Spin-exchange Rate Research Articles

A comparison of pulse and CW EPR [formula omitted]-relaxation measurements of an inhomogeneously broadened nitroxide spin probe undergoing Heisenberg spin exchange 2. The intercept discrepancy

Experimental confirmation of a theoretical prediction of a non-linear broadening of the spin packets of nitroxide free radicals due to Heisenberg spin exchange at low concentrations, C, is presented. A recent demonstration that spectra with resolved proton hyperfine structure may be analyzed efficiently and accurately was utilized to confirm the theory. As C→0, a plot of the spin-packet line width (SPW) curves downward due to the presence of proton hyperfine couplings that increase the number of distinguishable quantum spin states. At higher C, the broadening is linear with C and the results for the spin exchange rate constant determined from the slope of the broadening of the average spin-packet line width and electron spin echo measurements are in agreement. It is shown that applying modest digital smoothing does not change the values of the SPW. An example of a practical application of these methods to published work is presented, allowing an enigma to be resolved.

Experimental Observation of a Peculiar Effect in Electron Paramagnetic Resonance Spectra for Nitroxides Undergoing Fast Spin Exchange: Emission.

We report the experimental observation of an EPR spectral manifestation of spin exchange frequencies, ωex, larger than the 15N hyperfine separation, A0, predicted 50 years ago but previously not observed. For spectra with ωex/γA0 < 1, where γ is the gyromagnetic ratio of the electron, the spectrum consists of two "normal" spin modes each with one absorption and one dispersion component separated by Aabs < A0. Aabs decreases with ωex. In stark contrast, when ωex/γA0 > 1, the spectrum consists of two absorption spin modes, one of which is negative (emissive). We show that the experimental behavior of the spin modes agrees with theory: (a) the doubly integrated intensity of the first-derivative spectra remains constant because the increased intensity of the positive spin mode minus the negative emissive mode remains constant; (b) the value of the spin exchange rate constant Kex = ωex/C, where C is the molar concentration, is continuous through ωex/γA0 = 1.

Theoretical Study on Performing Movement-Related MEG with 83Kr-Based Atomic Comagnetometer

A K–Rb–83Kr-based atomic comagnetometer for performing movement-related Magnetoencephalography (MEG) is theoretically studied in this paper. Parameters such as the spin-exchange rates, the spin-dephasing rates and the polarization of the nuclear spins are studied to configure the comagnetometer. The results show that the nuclear spin can generate a magnetic field of around 700 nT, at which the nuclear spin can compensate for a wide range of magnetic fields. In this paper, we also show the fabrication process for hybrid optical-pumping vapor cells, whereby alkali metals are mixed in a glove box that is then connected to the alkali vapor-cell fabrication system.

Dramatic improvement in the “Bulk” hyperpolarization of [formula omitted]Xe via spin exchange optical pumping probed using in situ low-field NMR

We report on hyperpolarization of quadrupolar (I=3/2) 131Xe via spin-exchange optical pumping. Observations of the 131Xe polarization dynamics via in situ low-field NMR show that the estimated alkali-metal/131Xe spin-exchange rates can be large enough to compete with 131Xe spin relaxation. 131Xe polarization up to 7.6±1.5% was achieved in ∼8.5×1020 spins—a ∼100-fold improvement in the total spin angular momentum—potentially enabling various applications, including: measurement of spin-dependent neutron-131Xe s-wave scattering; sensitive searches for time-reversal violation in neutron-131Xe interactions beyond the Standard Model; and surface-sensitive pulmonary MRI.

A comparison of pulse and CW EPR [formula omitted]-relaxation measurements of an inhomogeneously broadened nitroxide spin probe undergoing Heisenberg spin exchange

Nitroxide spin probes are inhomogeneously broadened (IHB) by intramolecular hyperfine interactions with protons (deuterons) producing lines of Voigt shape. Thus, to study T2 relaxation by continuous wave (CW) EPR, the Voigt must be deconvoluted to find the Lorentzian component. For homogeneously broadened lines, T2 is obtained directly from the Lorentzian line widths ΔHppL; however, for IHB lines finding T2 from ΔHppL is more complicated. It has been known for many years that values of ΔHppL of high precision may be obtained from IHB lines; however, direct, accurate comparison of spin exchange frequencies obtained from electron spin echo decay and CW EPR data has been lacking. It is demonstrated here that despite complications in the interpretation of experiments, these two techniques yield the same spin exchange rate constant for spin probes that are the most difficult to treat.

