Nuclear Spin Research Articles

Light-Induced 1H NMR Hyperpolarization in Solids at 9.4 and 21.1 T.

The inherently low sensitivity of nuclear magnetic resonance (NMR) spectroscopy is the major limiting factor for its application to elucidate structure and dynamics in solids. In the solid state, nuclear spin hyperpolarization methods based on microwave-induced dynamic nuclear polarization (DNP) provide a versatile platform to enhance the bulk NMR signal of many different sample formulations, leading to significant sensitivity improvements. Here we show that 1H NMR hyperpolarization can also be generated in solids at high magnetic fields by optical irradiation of the sample. We achieved this by exploiting a donor-chromophore-acceptor molecule with an excited state electron-electron interaction similar to the nuclear Larmor frequency, enabling solid-state 1H photochemically induced DNP (photo-CIDNP) at high magnetic fields. Through hyperpolarization relay, we obtained bulk NMR signal enhancements εH by factors of ∼100 at both 9.4 and 21.1 T for the 1H signal of o-terphenyl in magic angle spinning (MAS) NMR experiments at 100 K. These findings open a pathway toward a general light-induced hyperpolarization approach for dye-sensitized high-field NMR in solids.

Overhauser enhanced liquid state nuclear magnetic resonance spectroscopy in one and two dimensions

Nuclear magnetic resonance (NMR) is fundamental in the natural sciences, from chemical analysis and structural biology, to medicine and physics. Despite its enormous achievements, one of its most severe limitations is the low sensitivity, which arises from the small population difference of nuclear spin states. Methods such as dissolution dynamic nuclear polarization and parahydrogen induced hyperpolarization can enhance the NMR signal by several orders of magnitude, however, their intrinsic limitations render multidimensional hyperpolarized liquid-state NMR a challenge. Here, we report an instrumental design for 9.4 Tesla liquid-state dynamic nuclear polarization that enabled enhanced high-resolution NMR spectra in one and two-dimensions for small molecules, including drugs and metabolites. Achieved enhancements of up to two orders of magnitude translate to signal acquisition gains up to a factor of 10,000. We show that hyperpolarization can be transferred between nuclei, allowing DNP-enhanced two-dimensional 13C–13C correlation experiments at 13C natural abundance. The enhanced sensitivity opens up perspectives for structural determination of natural products or characterization of drugs, available in small quantities. The results provide a starting point for a broader implementation of DNP in liquid-state NMR.

An advance in the arithmetic of the Lie groups as an alternative to the forms of the Campbell-Baker-Hausdorff-Dynkin theorem

The exponential of an operator or matrix is widely used in quantum theory, but it sometimes can be a challenge to evaluate. For non-commutative operators X and Y, according to the Campbell-Baker-Hausdorff-Dynkin theorem, e X+Y is not equivalent to e X e Y , but is instead given by the well-known infinite series formula. For a Lie algebra of a basis of three operators {X, Y, Z}, such that [X, Y] = κ Z for scalar κ and cyclic permutations, here it is proven that e a X+b Y is equivalent to e p Z e q X e−p Z for scalar p and q. Extensions for e a X+b Y+c Z are also provided. This method is useful for the dynamics of atomic and molecular nuclear and electronic spins in constant and oscillatory transverse magnetic and electric fields.

Excitation of long-lived nuclear spin order using spin-locking: a geometrical formalism.

Over the last two decades, numerous pulse sequences have been introduced for the excitation of long-lived spin order (LLS) in high fields. The long continuous wave (CW) or adiabatic pulses used in the SLIC and APSOC sequences should remind one of the spin-locking pulses that are used to induce cross-polarization (CP). Dynamics during these spin-lockings in CP experiments are explained through a geometrical formalism. However, the SLIC and APSOC sequences are described in terms of the energy-level picture or in the language of level anti-crossings. Motivated by this analogy, this work presents here a geometrical formalism for the LLS excitation by spin-locking pulses in weakly coupled systems. The formalism is similar to the one used for CP dynamics and reveals new pulse sequences involving CW or adiabatic locking. A similar formalism for the sustaining period of LLS is also provided, which reveals new features of the dynamics and suggests the usage of modulated spin-lockings for proper LLS sustaining. For strong and intermediate regimes, although a simple geometrical formalism seems infeasible, a new pulse sequence that employs a ramp-down adiabatic pulse for both LLS excitation and reconversion to observables in both these regimes is presented here. Given the similarities between LLS excitation and well-developed CP, it may be anticipated that this work would initiate the search for new LLS excitation methods and applications.

Encapsulated Atomic Hydrogen in Octamethyl-POSS cages: a Pulsed EPR Study.

