Nuclear Spin Precession Research Articles

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.

Preliminary searches for spin-dependent interactions using sidebands of nuclear spin-precession signals.

Various theories beyond the Standard Model predict new particles with masses in the sub-eV range with very weak couplings to ordinary matter. A new P-odd and T-odd interaction between polarized and unpolarized nucleons proportional to s⃗⋅r̂ is one such possibility, where r⃗=rr̂ is the spatial vector connecting the nucleons, and s⃗ is the spin of the polarized nucleon. Such an interaction involving a scalar coupling gsN at one vertex and a pseudoscalar coupling gpn at the polarized nucleon vertex can be induced by the exchange of spin-0 pseudoscalar bosons. We describe a new technique to search for interactions of this form and present the first measurements of this type. We show that future improvements to this technique can improve the laboratory upper bound on the product gsNgpn by two orders of magnitude for interaction ranges at the 100 micron scale.

Search for ultralight axion dark matter in a side-band analysis of a ${}^{199}$Hg free-spin precession signal

Ultra-low-mass axions are a viable dark matter candidate and may form a coherently oscillating classical field. Nuclear spins in experiments on Earth might couple to this oscillating axion dark-matter field, when propagating on Earth’s trajectory through our Galaxy. This spin coupling resembles an oscillating pseudo-magnetic field which modulates the spin precession of nuclear spins. Here we report on the null result of a demonstration experiment searching for a frequency modulation of the free spin-precession signal of 199Hg in a magnetic field. Our search covers the axion mass range 10^{-16} \textrm{eV} \lesssim m_a \lesssim 10^{-13} \textrm{eV}10−16eV≲ma≲10−13eV and achieves a peak sensitivity to the axion-nucleon coupling of g_{aNN} \approx 3.5 \times 10^{-6} \textrm{GeV}^{-1}gaNN≈3.5×10−6GeV−1.

Spin‐Decoupling and In‐Situ Nuclear Magnetometer with Hyperpolarized Nuclear Spin

AbstractThis paper investigates the dynamical properties of the spin‐coupling ensemble, with a focus on the spin‐decoupling phenomenon. The nuclear spin in such systems is significantly impacted by the electron spin when the main magnetic field approaches the Fermi contact field of nuclear spin, leading to measurement inaccuracies. A comprehensive dynamics model of the electron‐nuclear spin coupling ensemble has been established and analyzed. It proposes that the primary magnetic field augmenting effectively disentangles the precession frequency of the two spin‐coupling species, thereby yielding a spin‐decoupled state. Such a state allows nuclear spin serves as a high sensitive element for magnetic field measurements, while electron spin serves as a probe to acquire the precession of nuclear spin. With proposed method, a magnetic field resolution of 0.75 nT in a 12000 nT environment is achieved, indicating potential for magnetic field detection in geomagnetic environments. It further demonstrates measurements of electron spin Fermi contact interaction and polarization based on spin‐decoupling and in situ nuclear spin precession, results indicate measurement errors close to 1%. These results demonstrate the effectiveness of our approach in improving the accuracy and sensitivity of magnetic field measurements in spin‐coupled systems such as co‐magnetometers, nuclear magnetic resonance gyroscopes, and nuclear magnetometers.

Search for Spin-Dependent Gravitational Interactions at Earth Range.

Among the four fundamental forces, only gravity does not couple to particle spins according to the general theory of relativity. We test this principle by searching for an anomalous scalar coupling between the neutron spin and the Earth's gravity on the ground. We develop an atomic gas comagnetometer to measure the ratio of nuclear spin-precession frequencies between ^{129}Xe and ^{131}Xe, and search for a change of this ratio to the precision of 10^{-9} as the sensor is flipped in Earth's gravitational field. The null results of this search set an upper limit on the coupling energy between the neutron spin and the gravity on the ground at 5.3×10^{-22} eV (95% confidence level), resulting in a 17-fold improvement over the previous limit. The results can also be used to constrain several other anomalous interactions. In particular, the limit on the coupling strength of axion-mediated monopole-dipole interactions at the range of Earth's radius is improved by a factor of 17.

Precession-induced nonclassicality of the free induction decay of NV centers by a dynamical polarized nuclear spin bath

The ongoing exploration of the ambiguous boundary between the quantum and the classical worlds has spurred substantial developments in quantum science and technology. Recently, the nonclassicality of dynamical processes has been proposed from a quantum-information-theoretic perspective, in terms of witnessing nonclassical correlations with Hamiltonian ensemble simulations. To acquire insights into the quantum-dynamical mechanism of the process nonclassicality, here we propose to investigate the nonclassicality of the electron spin free-induction-decay process associated with an NV− center. By controlling the nuclear spin precession dynamics via an external magnetic field and nuclear spin polarization, it is possible to manipulate the dynamical behavior of the electron spin, showing a transition between classicality and nonclassicality. We propose an explanation of the classicality–nonclassicality transition in terms of the nuclear spin precession axis orientation and dynamics. We have also performed a series of numerical simulations supporting our findings. Consequently, we can attribute the nonclassical trait of the electron spin dynamics to the behavior of nuclear spin precession dynamics.