Measurement of rubidium vapor number density based on Faraday modulator

The actual vapor density characterizing the alkali metal spin-exchange rate remains a compelling issue for spin-exchange optical pumping. Based on the deduced relationship between the Faraday rotation angle and the rubidium vapor number density using the electrodynamics theory, we report a measurement of the number density for rubidium vapor sealed inside a cell based on a Faraday modulator. The measurement relies on the optical rotation angle due to rubidium vapor under a bias magnetic field (∼0.08 T) produced by a samarium–cobalt magnet. A Faraday modulator with a lock-in amplifier is used to accurately measure the tiny optical rotation angle in a temperature range of 387–468 K. In addition, a synchronization verification is performed by the photoelastic modulator (PEM). The recurring data showed that the two methods are consistent with each other. Compared with the PEM method, the Faraday modulator detection system does not need to adjust the optical axis difference of 45° in the PEM detection system, thereby reducing the complexity of the experiment and the error caused by the alignment of the optical axis, which showed that the Faraday modulator detection method more advantageous in measuring the alkali metal density.

Measuring Spin Polarization of a Spin-Exchange Relaxation-Free Atomic Magnetometer at Extremely Large Optical Depths

This paper presents a method for measuring the spin polarization of spin-exchange relaxation-free (SERF) atomic magnetometers at extremely large optical depths. Owing to the slowing-down effect, the spin polarization can be extracted by measuring the slowing-down factor extracted from the precession frequency. However, this technique is limited by a significant error in the regime of extremely large optical depths, where the pump beam intensity for achieving the optimized spin polarization of alkali atoms is significantly increased. We observed that the instantaneous precession frequency measured in the regime where the spin-exchange rate is not much larger than the Larmor frequency was no longer a constant but varied with the pump beam intensity. Thus, a method for measuring spin polarization based on the ratio of the precession frequency to the measured instantaneous precession frequency is proposed. Based on the proposed method, the spin polarization at a temperature of 473K and optical depth of 64 is measured. The measurement results were accordant with theoretical analysis. The expanded uncertainties of the experimental results varied between 1.8% and 9.6%. The proposed method is also applicable to other atomic devices operated in the SERF regime with extremely large optical depths, such as co-magnetometers and atomic spin gyroscopes.

Cross-Axis projection error in optically pumped magnetometers and its implication for magnetoencephalography systems

Optically pumped magnetometers (OPMs) developed for magnetoencephalography (MEG) typically operate in the spin-exchange-relaxation-free (SERF) regime and measure a magnetic field component perpendicular to the propagation axis of the optical-pumping photons. The most common type of OPM for MEG employs alkali atoms, e.g. 87Rb, as the sensing element and one or more lasers for preparation and interrogation of the magnetically sensitive states of the alkali atoms ensemble. The sensitivity of the OPM can be greatly enhanced by operating it in the SERF regime, where the alkali atoms’ spin exchange rate is much faster than the Larmor precession frequency. The SERF regime accommodates remnant static magnetic fields up to ±5 nT. However, in the presented work, through simulation and experiment, we demonstrate that multi-axis magnetic signals in the presence of small remnant static magnetic fields, not violating the SERF criteria, can introduce significant error terms in OPM's output signal. We call these deterministic errors cross-axis projection errors (CAPE), where magnetic field components of the MEG signal perpendicular to the nominal sensing axis contribute to the OPM signal giving rise to substantial amplitude and phase errors. Furthermore, through simulation, we have discovered that CAPE can degrade localization and calibration accuracy of OPM-based magnetoencephalography (OPM-MEG) systems.

In-situ triaxial residual magnetic field measurement based on optically-detected electron paramagnetic resonance of spin-polarized potassium

We present an approach that allows detecting all three components of the residual magnetic field inside shielding, based on the electron paramagnetic resonance (EPR) of spin-polarized K atoms. The residual field experienced by spin-polarized K atoms dominates Larmor precession frequency, the smaller the frequency is, the more benefits it has to realize spin-exchange relaxation-free (SERF) regime under a definite spin-exchange rate. The measurements are accomplished based on depopulation optical pumping and optically-detected peak of the K EPR spectrum. The EPR-based cross modulation method is employed to determine all three components of the residual field independently by modulating the frequency of transverse field and the strength of longitudinal field. The weighted averages of all measurements with the corresponding uncertainties are (9.60 ± 0.06) nT, (2.25 ± 0.03) nT, and (2.83 ± 0.17) nT along with the negative directions of their related axes, respectively.

