Nuclear Spin Density Research Articles

Spectroscopic investigations of Pr3+:CaWO4 at liquid-helium temperatures

Rare-earth ions doped into low nuclear-spin density host crystals provide a promising platform for quantum information storage and processing. Calcium tungstate $({\mathrm{CaWO}}_{4})$ is an attractive host crystal because it can be isotopically enriched to provide a nuclear spin free environment. Here, we report a spectroscopic investigation of the optical transitions and hyperfine transitions of praseodymium $(^{141}\mathrm{Pr}^{3+})$ doped in ${\mathrm{CaWO}}_{4}$ at liquid-helium temperatures. The hyperfine structures of the ${}^{3}{H}_{4}$(0) and ${}^{1}{D}_{2}$(0) states are determined by spectral hole burning. The results indicate that ${\mathrm{Pr}}^{3+}$:${\mathrm{CaWO}}_{4}$ is an appealing candidate for quantum memory in quantum information processing.

Scalable fabrication of graphene nanoribbon quantum dot devices with stable orbital-level spacing

Large-scale integration of quantum-dot devices is essential for realizing various quantum devices. Graphene-based quantum dots provide a promising platform for spin qubits because of their low nuclear spin density and weak spin-orbit interaction. However, the integration of graphene-based quantum dots remains a challenge. Here, we demonstrate the scalable fabrication of graphene nanoribbon-based quantum-dot devices using a nickel nanobar technique. Fine structures formed in the middle of the nanoribbons exhibit quantum-dot behavior, and more than 56% of devices fabricated on the same substrate show Coulomb diamond features, indicating that large-scale integration of graphene nanoribbon quantum-dot devices is possible with our method. Cryogenic measurements reveal orbital-level spacings between the ground and excited states that are stable up to high-temperature conditions of ~20 K. We explain this stability in terms of the very fine structures formed in the middle of the nanoribbons and their relatively low effective mass.

Single-Shot Spin Readout in Graphene Quantum Dots

Electrostatically defined quantum dots in bilayer graphene offer a promising platform for spin qubits with presumably long coherence times due to low spin-orbit coupling and low nuclear spin density. We demonstrate two different experimental approaches to measure the decay times of excited states. The first is based on direct current measurements through the quantum device. Pulse sequences are applied to control the occupation of ground and excited states. We observe a lower bound for the excited state decay on the order of hundred microseconds. The second approach employs a capacitively coupled charge sensor to study the time dynamics of the excited state using the Elzerman technique. We find that the relaxation time of the excited state is of the order of milliseconds. We perform single-shot readout of our two-level system with a visibility of $87.1\%$, which is an important step for developing a quantum information processor in graphene.

Methods to accelerate high-throughput screening of atomic qubit candidates in van der Waals materials

The discovery of atom-like spin emitters associated with defects in two-dimensional (2D) wide-bandgap (WBG) semiconductors presents new opportunities for highly tunable and versatile qubits. So far, the study of such spin emitters has focused on defects in hexagonal boron nitride (hBN). However, hBN necessarily contains a high density of nuclear spins, which are expected to create a strong incoherent spin-bath that leads to poor coherence properties of spins hosted in the material. Therefore, identification of new qubit candidates in other 2DWBG materials is necessary. Given the time demands of ab initio methods, new approaches for rapid screening and calculations of identifying properties of suitable atom-like qubits are required. In this work, we present two new methods for rapid estimation of the zero-phonon line (ZPL), a key property of atomic qubits in WBG materials. First, the ZPL is calculated by exploiting Janak’s theorem. For finite changes in occupation, we provide the leading-order estimate of the correction to the ZPL obtained using Janak’s theorem, which is more rapid than the standard method (ΔSCF). Next, we demonstrate an approach to converging excited states that is faster for systems with small strain than the standard approach used in the ΔSCF method. We illustrate these methods using the case of the singly negatively charged calcium vacancy in SiS2, which we are the first to propose as a qubit candidate. This work has the potential to assist in accelerating the high-throughput search for quantum defects in materials, with applications in quantum sensing and quantum computing.

Parahydrogen-Induced Hyperpolarization of Gases.