A dual-axis high-order harmonic and single-axis phase-insensitive demodulation atomic magnetometer for in situ NMR detection of Xe

Based on the parametric oscillation process, we demonstrate the dual-axis phase-sensitive demodulation (PSD) and single-axis phase-insensitive demodulation (PISD) for the atomic magnetometer in an in situ nuclear magnetic resonance (NMR) detection system, which can separate the precession signals of NMR from the oscillating magnetic fields. The two orthogonal magnetic fields can be detected simultaneously and independently by selecting the optimal demodulation phases with the traditional PSD method. The response signals of the parametric modulation magnetometer demodulated with high order harmonic signals are evaluated, which is a new exploration. The first order harmonic demodulation can present the best sensitivity about 250 fT/Hz1/2. The high order harmonic demodulation technology supplies a twofold 3 dB bandwidth. With the PISD method, a single-axis demodulation technique is proposed. The transverse nuclear spin precession magnetic fields can be extracted effectively with the demodulation R signal outputs by setting a specific longitudinal modulation magnetic field amplitude, which is a new demodulation strategy compared with the traditional demodulation method for the NMR system.

Stereographic projection to and from the Bloch sphere: Visualizing solutions of the Bloch equations and the Bloch–Riccati equation

Stereographic projection mapping is typically introduced to explain the point at infinity in the complex plane. After this brief exposure in the context of complex analysis, students rarely get an opportunity to fully appreciate stereographic projection mapping as an elegant and powerful technique on its own with many fruitful applications in the physical sciences. Here, using a classical description of nuclear magnetic resonance in the rotating frame, I show how stereographic projection mapping to and from the Bloch sphere can be used for visualizing solutions to Bloch's equation and the Bloch–Riccati equation, respectively. After developing the fundamentals of stereographic projection mapping using examples drawn from nuclear spin precession in the rotating frame, the method is then applied to visualizations of composite pulse excitation of a spin-1/2 system and to radiation damping in a system of isolated spins-1/2. In the case of the radiation-damped system, these visualizations provide particularly vivid illustrations of loxodromic Möbius transformation dynamics.

Indirect control of the 29SiV− nuclear spin in diamond

Coherent control and optical readout of the electron spin of the $^{29}$SiV$^{-}$ center in diamond has been demonstrated in literature, with exciting prospects for implementations as memory nodes and spin qubits. Nuclear spins may be even better suited for many applications in quantum information processing due to their long coherence times. Control of the $^{29}$SiV$^{-}$ nuclear spin using conventional NMR techniques is feasible, albeit at slow kilohertz rates due to the nuclear spin's low gyromagnetic ratio. In this work we theoretically demonstrate how indirect control using the electron spin-orbit effect can be employed for high-speed, megahertz control of the $^{29}$Si nuclear spin. We discuss the impact of the nuclear spin precession frequency on gate times and the exciting possibility of all optical nuclear spin control.

Ядерная спиновая динамика и флуктуации в анизотропной модели большого ящика

We consider the central spin model in the box approximation taking into account an external magnetic field and the anisotropy of the hyperfine interaction. From the exact Hamiltonian diagonalization we obtain analytical expressions for the nuclear spin dynamics in the limit of many nuclear spins. We predict the nuclear spin precession in zero magnetic field for the case of the anisotropic interaction between electron and nuclear spins. We calculate and describe the nuclear spin noise spectra in the thermodynamic equilibrium. The obtained results can be used for the analysis of the nuclear spin induced current fluctuations in organic semiconductors.

Nuclear spin dynamics and noise in anisotropic large box model-=SUP=-*-=/SUP=-

We consider the central spin model in the box approximation taking into account external magnetic field and anisotropy of the hyperfine interaction. From the exact Hamiltonian diagonalization we obtain analytical expressions for the nuclear spin dynamics in the limit of many nuclear spins. We predict the nuclear spin precession in zero magnetic field for the case of anisotropic interaction between electron and nuclear spins. We calculate and describe the nuclear spin noise spectra in the thermodynamic equilibrium. The obtained results can be used for the analysis of the nuclear spin induced current fluctuations in organic semiconductors. Keywords: central spin model, box model, nuclear spin dynamics.