Spin-polarization dependence of the Rb-Xe spin-exchange optical pumping process

We experimentally study the Rb-Xe spin-exchange optical pumping process. The dependence of the spin-exchange rate on the intensity of the pumping light is measured at different temperatures under low magnetic fields. We demonstrate that the spin-exchange rate will decrease as the Rb spin polarization increases, which agrees well with the theoretical prediction. In our measurement, three spin exchange and spin relaxation mechanisms, namely, the spin exchange rates between Rb and Xe atoms caused by van der Waals molecule (${\mathrm{\ensuremath{\Gamma}}}_{\mathrm{vdW}}$) and binary collision (${\mathrm{\ensuremath{\Gamma}}}_{\mathrm{bin}}$) processes, and the spin relaxation rate due to the wall collision of Xe atoms (${\mathrm{\ensuremath{\Gamma}}}_{\mathrm{w}}$), have comparable magnitudes. These rates are extracted separately from the measured data with different Rb spin polarization at various temperatures. Our work provides a comprehensive confirmation of the physical picture of the spin-exchange optical pumping process.

Theoretical models of spin-exchange optical pumping: Revisited and reconciled

Theoretical models for continuous-flow and stopped-flow spin-exchange optical pumping of 129Xe have long predicted much higher 129Xe polarization values than are measured experimentally, leading to a search for additional depolarization mechanisms. In this work, we show that a misapplication of the general theory of spin-exchange optical pumping along with the incorrect use of previously measured spin-exchange constants has been perpetuated in the past 20 years and is the main cause of the long-held discrepancy between theoretical and experimental 129Xe polarization values. Following the standard theory of spin-exchange optical pumping developed almost 40 years ago by Happer et al., we outline the common mistake made in the application of this theory in modern theoretical models and derive a simplified expression of the spin-exchange cross section that can be used to correctly predict 129Xe polarization values under any set of experimental conditions. We show that the complete expression of the spin-exchange cross section derived using the work of Happer et al. predicts spin-exchange rates tenfold higher than those previously assumed in theoretical models of continuous-flow and stopped-flow spin-exchange optical pumping and can fully rectify the long-standing discrepancy between theoretical and experimental polarization values.

Automated Low-Cost In Situ IR and NMR Spectroscopy Characterization of Clinical-Scale 129Xe Spin-Exchange Optical Pumping.

We present on the utility of in situ nuclear magnetic resonance (NMR) and near-infrared (NIR) spectroscopic techniques for automated advanced analysis of the 129Xe hyperpolarization process during spin-exchange optical pumping (SEOP). The developed software protocol, written in the MATLAB programming language, facilitates detailed characterization of hyperpolarized contrast agent production efficiency based on determination of key performance indicators, including the maximum achievable 129Xe polarization, steady-state Rb-129Xe spin-exchange and 129Xe polarization build-up rates, 129Xe spin-relaxation rates, and estimates of steady-state Rb electron polarization. Mapping the dynamics of 129Xe polarization and relaxation as a function of SEOP temperature enables systematic optimization of the batch-mode SEOP process. The automated analysis of a typical experimental data set, encompassing ∼300 raw NMR and NIR spectra combined across six different SEOP temperatures, can be performed in under 5 min on a laptop computer. The protocol is designed to be robust in operation on any batch-mode SEOP hyperpolarizer device. In particular, we demonstrate the implementation of a combination of low-cost NIR and low-frequency NMR spectrometers (∼$1,100 and ∼$300 respectively, ca. 2020) for use in the described protocols. The demonstrated methodology will aid in the characterization of NMR hyperpolarization hardware in the context of SEOP and other hyperpolarization techniques for more robust and less expensive clinical production of HP 129Xe and other contrast agents.

Mapping of Absolute Host Concentration and Exchange Kinetics of Xenon Hyper-CEST MRI Agents.

Xenon magnetic resonance imaging (MRI) provides excellent sensitivity through the combination of spin hyperpolarization and chemical exchange saturation transfer (CEST). To this end, molecular hosts such as cryptophane-A or cucurbit[n]urils provide unique opportunities to design switchable MRI reporters. The concentration determination of such xenon binding sites in samples of unknown dilution remains, however, challenging. Contrary to 1H CEST agents, an internal reference of a certain host (in this case, cryptophane-A) at micromolar concentration is already sufficient to resolve the entire exchange kinetics information, including an unknown host concentration and the xenon spin exchange rate. Fast echo planar imaging (EPI)-based Hyper-CEST MRI in combination with Bloch–McConnell analysis thus allows quantitative insights to compare the performance of different emerging ultra-sensitive MRI reporters.

