Nuclear Coherence Research Articles

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.

Unveiling sustainable synergy and ageing stability of bio-oils from cotton gin trash and plastic waste co-liquefaction for an integrated waste-to-energy solution

Co-liquefaction is an emerging technology aimed at enhancing bio-oil yield and quality, compensating for decrease in feedstock, increasing productivity, and adding revenue to bio-refineries. This study delves into the influence of plastic waste (PW) types during co-liquefaction with cotton gin trash (CGT) on the yield and quality of the produced crude oil. Various plastics, including PLA (polylactic acid), PVA (polyvinyl alcohol), PET (polyethylene terephthalate), LDPE (low-density polyethylene), HDPE (high-density polyethylene), PP (polypropylene), and PS (polystyrene), were investigated in a mixing ratio of 2:1 (CGT/plastic waste) at 320 °C and 2 hours in supercritical ethanol (ScEtOH), without catalyst, to produce energy-dense bio-oil under optimised conditions. The study presents the suitability of different types of plastic waste for co-feeding with CGT, along with their synergistic and antagonistic effects on product fraction yield (oil, solid, and gas), and oil energy yield. High bio-oil yields of 54.5 wt%, 53.7 wt%, and 43.1 wt% were achieved during co-liquefaction of CGT with PLA, PET and PVA, respectively. Bio-oil with the highest Higher Heating Values (HHV) was achieved through the co-liquefaction of CGT with PVA (30.6 MJ/kg) and PS (31.5 MJ/kg). The solid fractions obtained from co-liquefying CGT with PLA and PVA contained 46.9 wt% and 55.1 wt% carbon, respectively, making them potential sustainable sources for soil amendment. Furthermore, the bio-oils were characterised using gas chromatography-mass spectroscopy (GC-MS), two-dimensional nuclear magnetic spectroscopy-heteronuclear single quantum coherence (2D‐NMR-HSQC), elemental analysis, fourier transform infrared spectroscopy (FTIR), and thermogravimetric analysis (TGA) to assess their quality and stability. Solid residues were characterised to understand the extent of plastic degradation and their suitable applications. The results indicate that the co-liquefaction of lignocellulosic biomass with plastics represents a viable and promising approach for improving bio-oil quality and extending its shelf life.

Mechanochemical Tailoring of Lignin Structure: Influence of Different Particle Sizes in the Organosolv Process.

The autocatalyzed ethanolic organosolv process is gaining increasing attention for the sulfur-free isolation of lignin, which is subsequently used as a renewable substitute for various fossil-based applications. For the first time, the mechanochemical influence of seven different particle sizes of two different biomasses on the respective organosolv lignin structure is examined. Wine pruning (Pinot Noir) and wine pomace (Accent) are used for organosolv process with particle sizes ranging from 2.0-1.6mm to less than 0.25mm. As particle size decreases, the weight-average molecular weight increases, while the total phenol content decreases significantly. Additionally, the distribution of the lignin-typical monolignols and relevant substructures, as determined by two-dimensional heteronuclear nuclear magnetic resonance spectra single quantum coherence (HSQC), is observed. The degree of grinding of the biomass has a clear chemical-structural influence on the isolated HG and HGS organosolv lignins. Therefore, it is crucial to understand this influence to apply organosolv lignins in a targeted manner. In the future, particle size specifications in the context of the organosolv process should be expressed in terms of distribution densities rather than in terms of a smaller than specification.

Calibration of the Solid‐State Nuclear Magnetic Resonance Search for Axion‐Like Dark Matter

AbstractCalibration of nuclear‐magnetic‐resonance‐based searches for axion‐like dark matter can be performed by free induction decay (FID) measurements. This manu‐ script describes FID experiments on several solid materials, motivated by the Cosmic Axion Spin Precession Experiment (CASPEr) program. Experiments with207Pb nuclear spins in ferroelectrics, lead magnesium niobate‐lead titanate (PbMg1/3Nb2/3O3) (PbTiO3)1/3 (PMN‐PT) and lead zirconium titante PbZr0.52Ti0.48O3 (PZT) are directly relevant to the CASPEr‐electric search for the electric dipole moment interaction of axion‐like dark matter. Experiments with 31P nuclear spins in gadolinium‐doped hydroxypyromorphite Pb4.95Gd0.05(PO4)3OH (HPM:Gd) are used for apparatus calibration. The measurements characterized the nuclear spin ensemble coherence time and the magnetic resonance detection sensitivity for these samples. Calibration is performed using small tip‐angle pulses.