Electric current noise in mesoscopic organic semiconductors induced by nuclear spin fluctuations

We demonstrate that nuclear spin fluctuations lead to the electric current noise in the mesoscopic samples of organic semiconductors showing the pronounced magnetoresistance in weak fields. For the bipolaron and electron-hole mechanisms of organic magnetoresistance, the current noise spectrum consists of the high frequency peak related to the nuclear spin precession in the Knight field of the charge carriers and the low frequency peak related to the nuclear spin relaxation. The shape of the spectrum depends on the external magnetic and radiofrequency fields, which allows one to prove the role of nuclei in magnetoresistance experimentally.

A built-in coil system attached to the inside walls of a magnetically shielded room for generating an ultra-high magnetic field homogeneity.

The homogeneity of the magnetic field generated by a coil inside a magnetic shield is essential for many applications, such as ultra-low field nuclear magnetic resonance or spin precession experiments. In the course of upgrading the Berlin Magnetically Shielded Room (BMSR-2) with a new inserted Permalloy layer of side length 2.87m, we designed a built-in coil consisting of four identical square windings attached to its inside walls. The spacings of the four windings were optimized using a recently developed semi-analytic model and finite element analysis. The result reveals a strong dependence of the field homogeneity on the asymmetric placement of the inner two windings and on the chosen material permeability value μs. However, our model calculations also show that these experimental variations can be counterbalanced by an adjustment of the inner winding positions in the millimeter range. Superconducting quantum interference device-based measurements yield for our implementation after fine adjustments of a single winding position a maximum field change of less than 10 pT for a total field of B0 = 2.3 µT within a 10cm region along the coil axis, which is already better than the residual field of the upgraded BMSR-2.1 after degaussing. Measurements of free spin precession decay signals of polarized Xe129 nuclei show that the transverse relaxation time for the used cell is not limited by the inhomogeneity of the new built-in coil system.

Suppression of ambient stray field for alkali magnetometer of nuclear magnetic resonance gyroscopes: Modeling and experiment.

In nuclear magnetic resonance gyroscopes (NMRGs), an ambient stray field should be suppressed to maximize performance of the in situ parametrically modulated alkali magnetometer (PMAM). Transfer functions of the PMAM of NMRGs decoupled with lock-in amplifiers are obtained by theoretical and simulation identification. It is found that the frequency bandwidth of the PMAM of NMRGs decoupled by lock-in amplifiers depends largely upon the low-pass filter of the lock-in amplifiers. A dynamic Kalman filter is used to estimate the stray field disturbance that is fed back to field coils to compensate the disturbance in the PMAM. Simulation and experiment results show that the dynamic Kalman filter has adaptiveness to the frequency shift of the nuclear spin precession signal of NMRGs that is quasi-sinusoidal. The dynamic Kalman filter for the PMAM is efficient in suppressing the ambient stray field noise of broad band and low frequency.

Structure of the 11/2− isomeric state in La133

We report measurement of the $g$-factor for the ${11/2}^{\ensuremath{-}}$ isomeric state at 535 keV in $^{133}\mathrm{La}$, employing the time differential perturbed angular distribution technique (TDPAD). This isomer was populated in the reaction $^{126}\mathrm{Te}(^{11}\mathrm{B}$, $4n)^{133}\mathrm{La}$ at beam energy of 52 MeV. From the observed nuclear spin precession, analysed through combined, magnetic dipole and electric quadrupole hyperfine interactions, we obtain the $g$ factor for the $11/{2}^{\ensuremath{-}}$ state as $g=1.16\ifmmode\pm\else\textpm\fi{}0.07$. In addition, this analysis provides the spectroscopic quadrupole moment $|Q|=1.71\ifmmode\pm\else\textpm\fi{}0.34\phantom{\rule{3.33333pt}{0ex}}b$, yielding the deformation parameter $\ensuremath{\beta}=0.28\ifmmode\pm\else\textpm\fi{}0.10$. Further, we have performed theoretical calculations using the large-scale shell model and the Monte Carlo shell model. The results successfully describe the low-lying levels and the band structures of $^{133}\mathrm{La}$, and the calculated $g$ factor compares well with the values obtained from our experiment. The dominant configuration of $11/{2}^{\ensuremath{-}}$ isomeric state in $^{133}\mathrm{La}$ is inferred to be $\ensuremath{\pi}({h}_{11/2})\ensuremath{\bigotimes}^{132}\mathrm{Ba}({0}^{+})$.

Static weak magnetic field measurements based on low-field nuclear magnetic resonance.