Fast Dynamic Frequency Response-Based Multiparameter Measurement in Spin-Exchange Relaxation-Free Comagnetometers

As the measurement of multiple parameters in a spin-exchange relaxation-free (SERF) comagnetometer requires a long time and complex experimentation, we present a novel dynamic frequency response-based method for the accurate and rapid measurement of key parameters in a SERF comagnetometer. By testing the dynamic frequency response to a transverse oscillating magnetic field, we can obtain multiple parameters simultaneously and quickly without interrupting the operation of the comagnetometer. This method simultaneously measures the nuclear longitudinal relaxation rate and alkali metal number density within minutes, with uncertainties of less than 20.8% and 14.0%, respectively. The main error sources in the nuclear longitudinal relaxation rate and alkali metal number density are the spin-exchange rate constant and spin-exchange enhancement factor, respectively. In addition, the polarization of alkali metal and noble gas atoms can be obtained during the experimental process, and the fast measurement of these parameters is beneficial for applications requiring simultaneous and in situ measurement of spin ensemble performance.

Rapid 129Xe-Rb spin-exchange rate measurement by using an atomic magnetometer.

We propose a fast and accurate method for $^ {129} {\rm Xe}{-}{\rm Rb}$129Xe-Rb spin-exchange rate determination based on an atomic magnetometer at low magnetic field and low pressure. The $^ {129} {\rm Xe}{-}{\rm Rb}$129Xe-Rb spin-exchange rate can be estimated via the product of the maximum transverse spin polarization of $^ {129} {\rm Xe}$129Xe nuclei and the corresponding Rabi frequency. The velocity-averaged binary spin-exchange cross section and the rate constant for spin-exchange in $^ {129} {\rm Xe}{-}{\rm Rb}$129Xe-Rb van der Waals complexes are measured to be ${\langle \sigma \nu \rangle _{{\rm SE}}} = ( {1.26 \pm 0.13} ) \times {10^{ - 16}}\;{{\rm cm}^ 3 }{\rm /s}$⟨σν⟩SE=(1.26±0.13)×10-16cm3/s and ${\kappa _{^4{\rm He}}} = 1326 \pm (47)\,{{\rm s}^{ - 1 }}$κ 4He=1326±(47)s-1 in $^4{\rm He}$4He buffer gas, respectively. With respect to the method based on the longitudinal relaxation rate, the method presented in this work can greatly facilitate the measurement process, determining the spin-exchange rate in several minutes. Moreover, this method is more suitable for vapor cells with long longitudinal relaxation time.

Spin-exchange relaxation of naturally abundant Rb in a K–Rb–21Ne self-compensated atomic comagnetometer**Project supported by the National Key R&D Program of China (Grant Nos. 2016YFB0501600 and 2017YFB0503100), the National Natural Science Foundation of China (Grant Nos. 61773043, 61673041, 61721091, and 61703025), and the National Science Fund for Distinguished Young Scholars of China (Grant No. 61925301).

The total effective spin-exchange relaxation of naturally abundant Rb in a K–Rb–21Ne comagnetometer is analyzed, and the results show that the coexistence of 87Rb and 85Rb isotopes in the same volume can lead to a large extra spin-exchange broadening compared to pure 87Rb. This broadening mainly comes from the contribution of the equivalent reduction in the Rb spin-exchange rate. On this basis, an approximate relaxation model is proposed and experimentally demonstrated to be more accurate than that from a previous work. This study also provides a method for determining the properties of alkali-metal vapor cells.