Imaging of gases is a major challenge for any modality including MRI. NMR and MRI signals are directly proportional to the nuclear spin density and the degree of alignment of nuclear spins with applied static magnetic field, which is called nuclear spin polarization. The level of nuclear spin polarization is typically very low, i.e., one hundred thousandth of the potential maximum at 1.5 T and a physiologically relevant temperature. As a result, MRI typically focusses on imaging highly concentrated tissue water. Hyperpolarization methods transiently increase nuclear spin polarizations up to unity, yielding corresponding gains in MRI signal level of several orders of magnitude that enable the 3D imaging of dilute biomolecules including gases. Parahydrogen-induced polarization is a fast, highly scalable, and low-cost hyperpolarization technique. The focus of this Minireview is to highlight selected advances in the field of parahydrogen-induced polarization for the production of hyperpolarized compounds, which can be potentially employed as inhalable contrast agents.

Nuclear spin noise tomography in three dimensions with iterative simultaneous algebraic reconstruction technique (SART) processing.

We report three-dimensional spin noise imaging (SNI) of nuclear spin density from spin noise data acquired by Faraday detection. Our approach substantially extends and improves the two-dimensional SNI method for excitation-less magnetic resonance tomography reported earlier (Müller and Jerschow, 2006). This proof of principle was achieved by taking advantage of the particular continuous nature of spin noise acquired in the presence of constant magnitude magnetic field gradients and recent advances in nuclear spin noise spectroscopy acquisition as well as novel processing techniques. In this type of projection-reconstruction-based spin noise imaging the trade-off between signal-to-noise ratio (or image contrast) and resolution can be adjusted a posteriori during processing of the original time-domain data by iterative image reconstruction in a unique way not possible in conventional rf-pulse-dependent magnetic resonance imaging (MRI). The 3D SNI is demonstrated as a proof of concept on a commercial 700 MHz high-resolution NMR spectrometer, using a 3D-printed polymeric phantom immersed in water.

Spin-lattice relaxation in liquid entrapped in a nanocavity

We consider the spin lattice relaxation in bulk liquid and liquid entrapped in a nanocavity. The kinetic equation which describes the spin lattice relaxation is obtained by using the theory of the nonequilibrium state operator. A solution of the kinetic equation gives the quadrature expression for the relaxation time, T1. The calculated relaxation time agrees well with the experimental data.The spin-lattice relaxation time is calculated for nanocavities with a characteristic size much less than 700 nm, with the assumption that the spin-lattice relaxation mechanism is determined by nanocavity fluctuations. The resulting expression shows an explicit dependence of the relaxation time T1 on the volume, density of nuclear spins, and parameters of the cavity (shape and orientation relatively to the applied field). To compare with the experiment on the detection of the anisotropy of the relaxation time, we average the expression that describes the relaxation time over the orientation of the nanocavities relative to the applied magnetic field. The good agreement with the experimental data for fibril tissues was achieved by adjustment of few fitting parameters - the standard deviation, averaged fiber direction, and weight factors - which characterize the ordering of fibrils.

A suite-level review of the neutron single-crystal diffraction instruments at Oak Ridge National Laboratory.

The nascent suite of single-crystal neutron diffractometers at the Oak Ridge National Laboratory has no equal at any other neutron scattering facility worldwide and offers the potential to re-assert single-crystal diffraction using neutrons as a significant tool to study nuclear and magnetic structures of small unit cell crystals, nuclear structures of macromolecules, and diffuse scattering. Signature applications and features of single-crystal neutron diffraction are high resolution nuclear structure analysis, magnetic structure and spin density determinations, contrast variation (particularly D2O/H2O) for nuclear structural studies, lack of radiation damage when using crystals of biological molecules such as proteins, and the fidelity to measure nuclear and magnetic diffuse scattering with elastic discrimination.