Encapsulated atomic hydrogen in polyhedral oligomeric silsesquioxane (POSS) cages is a promising candidate for spin-based quantum technologies. Key parameters such as spin relaxation times and magnetic interactions with surrounding electron and nuclear spins can be typically probed with advanced electron paramagnetic resonance (EPR) methods. Here we present a detailed pulsed EPR study of the species H@Si8O12R8 with R=CH3, namely encapsulated atomic hydrogen in the octamethyl POSS derivative. The temperature dependence of the spin-lattice relaxation rate 1/T1 is analyzed in terms of a Raman process with a Debye temperature of ΘD=145 K and a thermally activated process with Ea=794 K (552 cm-1), whereas, the phase memory time TM shows the typical shortening behaviour at T<150 K observed for all methyl-containing derivatives. The hyperfine coupling of the cage 29Si nuclei is measured by hyperfine sublevel correlation (HYSCORE) spectroscopy and is found to fulfil the so-called "matching condition" at the low-field EPR transition. The potential of this paramagnetic molecule to perform one-qubit quantum operations is probed by room-temperature Rabi oscillations.

Visualizing Metabolism in Biotechnologically Important Yeasts with dDNP NMR Reveals Evolutionary Strategies and Glycolytic Logic.

Saccharomyces cerevisiae has long been a pillar of biotechnological production and basic research. More recently, strides to exploit the functional repertoire of nonconventional yeasts for biotechnological production have been made. Genomes and genetic tools for these yeasts are not always available, and yeast genomics alone may be insufficient to determine the functional features in yeast metabolism. Hence, functional assays of metabolism, ideally in the living cell, are best suited to characterize the cellular biochemistry of such yeasts. Advanced in cell NMR methods can allow the direct observation of carbohydrate influx into central metabolism on a seconds time scale: dDNP NMR spectroscopy temporarily enhances the nuclear spin polarization of substrates by more than 4 orders of magnitude prior to functional assays probing central metabolism. We use various dDNP enhanced carbohydrates for in-cell NMR to compare the metabolism of S. cerevisiae and nonconventional yeasts, with an emphasis on the wine yeast Hanseniaspora uvarum. In-cell observations indicated more rapid exhaustion of free cytosolic NAD+ in H. uvarum and alternative routes for pyruvate conversion, in particular, rapid amination to alanine. In-cell observations indicated that S. cerevisiae outcompetes other biotechnologically relevant yeasts by rapid ethanol formation due to the efficient adaptation of cofactor pools and the removal of competing reactions from the cytosol. By contrast, other yeasts were better poised to use redox neutral processes that avoided CO2-emission. Beyond visualizing the different cellular strategies for arriving at redox neutral end points, in-cell dDNP NMR probing showed that glycolytic logic is more conserved: nontoxic precursors of cellular building blocks formed high-population intermediates in the influx of glucose into the central metabolism of eight different biotechnologically important yeasts. Unsupervised clustering validated that the observation of rapid intracellular chemistry is a viable means to functionally classify biotechnologically important organisms.

Modeling Ligand Exchange Kinetics in Iridium Complexes Catalyzing SABRE Nuclear Spin Hyperpolarization.

Large signal enhancements can be obtained for NMR analytes using the process of nuclear spin hyperpolarization. Organometallic complexes that bind parahydrogen can themselves become hyperpolarized. Moreover, if parahydrogen and a to-be-hyperpolarized analyte undergo chemical exchange with the organometallic complex it is possible to catalytically sensitize the detection of the analyte via hyperpolarization transfer through spin-spin coupling in this organometallic complex. This process is called Signal Amplification By Reversible Exchange (SABRE). Signal intensity gains of several orders of magnitude can thus be created for various compounds in seconds. The chemical exchange processes play a defining role in controlling the efficiency of SABRE because the lifetime of the complex must match the spin-spin couplings. Here, we show how analyte dissociation rates in the key model substrates pyridine (the simplest six-membered heterocycle), 4-aminopyridine (a drug), and nicotinamide (an essential vitamin biomolecule) can be examined. This is achieved for the most widely employed SABRE motif that is based on IrIMes-derived catalysts by 1H 1D and 2D exchange NMR spectroscopy techniques. Several kinetic models are evaluated for their accuracy and simplicity. By incorporating variable temperature analysis, the data yields key enthalpies and entropies of activation that are critical for understanding the underlying SABRE catalyst properties and subsequently optimizing behavior through rational chemical design. While several studies of chemical exchange in SABRE have been reported, this work also aims to establish a toolkit on how to quantify chemical exchange in SABRE and ensure that data can be compared reliably.