Non-linear correlation functions and zero-point energy flow in mixed quantum-classical semiclassical dynamics.

Mixed quantum classical (MQC)-initial value representation (IVR) is a recently introduced semiclassical framework that allows for selective quantization of the modes of a complex system. In the quantum limit, MQC reproduces the semiclassical Double Herman-Kluk IVR results, accurately capturing nuclear quantum coherences and conserving zero-point energy. However, in the classical limit, although MQC mimics the Husimi-IVR for real-time correlation functions with linear operators, it is significantly less accurate for non-linear correlation functions with errors even at time zero. Here, we identify the origin of this discrepancy in the MQC formulation and propose a modification. We analytically show that the modified MQC approach is exact for all correlation functions at time zero, and in a study of zero-point energy (ZPE) flow, we numerically demonstrate that it correctly obtains the quantum and classical limits as a function of time. Interestingly, although classical-limit MQC simulations show the expected, unphysical ZPE leakage, we find that it is possible to predict and even modify the direction of ZPE flow through selective quantization of the system, with the quantum-limit modes accepting energy but preserving the minimum quantum mechanically required energy.

Probing site-resolved correlations in a spin system of ultracold molecules

Synthetic quantum systems with interacting constituents play an important role in quantum information processing and in explaining fundamental phenomena in many-body physics. Following impressive advances in cooling and trapping techniques, ensembles of ultracold polar molecules have emerged as a promising platform that combines several advantageous properties1-11. These include a large set of internal states with long coherence times12-17 and long-range, anisotropic interactions. These features could enable the exploration of intriguing phases of correlated quantum matter, such as topological superfluids18, quantum spin liquids19, fractional Chern insulators20 and quantum magnets21,22. Probing correlations in these phases is crucial to understanding their properties, necessitating the development of new experimental techniques. Here we use quantum gas microscopy23 to measure the site-resolved dynamics of quantum correlations of polar 23Na87Rb molecules confined in a two-dimensional optical lattice. By using two rotational states of the molecules, we realize a spin-1/2 system with dipolar interactions between particles, producing a quantum spin-exchange model21,22,24,25. We study the evolution of correlations during the thermalization process of an out-of-equilibrium spin system for both spatially isotropic and anisotropic interactions. Furthermore, we examine the correlation dynamics of a spin-anisotropic Heisenberg model engineered from the native spin-exchange model by using periodic microwave pulses26-28. These experiments push the frontier of probing and controlling interacting systems of ultracold molecules, with prospects for exploring new regimes of quantum matter and characterizing entangled states that are useful for quantum computation29,30 and metrology31.

Phase separation in alkali silicate glasses detected through inverse Laplace transform of29Si nuclear magnetic resonance echo train decay

The ratio of Si-29 nuclear magnetic resonance coherence lifetimes for Q4and Q3sites under magic-angle spinning and a π-pulse train in silicate glasses can detect phase separation, even at small scales where the glass appears optically homogenous.

Effects of Microwave Gating on Nuclear Spin Echoes in Dynamic Nuclear Polarization.

Dipolar or quadrupolar echoes allow one to observe undistorted powder patterns, in contrast to simple Fourier transformations of free induction decays (FIDs). In this work, the buildup of proton polarization due to dynamic nuclear polarization (DNP) is monitored by observing echoes rather than FIDs. When the microwave irradiation is interrupted during the buildup of DNP, the electrons relax back to their Boltzmann distribution at high fields (B0 = 6.7 T) and low temperatures 1.2 < Tsample < 4.0 K, so that dipolar flip-flop-flip terms involving two electrons and one proton become largely ineffective as a mechanism of proton decoherence. This leads to a prolongation of the nuclear coherence lifetime T2'(1H). The increase in T2'(1H) leads to transient surges of the amplitudes of spin echoes. Conversely, transient slumps of spin echoes are observed when the microwave irradiation is switched back on, due to a shortening of nuclear coherence lifetimes.