Spin-selective electron transfer reactions of radical pairs: Beyond the Haberkorn master equation

Radical pair recombination reactions are normally described using a quantum mechanical master equation for the electronic and nuclear spin density operator. The electron spin state selective (singlet and triplet) recombination processes are described with a Haberkorn reaction term in this master equation. Here we consider a general spin state selective electron transfer reaction of a radical pair and use Nakajima-Zwanzig theory to derive the master equation for the spin density operator, thereby elucidating the relationship between non-adiabatic reaction rate theory and the Haberkorn reaction term. A second order perturbation theory treatment of the diabatic coupling naturally results in the Haberkorn master equation with an additional reactive scalar electron spin coupling term. This term has been neglected in previous spin chemistry calculations, but we show that it will often be quite significant. We also show that beyond the second order in perturbation theory, i.e., beyond the Fermi golden rule limit, an additional reactive singlet-triplet dephasing term appears in the master equation. A closed form expression for the reactive scalar electron spin coupling in terms of the Marcus theory parameters that determine the singlet and triplet recombination rates is presented. By performing simulations of radical pair reactions with the exact hierarchical equations of motion method, we demonstrate that our master equations provide a very accurate description of radical pairs undergoing spin-selective non-adiabatic electron transfer reactions. The existence of a reactive electron spin coupling may well have implications for biologically relevant radical pair reactions such as those which have been suggested to play a role in avian magnetoreception.

Broadband quantitative NQR for authentication of vitamins and dietary supplements

We describe hardware, pulse sequences, and algorithms for nuclear quadrupole resonance (NQR) spectroscopy of medicines and dietary supplements. Medicine and food safety is a pressing problem that has drawn more and more attention. NQR is an ideal technique for authenticating these substances because it is a non-invasive method for chemical identification. We have recently developed a broadband NQR front-end that can excite and detect 14N NQR signals over a wide frequency range; its operating frequency can be rapidly set by software, while sensitivity is comparable to conventional narrowband front-ends over the entire range. This front-end improves the accuracy of authentication by enabling multiple-frequency experiments. We have also developed calibration and signal processing techniques to convert measured NQR signal amplitudes into nuclear spin densities, thus enabling its use as a quantitative technique. Experimental results from several samples are used to illustrate the proposed methods.

A quantum spin-probe molecular microscope.

Imaging the atomic structure of a single biomolecule is an important challenge in the physical biosciences. Whilst existing techniques all rely on averaging over large ensembles of molecules, the single-molecule realm remains unsolved. Here we present a protocol for 3D magnetic resonance imaging of a single molecule using a quantum spin probe acting simultaneously as the magnetic resonance sensor and source of magnetic field gradient. Signals corresponding to specific regions of the molecule's nuclear spin density are encoded on the quantum state of the probe, which is used to produce a 3D image of the molecular structure. Quantum simulations of the protocol applied to the rapamycin molecule (C51H79NO13) show that the hydrogen and carbon substructure can be imaged at the angstrom level using current spin-probe technology. With prospects for scaling to large molecules and/or fast dynamic conformation mapping using spin labels, this method provides a realistic pathway for single-molecule microscopy.

Macroscopic nuclear spin diffusion constants of rotating polycrystalline solids from first-principles simulation

A method for quantitatively calculating nuclear spin diffusion constants directly from crystal structures is introduced. This approach uses the first-principles low-order correlations in Liouville space (LCL) method to simulate spin diffusion in a box, starting from atomic geometry and including both magic-angle spinning (MAS) and powder averaging. The LCL simulations are fit to the 3D diffusion equation to extract quantitative nuclear spin diffusion constants. We demonstrate this method for the case of 1H spin diffusion in ice and l-histidine, obtaining diffusion constants that are consistent with literature values for 1H spin diffusion in polymers and that follow the expected trends with respect to magic-angle spinning rate and the density of nuclear spins. In addition, we show that this method can be used to model 13C spin diffusion in diamond and therefore has the potential to provide insight into applications such as the transport of polarization in non-protonated systems.