Impact of Zeeman and hyperfine interactions on the magnetic properties of paramagnetic metal Ions: III. Analysis of the local interactions in a single crystal of 173Yb3+ doped Y5SiO5

The electron spin echo envelope modulation (ESEEM) technique is a direct method to probe the nuclear spin coherences induced by electron spin transitions. Recently, this approach was used to study an isotopically pure Y2SiO5 crystal doped with 173Yb3+ ions, and the presence of the Fermi contact interaction was proposed to explain the frequency comb detected in the two-pulse ESEEM experiment [Solovarov N. K. et al. JETP Letters 115 (6): 362–67]. Here we simulate the Fourier images of the ESEEM data. The numerical analysis shows that the modulation is mainly due to the nuclear spin coherences induced by the dipole–dipole interactions. However, the correlation between the experimental and simulated data is better when the super-hyperfine interactions of the nearby yttrium nuclei have an additional isotropic contribution. The analysis of the rescaled X-band ESEEM spectra shows that for the EPR transitions at magnetic fields > 100 mT, the main contribution to the modulation comes from the oscillations of the individual nuclei and the effect of interference between coherences originating from several nuclei is not strong. Further experiments to distinguish the sources of the echo modulation are discussed.

Cross-correlated relaxation in the NMR of near-equivalent spin pairs: Longitudinal relaxation and long-lived singlet order.

The evolution of nuclear spin state populations is investigated for the case of a 13C2-labeled triyne in solution, for which the near-equivalent coupled pairs of 13C nuclei experience cross-correlated relaxation mechanisms. Inversion-recovery experiments reveal different recovery curves for the main peak amplitudes, especially when the conversion of population imbalances to observable coherences is induced by a radio frequency pulse with a small flip angle. Measurements are performed over a range of magnetic fields by using a sample shuttle apparatus. In some cases, the time constant TS for decay of nuclear singlet order is more than 100 times larger than the time constant T1 for the equilibration of longitudinal magnetization. The results are interpreted by a theoretical model incorporating cross-correlated relaxation mechanisms, anisotropic rotational diffusion, and an external random magnetic field. A Lindbladian formalism is used to describe the dissipative dynamics of the spin system in an environment of finite temperature. Good agreement is achieved between theory and experiment.

Hardware-efficient error-correcting codes for large nuclear spins

Hardware-efficient error-correcting codes for large nuclear spins

Impact of Zeeman and hyperfine interactions on the magnetic properties of paramagnetic metal ions: II. Super-hyperfine interactions with surrounding nuclei

The anisotropic Zeeman and strong hyperfine interactions of a Kramers ion can significantly affect its magnetic properties as well as the interactions with the nearby nuclei. The interactions with the local environment are described in the preceding article. In the current work, the change of the spin states of distant nuclei is studied. Analytical expressions describing the depth of the electron spin echo envelope modulation (ESEEM) are obtained for the ions with anisotropic Zeeman and strong hyperfine interactions. Due to the g-tensor anisotropy, the electron Zeeman interaction axis is tilted in respect to the direction of the external magnetic field which makes non-collinear with the Zeeman interaction axes of the ion and the nearby nuclei and significantly modifies the nuclear spin states. Thus, the isotropic hyperfine interaction, and particularly the Fermi contact interaction can directly contribute to the ESEEM. An additional factor, that can significantly modify the ESEEM signal is the mixing of the multiple oscillations arising when several nuclei occur in optimal conditions for the generation of the nuclear coherence. This situation arises when several EPR transitions of the ion covering a wide range of magnetic fields are examined.

Toward Programmable Quantum Processors Based on Spin Qubits with Mechanically Mediated Interactions and Transport.

Solid-state spin qubits are promising candidates for quantum information processing, but controlled interactions and entanglement in large, multiqubit systems are currently difficult to achieve. We describe a method for programmable control of multiqubit spin systems, in which individual nitrogen-vacancy (NV) centers in diamond nanopillars are coupled to magnetically functionalized silicon nitride mechanical resonators in a scanning probe configuration. Qubits can be entangled via interactions with nanomechanical resonators while programmable connectivity is realized via mechanical transport of qubits in nanopillars. To demonstrate the feasibility of this approach, we characterize both the mechanical properties and the magnetic field gradients around the micromagnet placed on the nanobeam resonator. We demonstrate coherent manipulation of a spin qubit in the proximity of a transported micromagnet by utilizing nuclear spin memory and use the NV center to detect the time-varying magnetic field from the oscillating micromagnet, extracting a spin-mechanical coupling of 7.7(9)Hz. With realistic improvements, the high-cooperativity regime can be reached, offering a new avenue toward scalable quantum information processing with spin qubits.