Nuclear and electronic coherence in superfluid helium

A semi-phenomenological model of a many-particle system of 4He atoms is proposed, in which a helium atom is considered as a complex consisting of a nucleus and a bound pair of electrons in the singlet state. At zero temperature, there are two Bose–Einstein condensates of particles with opposite charges, namely, a condensate of positively charged nuclei and a condensate of negatively charged electron pairs. It is shown that in such a system there exist two excitation branches: sound and optical. On the basis of this model an interpretation of experiments on the study of the electrical activity of superfluid helium is proposed. The frequency at which the resonant absorption of a microwave radiation is observed is interpreted as a gap in the optical branch. It is shown that the distribution of the electric potential in a standing wave in a resonator is similar to that observed experimentally.

Signatures of electronic and nuclear coherences in ultrafast molecular x-ray and electron diffraction.

Femtosecond x-ray and electron diffraction hold promise to image the evolving structures of single molecules. We present a unified quantum-electrodynamical formulation of diffraction signals, based on the exact many-body nuclear + electronic wavefunction that can be extracted from quantum chemistry simulations. This gives a framework for analyzing various approximate molecular dynamics simulations. We show that the complete description of ultrafast diffraction signals contains interesting contributions involving mixed elastic and inelastic scattered photons that are usually masked by other larger contributions and are neglected. These terms include overlaps of nuclear wavepackets between different electronic states that provide an electronic decoherence mechanism and are important for the time-resolved imaging of conical intersections.

Spin–spin relaxation of nuclear quadrupole resonance coherences and the important role of degenerate energy levels

We present an extension of a Redfield approach for calculating spin–spin relaxation rates of zero-field nuclear quadrupole resonance (NQR) coherences, which was published in [Kruk et al., PCCP, 2018, 20, 23414–23426]. The oversimplification of the secular approximation made in the recent paper makes the calculation invalid for zero-field NQR and has led to partially large deviations between predicted and experimental data from Bi-containing molecular crystals. Furthermore, these deviations led to speculations about an additional dipole–dipole relaxation mechanism besides the main electric field gradient (EFG) fluctuations. Here, we demonstrate how a complete application of the Redfield relaxation expression eliminates the deviation from experimental data without the need for additional assumptions. In particular, we point out the important role of off-diagonal elements in the Redfield relaxation matrix within the 3/2–1/2 block appearing due to degenerate energy levels. The resulting coupling between single and double coherence spin density elements leads to a faster coherence decay than for all other transitions. The pseudo rotational model for EFG fluctuations, as proposed in the earlier publication and usually applied for isotropic liquids, is extended in a second analysis by introducing a vibrational mode to account for the case of crystalline solids.

Long-Lived Nuclear Coherences inside Helium Nanodroplets.

Much of our knowledge about dynamics and functionality of molecular systems has been achieved with femtosecond time-resolved spectroscopy. Despite extensive technical developments over the past decades, some classes of systems have eluded dynamical studies so far. Here, we demonstrate that superfluid helium nanodroplets, acting as a thermal bath of 0.4K temperature to stabilize weakly bound or reactive systems, are well suited for time-resolved studies of single molecules solvated in the droplet interior. By observing vibrational wave packet motion of indium dimers (In_{2}) for tens of picoseconds, we demonstrate that the perturbation imposed by this quantum liquid can be lower by a factor of 10-100 compared to any other solvent, which uniquely allows us to study processes depending on long nuclear coherence in a dissipative environment. Furthermore, tailor-made microsolvation environments inside droplets will enable us to investigate the solvent influence on intramolecular dynamics in a wide tuning range from molecular isolation to strong molecule-solvent coupling.

Coherent electrical control of a single high-spin nucleus in silicon.