Regional absolute conductivity reconstruction using projected current density in MREIT

Magnetic resonance electrical impedance tomography (MREIT) is a non-invasive technique for imaging the internal conductivity distribution in tissue within an MRI scanner, utilizing the magnetic flux density, which is introduced when a current is injected into the tissue from external electrodes. This magnetic flux alters the MRI signal, so that appropriate reconstruction can provide a map of the additional z-component of the magnetic field (Bz) as well as the internal current density distribution that created it. To extract the internal electrical properties of the subject, including the conductivity and/or the current density distribution, MREIT techniques use the relationship between the external injection current and the z-component of the magnetic flux density B = (Bx, By, Bz). The tissue studied typically contains defective regions, regions with a low MRI signal and/or low MRI signal-to-noise-ratio, due to the low density of nuclear magnetic resonance spins, short T2 or T*2 relaxation times, as well as regions with very low electrical conductivity, through which very little current traverses. These defective regions provide noisy Bz data, which can severely degrade the overall reconstructed conductivity distribution. Injecting two independent currents through surface electrodes, this paper proposes a new direct method to reconstruct a regional absolute isotropic conductivity distribution in a region of interest (ROI) while avoiding the defective regions. First, the proposed method reconstructs the contrast of conductivity using the transversal J-substitution algorithm, which blocks the propagation of severe accumulated noise from the defective region to the ROI. Second, the proposed method reconstructs the regional projected current density using the relationships between the internal current density, which stems from a current injection on the surface, and the measured Bz data. Combining the contrast conductivity distribution in the entire imaging slice and the reconstructed regional projected current density, we propose a direct non-iterative algorithm to reconstruct the absolute conductivity in the ROI. The numerical simulations in the presence of various degrees of noise, as well as a phantom MRI imaging experiment showed that the proposed method reconstructs the regional absolute conductivity in a ROI within a subject including the defective regions. In the simulation experiment, the relative L2-mode errors of the reconstructed regional and global conductivities were 0.79 and 0.43, respectively, using a noise level of 50 db in the defective region.

The effect of surface conductance on lateral gated quantum devices in Si/SiGe heterostructures

Quantum dots in Si/SiGe heterostructures are expected to have relatively long electron spin decoherence times, because of the low density of nuclear spins and the weak coupling between nuclear and electron spins. We provide experimental evidence suggesting that electron motion in a conductive layer parallel to the two-dimensional electron gas, possibly resulting from the donors used to dope the Si quantum well, is responsible for the well-known difficulty in achieving well-controlled dots in this system. Charge motion in the conductive layer can cause depletion on large length scales, making electron confinement in the dot impossible, and can give rise to noise that can overwhelm the single-electron charging signal. Results of capacitance versus gate bias measurements to characterize this conductive layer are presented.

Nanoscale magnetic resonance imaging

We have combined ultrasensitive magnetic resonance force microscopy (MRFM) with 3D image reconstruction to achieve magnetic resonance imaging (MRI) with resolution <10 nm. The image reconstruction converts measured magnetic force data into a 3D map of nuclear spin density, taking advantage of the unique characteristics of the "resonant slice" that is projected outward from a nanoscale magnetic tip. The basic principles are demonstrated by imaging the (1)H spin density within individual tobacco mosaic virus particles sitting on a nanometer-thick layer of adsorbed hydrocarbons. This result, which represents a 100 million-fold improvement in volume resolution over conventional MRI, demonstrates the potential of MRFM as a tool for 3D, elementally selective imaging on the nanometer scale.

Isotopically engineered Si and Ge for spintronics and quantum computation

Si, Ge as well as SiGe structures are the promising materials for spintronics and quantum computation due to the fact that in both crystals only one isotope ( 29Si and 73Ge) has nuclear spin. As a result, isotope engineering of Si and Ge permits to control the density of nuclear spins and vary the spin coherence time, a crucial parameter in spintronics. In the first part we discuss the NMR study of nuclear spin decoherence in Ge single crystals with different abundance of the 73Ge isotope. It was observed that the slow component of the dephasing process is elongated with depletion of Ge crystal with isotope 73Ge. The second part is devoted to the development of the Kane's model of nuclear spin-based quantum computer, which uses the nuclear spin of 31P impurity atoms in a 28Si matrix as quantum bits (qubits). We discuss a new method of placing 31P atoms in a 28Si based on neutron-transmutation-doping of isotopically engineered Si and Ge. In the proposed structure, interqubit coupling is due to indirect hyperfine interaction of 31P nuclear spins with electrons localized in a 28Si quasi-one-dimensional nanowire, which allows one to control the coupling between distant qubits.

