.cm-1) at low humidifies. The proton conductivity behavior of the membranes based on Nafion and these ionic nanopeapods is investigated in broad ranges of temperature (25-140°C) and humidity (20-100 RH%). Water and proton self-diffusion coefficients are measured using a DOTY Z-gradient probe by the NMR pulse gradient spin–echo technique (NMR-PGSE), using the Hahn spin–echo pulse sequence to confirm the proton dynamic inside the CNTs in the presence of superacids. Arrhenius plot of NMR-based diffusion coefficients, as well as ionic conductivities (based on the electrochemical impedance spectroscopy), are used to evaluate the ease of proton transportat inside the CNTs. The fabricated nanohybrid nanocomposite membranes showed outstanding characteristics including fourfold increase in the maximum power density. These newly designed ionic nanosystems have great potentials to impact high-performance PEMFC applications.

Decoherence of an exchange qubit by hyperfine interaction

We study three-electron-spin decoherence in a semiconductor triple quantum dot with a linear geometry. The three electron spins are coupled by exchange interactions J_{12} and J_{23}, and we clarify inhomogeneous and homogeneous dephasing dynamics for a logical qubit encoded in the (S=1/2,S_{z} =1/2) subspace. We first justify that qubit leakage via the fluctuating Overhauser field can be effectively suppressed by sufficiently large Zeeman and exchange splittings. For J_{12}=J_{23} and the case of J_{12} and J_{23} being different, we construct an effective pure dephasing Hamiltonian with the Zeeman splitting much larger than the exchange splitting. Both effective Hamiltonians have the same order of magnitude as that for a single-spin qubit, and the relevant dephasing time scales are of the same order as those for a single spin. We provide estimates of the dynamics of three-spin free induction decay, the decay of a Hahn spin echo, and the decay of echoes from a CPMG pulse sequence for GaAs quantum dots.

Experimental Recovery of a Qubit from Partial Collapse

We describe and implement a method to restore the state of a single qubit, in principle perfectly, after it has partially collapsed. The method resembles the classical Hahn spin echo but works on a wider class of relaxation processes, in which the quantum state partially leaves the computational Hilbert space. It is not guaranteed to work every time, but successful outcomes are heralded. We demonstrate, using a single trapped ion, a better performance from this recovery method than can be obtained employing projection and postselection alone. The demonstration features a novel qubit implementation that permits both partial collapse and coherent manipulations with high fidelity.

Dynamic and inherent B0 correction for DTI using stimulated echo spiral imaging

To present a novel technique for high-resolution stimulated echo diffusion tensor imaging with self-navigated interleaved spirals readout trajectories that can inherently and dynamically correct for image artifacts due to spatial and temporal variations in the static magnetic field (B0) resulting from eddy currents, tissue susceptibilities, subject/physiological motion, and hardware instabilities. The Hahn spin echo formed by the first two 90° radiofrequency pulses is balanced to consecutively acquire two additional images with different echo times and generate an inherent field map, while the diffusion-prepared stimulated echo signal remains unaffected. For every diffusion-encoding direction, an intrinsically registered field map is estimated dynamically and used to effectively and inherently correct for off-resonance artifacts in the reconstruction of the corresponding diffusion-weighted image. After correction with the dynamically acquired field maps, local blurring artifacts are specifically removed from individual stimulated echo diffusion-weighted images and the estimated diffusion tensors have significantly improved spatial accuracy and larger fractional anisotropy. Combined with the self-navigated interleaved spirals acquisition scheme, our new method provides an integrated high-resolution short-echo time diffusion tensor imaging solution with inherent and dynamic correction for both motion-induced phase errors and off-resonance effects.