Nuclear spins are highly coherent quantum objects. In large ensembles, their control and detection via magnetic resonance is widely exploited, for example, in chemistry, medicine, materials science and mining. Nuclear spins also featured in early proposals for solid-state quantum computers1 and demonstrations of quantum search2 and factoring3 algorithms. Scaling up such concepts requires controlling individual nuclei, which can be detected when coupled to an electron4-6. However, the need to address the nuclei via oscillating magnetic fields complicates their integration in multi-spin nanoscale devices, because the field cannot be localized or screened. Control via electric fields would resolve this problem, but previous methods7-9 relied on transducing electric signals into magnetic fields via the electron-nuclear hyperfine interaction, which severely affects nuclear coherence. Here we demonstrate the coherent quantum control of a single 123Sb (spin-7/2) nucleus using localized electric fields produced within a silicon nanoelectronic device. The method exploits an idea proposed in 196110 but not previously realized experimentally with a single nucleus. Our results are quantitatively supported by a microscopic theoretical model that reveals how the purely electrical modulation of the nuclear electric quadrupole interaction results in coherent nuclear spin transitions that are uniquely addressable owing to lattice strain. The spin dephasing time, 0.1 seconds, is orders of magnitude longer than those obtained by methods that require a coupled electron spin to achieve electrical driving. These results show that high-spin quadrupolar nuclei could be deployed as chaotic models, strain sensors and hybrid spin-mechanical quantum systems using all-electrical controls. Integrating electrically controllable nuclei with quantum dots11,12 could pave the way to scalable, nuclear- and electron-spin-based quantum computers in silicon that operate without the need for oscillating magnetic fields.

Collective Quantum Memory Activated by a Driven Central Spin.

Coupling a qubit coherently to an ensemble is the basis for collective quantum memories. A single driven electron in a quantum dot can deterministically excite low-energy collective modes of a nuclear spin ensemble in the presence of lattice strain. We propose to gate a quantum state transfer between this central electron and these low-energy excitations-spin waves-in the presence of a strong magnetic field, where the nuclear coherence time is long. We develop a microscopic theory capable of calculating the exact time evolution of the strained electron-nuclear system. With this, we evaluate the operation of quantum state storage and show that fidelities up to 90% can be reached with a modest nuclear polarization of only 50%. These findings demonstrate that strain-enabled nuclear spin waves are a highly suitable candidate for quantum memory.

Advances and opportunities in ultrafast X-ray crystallography and ultrafast structural optical crystallography of nuclear and electronic protein dynamics.

Both nuclear and electronic dynamics contribute to protein function and need multiple and complementary techniques to reveal their ultrafast structural dynamics response. Real-space information obtained from the measurement of electron density dynamics by X-ray crystallography provides aspects of both, while the molecular physics of coherence parameters and frequency-frequency correlation needs spectroscopy methods. Ultrafast pump-probe applications of protein dynamics in crystals provide real-space information through direct X-ray crystallographic structure analysis or through structural optical crystallographic analysis. A discussion of methods of analysis using ultrafast macromolecular X-ray crystallography and ultrafast nonlinear structural optical crystallography is presented. The current and future high repetition rate capabilities provided by X-ray free electron lasers for ultrafast diffraction studies provide opportunities for optical control and optical selection of nuclear coherence which may develop to access higher frequency dynamics through improvements of sensitivity and time resolution to reveal coherence directly. Specific selection of electronic coherence requires optical probes, which can provide real-space structural information through photoselection of oriented samples and specifically in birefringent crystals. Ultrafast structural optical crystallography of photosynthetic energy transfer has been demonstrated, and the theory of two-dimensional structural optical crystallography has shown a method for accessing the structural selection of electronic coherence.

Depolymerization of Laccase-Oxidized Lignin in Aqueous Alkaline Solution at 37 °C

Lignin depolymerization is a coveted process for the generation of high-value compounds from a low-cost feedstock. This report describes a chemoenzymatic approach for the depolymerization of lignin involving a laccase-catalyzed oxidation under ambient air at room temperature followed by a base (NaOH)-induced depolymerization in aqueous solution at 37 °C. Two-dimensional nuclear magnetic resonance heteronuclear single quantum coherence spectroscopy, gel permeation chromatography, and liquid chromatography-electrospray ionization-quadrupole-time of flight-mass spectrometry (LC-ESI-Q-TOF-MS) analysis indicated the degradation of lignin and the formation of water-soluble fractions containing guaiacol, syringol, vanillic acid, m-anisic acid, and veratric acid. Furthermore, guaiacol and veratric acid are the main final products in the chemoenzymatic decomposition of a β-O-4 model compound.