To measure the residual magnetic field, which is a kind of static magnetic fields in the magnetic shields, is a tough task in the design of the cylindrical magnetic shields. Here, we demonstrate a method to measure static weak magnetic fields based on low-field nuclear magnetic resonance (NMR), where the static magnetic field's strength can be obtained by measuring nuclear spin precession's frequency. Atomic magnetometers can be adopted to sense the nuclear spin precession, and the nuclear spin can be adopted to measure the static magnetic field through this indirect method to obtain the static magnetic field's strength. With this method, some adverse factors that can make atomic magnetometers yield fluctuations, such as fluctuations in the light intensity and misalignment of the pump and probe beams, can be avoid. We also measure the axial residual magnetic field in the magnetic shields, where the magnetic field's strength is about 235 pT in the direction along the pump beam. By monitoring NMR signals from protons and fluorine nuclei, we realize a nuclear-spin comagnetometer, which can be used to detect static weak magnetic fields. The possibility of using a miniaturized atomic magnetometer sensor (MAMS) for static field measurements is also discussed.

Tracking the precession of single nuclear spins by weak measurements.

Nuclear magnetic resonance (NMR) spectroscopy is a powerful technique for analysing the structure and function of molecules, and for performing three-dimensional imaging of their spin densities. At the heart of NMR spectrometers is the detection of electromagnetic radiation, in the form of a free induction decay signal1, generated by nuclei precessing around an applied magnetic field. Whereas conventional NMR requires signals from 1012 or more nuclei, recent advances in sensitive magnetometry2,3 have dramatically lowered the required number of nuclei to a level where a few or even individual nuclear spins can be detected4-6. It is unclear whether continuous detection of the free induction decay can still be applied at the single-spin level, or whether quantum back-action (the effect thata detector has on the measurement itself) modifies or suppresses the NMR response. Here we report the tracking of single nuclear spin precession using periodic weak measurements7-9. Our experimental system consists of nuclear spins in diamond that are weakly interacting with the electronic spin of a nearby nitrogen vacancy centre, acting as an optically readable meter qubit. We observe and minimize two important effects of quantum back-action: measurement-induced decoherence10 and frequency synchronization with the sampling clock11,12. We use periodic weak measurements to demonstrate sensitive, high-resolution NMR spectroscopy of multiple nuclear spins with a priori unknown frequencies. Our method may provide a useful route to single-molecule NMR13,14 at atomic resolution.

Nonvanishing effect of detuning errors in dynamical-decoupling-based quantum sensing experiments

Characteristic dips appear in the coherence traces of a probe qubit when dynamical decoupling (DD) is applied in synchrony with the precession of target nuclear spins, forming the basis for nanoscale nuclear magnetic resonance (NMR). The frequency of the microwave control pulses is chosen to match the qubit transition but this can be detuned from resonance by experimental errors, hyperfine coupling intrinsic to the qubit, or inhomogeneous broadening. The detuning acts as an additional static field which is generally assumed to be completely removed in Hahn echo and DD experiments. Here we demonstrate that this is not the case in the presence of finite pulse-durations, where a detuning can drastically alter the coherence response of the probe qubit, with important implications for sensing applications. Using the electronic spin associated with a nitrogen-vacancy centre in diamond as a test qubit system, we analytically and experimentally study the qubit coherence response under CPMG and XY8 dynamical decoupling control schemes in the presence of finite pulse-durations and static detunings. Most striking is the splitting of the NMR resonance under CPMG, whereas under XY8 the amplitude of the NMR signal is modulated. Our work shows that the detuning error must not be neglected when extracting data from quantum sensor coherence traces.

Nanometrology of field gradient using donor spins in silicon

We proposed a novel scheme for nanometrology of magnetic field gradient based on Kane’s silicon quantum computer proposal. When the system is placed in an unknown magnetic field gradient, the inhomogeneous precession of the donor nuclear spins records the field gradient information to the phase pattern of donor nuclear spins. By adding AC voltage modulations on each A-gate to induce hyperfine-mediated electron-nuclear collective flip-flop process, we demonstrate that the gradient value can be obtained by tuning the modulation phases of the A-gates. Errors of the measurements of such scheme is discussed and estimated. It is also discussed that in presence of the external field with a known gradient, the same system is possible to be used to obtain the unknown displacement of donor locations.

Determination of the position of a single nuclear spin from free nuclear precessions detected by a solid-state quantum sensor

We report on a nanoscale quantum-sensing protocol which tracks a free precession of a single nuclear spin and is capable of estimating an azimuthal angle---a parameter which standard multipulse protocols cannot determine---of the target nucleus. Our protocol combines pulsed dynamic nuclear polarization, a phase-controlled radiofrequency pulse, and a multipulse AC sensing sequence with a modified readout pulse. Using a single nitrogen-vacancy center as a solid-state quantum sensor, we experimentally demonstrate this protocol on a single 13C nuclear spin in diamond and uniquely determine the lattice site of the target nucleus. Our result paves the way for magnetic resonance imaging at the single-molecular level.