Effect of Low Refocusing Angle in T1-Weighted Spin Echo and Fast Spin Echo MRI on Low-Contrast Detectability: A Comparative Phantom Study at 1.5 and 3 Tesla

MRI tissue contrast is not well preserved at high field. In this work, we used a phantom with known, intrinsic contrast (3.6%) for model tissue pairs to test the effects of low angle refocusing pulses and magnetization transfer from adjacent slices on intrinsic contrast at 1.5 and 3 Tesla. Only T1-weighted spin echo sequences were tested since for such sequences the contrast loss, tissue heating, and image quality degradation at high fields seem to present significant diagnostic and quality issues. We hypothesized that the sources of contrast loss could be attributed to low refocusing angles that do not fulfill the Hahn spin echo conditions or to magnetization transfer effects from adjacent slices in multislice imaging. At 1.5 T the measured contrast was 3.6% for 180° refocusing pulses and 2% for 120° pulses, while at 3 T, it was 4% for 180° and only 1% for 120° refocusing pulses. There was no significant difference between single slice and multislice imaging suggesting little or no role played by magnetization transfer in the phantom chosen. Hence, one may conclude that low angle refocusing pulses not fulfilling the Hahn spin echo conditions are primarily responsible for significant deterioration of T1-weighted spin echo image contrast in high-field MRI.

Rephasing of optically driven atomic coherences by rapid adiabatic passage in Pr3+:Y2SiO5

We present experimental investigations of rephasing optically driven atomic coherences, prepared by electromagnetically induced transparency in a Pr${}^{3+}$:Y${}_{2}$SiO${}_{5}\phantom{\rule{0.16em}{0ex}}$ crystal. In particular, we systematically study rephasing based on rapid adiabatic passage and compare the performance of the latter with standard rephasing based on Hahn spin echoes. The data clearly demonstrate the superior performance of rapid adiabatic passage for any application of rephasing, which suffers from large inhomogeneous broadenings in the medium or inevitable fluctuations in the experimental parameters.

Magnetic resonance elastometry using a single-sided permanent magnet

In this paper, we describe a magnetic resonance method of measuring material elasticity using a single-sided magnet with a permanent static field gradient. This method encodes sample velocity in a reciprocal space using Hahn spin-echoes with variable timing. The experimental results show a strong correlation between magnetic resonance signal attenuation and elasticity when an oscillating force is applied on the sample. This relationship in turn provides us with information about the displacement velocity experienced by the sample, which is inversely proportional to Young's modulus. The proposed method shows promise in offering a portable and cost-effective magnetic resonance elastography system.

Simultaneous convection compensation and solvent suppression in biomolecular NMR diffusion experiments

Thermal convection and high intensity solvent resonances can significantly hamper diffusion estimates in pulsed gradient spin-echo nuclear magnetic resonance diffusion experiments on biomolecule samples. To overcome these two problems, a new double functional NMR diffusion sequence, double echo PGSTE-WATERGATE, is presented. The new sequence provides excellent convection compensation and solvent suppression (with a suppression factor in excess of at least 10(5) in a single scan) in biomolecular NMR diffusion experiments. Due to its stimulated echo nature, the new sequence is much less susceptible to spin-spin relaxation than Hahn spin-echo based sequences. Furthermore, the new sequence is not susceptible to spin diffusion due to the application of bipolar pulsed gradients. The new sequence is also much easier to set up compared to previously developed stimulated echo based convection compensation and solvent suppression sequence. The utility of the new sequence is demonstrated on an aqueous lysozyme sample.

Herman Yaggi Carr, PhD (1924–2008): A tribute

Herman Yaggi Carr, PhD (1924–2008): A tribute

MQ-PGSTE: A new multi-quantum STE-based PGSE NMR sequence

A new multi-quantum stimulated echo based pulsed gradient spin-echo sequence, MQ-PGSTE, has been developed for measuring translational diffusion. The new sequence provides a higher signal-to-noise ratio than the (Hahn spin-echo based) MAXY-D sequence at long diffusion times, and thus potentially affords better diffusion measurements on macromolecule samples. Based on multi-quantum coherence encoding, the MQ-PGSTE sequence needs considerably lower gradient strengths for diffusion characterization compared to standard single quantum pulsed gradient spin-echo sequences. By using the new sequence, the diffusion coefficient of l-[3- 13C]-alanine was found to be 8.1 ± 0.1 × 10 −10 m 2 s −1, which is in line with the value obtained by the use of the standard stimulated echo based pulsed gradient spin-echo sequence.