Tight-binding Kondo model and spin-exchange collision rate of alkaline-earth-metal atoms in a mixed-dimensional optical lattice

We study the two-body problem of the ultracold fermionic alkaline-earth (like) atoms in the electronic $^1$S$_0$ state ($g$-state) and $^3$P$_0$ state ($e$-state), which are confined in a quasi-one-dimensional (quasi-1D) tube. In addition, in the axial direction, the $g$-atom experience a 1D optical lattice and the $e$-atom is localized by a harmonic potential. In this work, we propose two appropriate tight-binding models, which are applicable for the cases that the odd-wave scattering between the $g$- and $e$-atom is negligible or not, respectively. We further give a microscopic derivation for the inter-atomic interaction parameters of these tight-binding models, by exactly calculating the low-energy inter-atomic scattering amplitude. Our results show that, as one can predict, these interaction parameters can be efficiently controlled by the confinement potentials. We further exam the simple "projection approximation" with which one derives the interaction parameters by directly projecting the 3D Huang-Yang pseudopotential on the ground state of the confinement and the lowest band of the optical lattice. We find that one should be very careful about determining the interaction parameters in the tight-binding models. Furthermore, we calculate the spin-exchanging rate, which dependents on the incident quasi-momentum $k$ of the $g$-atom, for the recent experiment (L. Riegger, {\it et. al.,} Phys. Rev. Lett. {\bf 120}, 143601 (2018)) of $^{173}$Yb atoms in this quasi-(1+0)D system, and study finite-momentum effect in this experiment. Our results show that in this system the finite-momentum effect of the $g$-atom is very significant, and the momentum of the $g$-atoms in this experiment may be pretty high (already in the second Brillouin zone of the optical lattice)

Generation of atomic spin orientation with a linearly polarized beam in room-temperature alkali-metal vapor

Traditionally, atomic spin orientation is achieved by the transfer of angular momentum from polarised light to an atomic system. We demonstrate the mechanism of orientation generation in room-temperature caesium vapours that combines three elements: optical pumping, non-linear spin dynamics and spin-exchange collisions. Through the variation of the spin-exchange relaxation rate, the transition between an aligned and an oriented atomic sample is presented. The observation is performed by monitoring the atomic radio-frequency spectra. The measurement configuration discussed, paves the way to simple and robust radio-frequency atomic magnetometers that are based on a single low power laser diode that approach the performance of multi-laser pump-probe systems.

New Paradigm of Spin Exchange and its Manifestations in EPR Spectroscopy

Theoretical results are presented, which have been confirmed experimentally and became basis for a new paradigm of spin exchange between paramagnetic particles in solutions and measurement of the spin exchange rate by EPR spectroscopy. Fundamental changes in the basics of spin exchange in solutions are associated with the transfer of coherence back from the interaction partner. It was shown that the transfer of spin coherence in random bimolecular collisions creates collective modes of evolution of quantum coherence of electron spins of paramagnetic particles. The EPR spectrum is the sum of the resonance lines. In the case of a slow spin coherence transfer, each spectral line has a mixed shape, it is the sum of the symmetric absorption line and the antisymmetric dispersion line. In the case of fast spin coherence transfer, only one collective mode is manifested in the EPR spectrum, the other modes are not manifested, since they are very weakly excited by the external microwave field, and they can be considered as forbidden lines in the spectrum or “dark” modes. The establishment of the mixed shape of the spectrum individual lines has fundamentally changed the protocol for finding the rate of bimolecular spin exchange caused by the exchange interaction. In the current existing paradigm, the contribution of the dipole–dipole interaction to the spin coherence transfer was mistakenly neglected.

Thermal atom-ion collisions in a K- Yb+ hybrid system

We present experimental studies of atom-ion collisions using buffer-gas cooled, trapped ytterbium (Yb$^+$) ions immersed in potassium (K) vapor. The range of the collisional temperature is on the order of several hundred kelvin (thermal regime). We have determined various collisional rate coefficients of the Yb$^+$ ion per K-atom number density. We find the upper bounds of charge-exchange rate coefficients $\kappa_{\rm ce}$ to be $(12.7\pm1.6)\times10^{-14}$ cm$^3$s$^{-1}$ for K-$^{171}$Yb$^+$ and $(5.3\pm0.7)\times10^{-14}$ cm$^3$s$^{-1}$ for K-$^{172}$Yb$^+$. For both isotopes, the spin-destruction rate coefficient $\kappa_{\rm sd}$ has an upper bound at $(1.46\pm0.77)\times10^{-9}$ cm$^3$s$^{-1}$. The spin-exchange rate coefficient $\kappa_{\rm se}$ is measured to be $(1.64\pm0.51)\times10^{-9}$ cm$^3$s$^{-1}$. The relatively low charge-exchange rate reported here demonstrates the advantage of using K atoms to sympathetically cool Yb$^+$ ions, and the relatively high spin-exchange rate may benefit research work in quantum metrology and quantum information processing on an atom-ion platform using K atoms and Yb$^+$ ions.