Long-lived spin echoes in a magnetically dilute system: An NMR study of Ge single crystals

Owing to the well-developed technology, isotopic engineering of Si and Ge semiconductors permits one to control the density of nuclear spins and vary the spin coherence time, a crucial parameter in spintronics and quantum computing where nuclear spin is used as a qubit. In the present paper, we report on the NMR study of $^{73}\mathrm{Ge}$ nuclear spin decoherence in germanium single crystals with different abundances of the $^{73}\mathrm{Ge}$ isotope. Our measurements of Hahn- and solid-echo decays show that they are well fit by a superposition of two exponentials; at that, the deviation from the single exponential is more pronounced in the more spin-diluted sample, causing long-lived echoes. We show that the decay of these echoes becomes slower with the reduction of $^{73}\mathrm{Ge}$ abundance and is therefore caused by dipole-dipole interaction, reflecting the fundamental decoherence process in the spin system. The fast decay at the beginning of the relaxation process is shown to be mainly caused by the quadrupole interaction. Our experimental findings are supported by the calculations of Hahn- and solid-echo decays in the germanium crystals under study. Quite good agreement between the theory and experiment is demonstrated.

On the feasibility of elastic wave visualization within polymeric solids using magnetic resonance elastography.

In this paper, the feasibility of extending previously described magnetic resonance elastography (MRE) dynamic displacement (and associated elasticity) measurement techniques, currently used successfully in tissue, to solid materials which have much higher shear rigidity and much lower nuclear spin densities, is considered. Based on these considerations, the MRE technique is modified in a straightforward manner and used to directly visualize shear wave displacements within two polymeric materials, one of which is relatively stiff.

129Xe NMR – highly polarized thin films

We studied the macroscopic effects of nuclear magnetization. Highly polarized xenon is often used to increase the sensitivity in NMR investigations of porous media, diluted liquids or for imaging in the gas phase. In the condensed phase, however, highly nuclear spin polarized xenon also possesses a sizable magnetization due to the nuclear spin density. This results in an additional magnetic field, that is used to measure the polarization of the sample, when only the particle density is known. Here we find P z ≈0.8 corresponding to a spin temperature of 0.5 mK. We use isotopically enriched xenon with a 129Xe abundance of 0.71. At high abundance of 129Xe and high nuclear polarization the dipolar linewidth is considerably reduced. We find for small angle excitation a reduction from 650 Hz to 400 Hz. We investigate this using a thin film geometry. The susceptibility effects of the substrate and the Xe film are treated. The macroscopic angle between the normal of the film and the external field strongly changes the polarization induced line shift and line width. The first follows an expected cos 2 θ dependence with an understood amplitude the latter however is not understood up to now. Relaxation of 129Xe in the condensed film is observed to be T 1=15±1.8 min, much faster than expected. To cite this article: P. Gerhard et al., C. R. Physique 5 (2004).

Visualizing the internal physical characteristics of carbonate sediments with magnetic resonance imaging and petrography

ABSTRACT Magnetic resonance (MR) images are analyzed in conjunction with petrographic data to evaluate the textural characteristics of rocks dominated by fabric-selective dolomitization. The magnetic resonance imaging (MRI) measurements reveal the three-dimensional geometry of the physical sedimentary structures and the trace fossils that influenced dolomitization and porosity development. Because MRI images represent composites of nuclear spin density and MR relaxation times, each of which can be related to pore size, stronger MRI image intensity must be calibrated to know porous zones by integrating petrological data with MR data. Pairing of MR images with petrography helps map the distribution of porosity in diagenetically altered rock. The data presented herein show the potential of a new class of MRI technique as an imaging tool for low-porosity rocks. The results demonstrate that MRI technology can significantly enhance petrological studies. Notable results include 1) the successful resolution of the porosity distribution in carbonate rocks characterized by low porosity (generally less than 6%); 2) the successful acquisition of the three-dimensional data required to model the porous network; and 3) recognition that the complex distribution of porosity and its relationship to the matrix show that this fabric represents a dual porosity/permeability system and may reduce the resource quality of similary burrowed carbonate rocks. End_Page 363------------------------