Robust Nuclear Spin Polarization via Ground-State Level Anticrossing of Boron Vacancy Defects in Hexagonal Boron Nitride.

Nuclear spin polarization plays a crucial role in quantum information processing and quantum sensing. In this work, we demonstrate a robust and efficient method for nuclear spin polarization with boron vacancy (V_{B}^{-}) defects in hexagonal boron nitride (h-BN) using ground-state level anticrossing (GSLAC). We show that GSLAC-assisted nuclear polarization can be achieved with significantly lower laser power than excited-state level anticrossing, making the process experimentally more viable. Furthermore, we have demonstrated direct optical readout of nuclear spins for V_{B}^{-} in h-BN. Our findings suggest that GSLAC is a promising technique for the precise control and manipulation of nuclear spins in V_{B}^{-} defects in h-BN.

Spectral hole-burning studies of a mononuclear Eu(III) complex reveal narrow optical linewidths of the 5D0 → 7F0 transition and seconds long nuclear spin lifetimes.

Coordination complexes of rare-earth ions (REI) show optical transitions with narrow linewidths enabling the creation of coherent light-matter interfaces for quantum information processing (QIP) applications. Among the REI-based complexes, Eu(III) complexes showing the 5D0 → 7F0 transition are of interest for QIP applications due to the narrow linewidths associated with the transition. Herein, we report on the synthesis, structure, and optical properties of a novel Eu(III) complex and its Gd(III) analogue composed of 2,9-bis(pyrazol-1-yl)-1,10-phenanthroline (dpphen) and three nitrate (NO3) ligands. The Eu(III) complex-[Eu(dpphen)(NO3)3]-showed sensitized metal-centred emission (5D0 → 7FJ; J = 0,1,2,3, 4, 5, or 6) in the visible region, upon irradiation of the ligand-centered band at 369 nm, with the 5D0 → 7F0 transition centred at 580.9 nm. Spectral hole-burning (SHB) studies of the complex with stoichiometric Eu(III) concentration revealed a narrow homogeneous linewidth (Γh) of 1.55 MHz corresponding to a 0.205 µs long optical coherence lifetime (T2opt). Remarkably, long nuclear spin lifetimes (T1spin) of up to 41 s have been observed for the complex. The narrow optical linewidths and long T1spin lifetimes obtained for the Eu(III) complex showcase the utility of Eu(III) complexes as tunable, following molecular engineering principles, coherent light-matter interfaces for QIP applications.

The Xe isotope nuclear resonance frequency shift of NMR angular velocity sensors due to transverse gradient magnetic fields

The nuclear magnetic resonance (NMR) angular velocity sensor detects angular velocity by measuring the shift in the nuclear spin precession frequency, which is of fundamental interest. Recent studies have revealed the parameter dependency of nuclei frequency shifts induced by non-uniformly distributed polarized pump beams, temperature, and magnetic field properties. In this study, we investigated the effect of the linear transverse gradient magnetic field on the frequency ratio shift of the Xe isotope nuclear resonance frequency in the NMR sensors. A theoretical analysis method was proposed based on the Fermi contact interaction in atomic polarization and the spin-diffusion relaxation of 129Xe and 131Xe nuclei. The frequency ratio shift of the Xe isotope under different x-axis gradient magnetic fields was measured experimentally. Furthermore, we eliminated the equivalent residual magnetic field through a feedback system and compensated for the original gradient magnetic field in the system, which contributed to accurately revealing the frequency shift induced by the magnetic field gradient. The results indicate that the frequency ratio shift of the Xe isotope is proportional to the strength of the second-order linear transverse gradient magnetic field. This study provides a reference for the analysis and evaluation of the presence of the gradient magnetic field in the NMR angular velocity sensor.

Accurate hyperfine tensors for solid state quantum applications: case of the NV center in diamond

The decoherence of point defect qubits is often governed by the electron spin-nuclear spin hyperfine interaction that can be parameterized by using ab inito calculations in principle. So far most of the theoretical works have focused on the hyperfine interaction of the closest nuclear spins, while the accuracy of the predictions for distinct nuclear spins is barely discussed. Here we demonstrate for the case of the NV center in diamond that the absolute relative error of the computed hyperfine parameters can exceed 100% using an industry standards first-principles code. To overcome this issue, we implement an alternative method and report on significantly improved hyperfine values with O\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{{{{{{\\mathcal{O}}}}}}}}$$\\end{document}(1%) relative mean error at all distances. The provided accurate hyperfine data for the NV center enables high-precision simulation of NV quantum nodes for quantum information processing and positioning of nuclear spins by comparing experimental and theoretical hyperfine data.