Blueprint for nanoscale NMR

Nitrogen vacancy (NV) centers in diamond have been used as ultrasensitive magnetometers to perform nuclear magnetic resonance (NMR) spectroscopy of statistically polarized samples at 1–100 nm length scales. However, the spectral linewidth is typically limited to the kHz level, both by the NV sensor coherence time and by rapid molecular diffusion of the nuclei through the detection volume which in turn is critical for achieving long nuclear coherence times. Here we provide a blueprint supported by detailed theoretical analysis for a set-up that combines a sensitivity sufficient for detecting NMR signals from nano- to micron-scale samples with a spectral resolution that is limited only by the nuclear spin coherence, i.e. comparable to conventional NMR. Our protocol detects the nuclear polarization induced along the direction of an external magnetic field with near surface NV centers using lock-in detection techniques to enable phase coherent signal averaging. Using the NV centers in a dual role of NMR detector and optical hyperpolarization source to increase signal to noise, and in combination with Bayesian inference models for signal processing, nano/microscale NMR spectroscopy can be performed on sample concentrations in the micromolar range, several orders of magnitude better than the current state of the art.

Unique self-catalyzed cationic ring-opening polymerization of a high performance deoxybenzoin-based 1,3-benzoxazine monomer

An asymmetric bis(1,3-benzoxazine) monomer based on deoxybenzoin has been synthesized through Mannich condensation. The chemical structure of this deoxybenzoin-based monomer has been confirmed using 1H NMR, 13C NMR, FT-IR and elemental analysis. The assignments for the oxazine protons and carbon atoms in the asymmetric structure have also been confirmed using two-dimensional (2D) NMR techniques, including 1H-1H nuclear Overhauser effect spectroscopy (NOESY) and 1H-13C heteronuclear multiple quantum coherence spectroscopy (HMQC). In addition, the effect of incorporation of deoxybenzoin on the mode of polymerization of benzoxazine has been investigated using differential scanning calorimetry (DSC), in situ FT-IR and 1H NMR spectroscopy. This deoxybenzoin containing bis(benzoxazine) exhibits a low polymerization temperature resulting from a unique self-catalyzed cationic polymerization mechanism. Furthermore, the thermal stability of the resulting polybenzoxazine has been studied using thermogravimetric analysis (TGA). This deoxybenzoin-based polybenzoxazine exhibits high thermal stability and low flammability, with a Td5 temperature of 403 °C, a high char yield value (68%) and low total heat release (THR of 11.4 kJ/g).

Propagation of nonstationary electronic and nuclear states: attosecond dynamics in LiF

ABSTRACTRapid optical excitation of a molecule produces a nonstationary state localised in the Franck–Condon region. To move out of that region, one needs to propagate both the electronic and the nuclear state. We formulate the motion on a grid of nuclear coordinate. The coupling to the electric field is fully included in the Hamiltonian used for propagation. We use perturbation theory to analyse the results of dynamics from one grid point to another. The nonadiabatic coupling terms arise from propagating the electronic states. We apply the formalism to the simple case of a diatomic molecule in an approximate but accurate scheme that allows performing computation on a limited number of grid points. As the coherent dynamics unfolds, we expand the grid in the direction of the wave packet motion with the quantum chemical calculations of the electronic structure performed ‘on the fly’. The LiF molecule excited by a one-cycle IR pulse is used as a computational example. The 30-fs propagation through the crossing of the ionic and covalent states is overall adiabatic. The role of electron–nuclear coherences is emphasised.

Protecting a Diamond Quantum Memory by Charge State Control.

In recent years, solid-state spin systems have emerged as promising candidates for quantum information processing. Prominent examples are the nitrogen-vacancy (NV) center in diamond, phosphorus dopants in silicon (Si:P), rare-earth ions in solids, and VSi-centers in silicon-carbide. The Si:P system has demonstrated that its nuclear spins can yield exceedingly long spin coherence times by eliminating the electron spin of the dopant. For NV centers, however, a proper charge state for storage of nuclear spin qubit coherence has not been identified yet. Here, we identify and characterize the positively charged NV center as an electron-spin-less and optically inactive state by utilizing the nuclear spin qubit as a probe. We control the electronic charge and spin utilizing nanometer scale gate electrodes. We achieve a lengthening of the nuclear spin coherence times by a factor of 4. Surprisingly, the new charge state allows switching of the optical response of single nodes facilitating full individual addressability.