Tunable Quantum Coherence of Luminescent Molecular Spins Organized via Block Copolymer Self‐Assembly

AbstractElectronic or nuclear spins represent promising candidates of qubits for applications in quantum information technologies and spintronic devices. However, it remains a challenge to achieve scalable and spatially defined organization of a large number of spins as qubits, which is essential in the feasible fabrication of quantum circuits. A strategy of block copolymer self‐assembly to organize molecular spins as qubits across molecular to micro‐/nano‐scales in polymeric films of organic luminescent radicals centered in star‐like block copolymers is reported. Scalable and spatially defined organization of the molecular spins in polymeric films with long‐range periodic ordering has not only been achieved but also controllable spin‐lattice relaxation dynamics and spin coherence lifetimes that can be finely tuned by the domain sizes and rigidities of the polymeric matrices.

Toward Ultra-High-Quality-Factor Wireless Masing Magnetic Resonance Sensing.

It has recently been shown that a bolus of hyperpolarized nuclear spins can yield stimulated emission signals similar in nature to maser signals, potentially enabling new ways of sensing hyperpolarized contrast media, including most notably [1-13C]pyruvate that is under evaluation in over 50 clinical trials for metabolic imaging of cancer. The stimulated NMR signal emissions lasting for minutes do not require radio-frequency excitation, offering unprecedented advantages compared to conventional MR sensing. However, creating nuclear spin maser emission is challenging in practice due to stringent fundamental requirements, making practical in vivo applications hardly possible using conventional passive MR detectors. Here, we demonstrate the utility of a wireless NMR maser detector, the quality factor of which was enhanced 22-fold (to 1,670) via parametric pumping. This active-feedback technique breaks the intrinsic fundamental limit of NMR detector circuit quality factor. We show the use of parametric pumping to reduce the threshold requirement for inducing nuclear spin masing at 300 MHz resonance frequency in a preclinical MRI scanner. Indeed, stimulated emission from hyperpolarized protons was obtained under highly unfavorable conditions of low magnetic field homogeneity (T2* of 3 ms). Greater gains of the quality factor of the MR detector (up to 1 million) were also demonstrated.

Microscopic understanding of NMR signals by dynamic mean-field theory for spins

A recently developed dynamic mean-field theory for disordered spins (spinDMFT) is shown to capture the spin dynamics of nuclear spins very well. The key quantities are the spin autocorrelations. In order to compute the free induction decay (FID), pair correlations are needed in addition. They can be computed on spin clusters of moderate size which are coupled to the dynamic mean fields determined in a first step by spinDMFT. We dub this versatile approach non-local spinDMFT (nl-spinDMFT). It is a particular asset of nl-spinDMFT that one knows from where the contributions to the FID stem. We illustrate the strengths of nl-spinDMFT in comparison to experimental data for CaF2. Furthermore, spinDMFT provides the dynamic mean fields explaining the FID of the nuclear spins of 13C in adamantane up to some static noise. The spin Hahn echo in adamantane is free from effects of static noise and agrees excellently with the spinDMFT results without further fitting.

Ligand Effects on the Spin Relaxation Dynamics and Coherent Manipulation of Organometallic La(II) Potential Qudits.

We present pulsed electron paramagnetic resonance (EPR) studies on three La(II) complexes, [K(2.2.2-cryptand)][La(Cp')3] (1), [K(2.2.2-cryptand)][La(Cp″)3] (2), and [K(2.2.2-cryptand)][La(Cptt)3] (3), which feature cyclopentadienyl derivatives as ligands [Cp' = C5H4SiMe3; Cp″ = C5H3(SiMe3)2; Cptt = C5H3(CMe3)2] and display a C3 symmetry. Long spin-lattice relaxation (T1) and phase memory (Tm) times are observed for all three compounds, but with significant variation in T1 among 1-3, with 3 being the slowest relaxing due to higher s-character of the SOMO. The dephasing times can be extended by more than an order of magnitude via dynamical decoupling experiments using a Carr-Purcell-Meiboom-Gill (CPMG) sequence, reaching 161 μs (5 K) for 3. Coherent spin manipulation is performed by the observation of Rabi quantum oscillations up to 80 K in this nuclear spin-rich environment (1H, 13C, and 29Si). The high nuclear spin of 139La (I = 7/2), and the ability to coherently manipulate all eight hyperfine transitions, makes these molecules promising candidates for application as qudits (multilevel quantum systems featuring d quantum states; d >2) for performing quantum operations within a single molecule. Application of HYSCORE techniques allows us to quantify the electron spin density at ligand nuclei and interrogate the role of functional groups to the electron spin relaxation properties.