Spin-exchange Relaxation Research Articles

Synchronous achievement of laser frequency stabilization and tunability via modulation transfer spectroscopy on the rubidium D1 line

In the Spin Exchange Relaxation Free (SERF) magnetometer, the laser frequency must be stabilized at the alkali D1 line and tunable within a range of several gigahertz (GHz). We theoretically and experimentally analyzed the modulated sideband and resonant frequencies on the D1 transition line of rubidium (Rb) atoms using a modulation transfer spectroscopy (MTS) frequency stabilization system. The laser's self-estimated frequency stability shows the Allan deviation of 1.5 × 10−12/τ for resonance peak stabilization and 1.4 × 10−12/τ for sideband stabilization. The spectrum of the modulated laser interacting with the rubidium D1 line exhibits several absorption peaks and MTS signals across a 6 GHz scanning frequency range, which can be used to lock and tune the laser. This method enhances the application of distributed feedback semiconductor lasers in Rb atom-based magnetometers.

Suppression of spin-exchange relaxation in Bell-Bloom magnetometer

The atomic spin-exchange relaxation is the most important limitation of the sensitivity for the optically pump magnetometers operated on non-zero magnetic field environment. In this paper, a method with 2π magnetic field pulse modulation is proposed to suppress the spin-exchange relaxation by counteracting the Larmor precession effect caused by the external magnetic field, which allows being operated under non-zero magnetic field. This method applies an additional periodic 2π pulse magnetic field repeated with the Larmor precession frequency on the conventional Bell-Bloom magnetometer. The theoretical model of the Bell-Bloom magnetometer responding with 2π pulse magnetic field is established, and the suppression of the spin-exchange relaxation is demonstrated experimentally. This method reduces the spin-exchange relaxation by 91.4% and improves the magnetometer response by 74.0%, which is directly beneficial to the sensitivity of the atomic magnetometer applied in μT-scale magnetic field.

Light narrowing over broad temperature range with paraffin-coated vapor cells

This study reports light narrowing in paraffin-coated vapor cells from room temperature 27 to 59 °C, where spin-exchange relaxation is suppressed. By means of a coating lock and eliminating the reservoir effect, an ultra-narrow magnetic resonance linewidth of 0.36 Hz and an atomic coherence lifetime of T2=0.9 s are achieved. In cells free of buffer gas, the narrow linewidth over this broad temperature range is a result of enhanced spin polarization, which is facilitated by the effective suppression of radiation trapping benefiting from the stability of the vapor density. Using such cells in atomic magnetometers, the photon shot noise limit is estimated as 0.2 fT/Hz1/2 and the spin-projection noise limit is estimated as 1.1 fT/Hz1/2. Also, a magnetometer system with the stable coated cell is identified, which demonstrates the potential for achieving relatively stable magnetometer sensitivity without precisely controlling the cell temperature. The long coherence lifetime and the broad operating temperature range expand the potential applications of quantum memory and other quantum sensors such as atomic clocks.

Radio-Frequency Magnetometry Based on Parametric Resonances.

We propose and demonstrate a radio-frequency (rf) atomic magnetometer based on parametric resonances. Previously, most rf atomic magnetometers are based on magnetic resonances and their sensitivities are often limited by spin-exchange relaxation. Here, we introduce a novel scheme for an rf magnetometer where the rf magnetic field is measured by exciting the parametric resonances instead of magnetic resonances using parametric modulation fields. In this way, the spin-exchange relaxation is almost eliminated. Benefiting from the low spin relaxation rate, the parametric resonance scheme exhibits a narrower linewidth and stronger signal, which results in a higher sensitivity. With a 6×6×3 mm^{3} Rb atomic vapor cell, we developed an rf atomic magnetometer with a noise floor of 2 fT/Hz^{1/2}, which is about one order of magnitude higher than the sensitivity achieved in the magnetic-resonance-based scheme. The presented rf detection scheme holds promise in advancing rf atomic magnetometers and brings new insight into their various applications.

Investigating Cu-Site Doped Cu-Sb-S Nanoparticles Using Photoelectron and Electron Paramagnetic Resonance Spectroscopy.

Tetrahedrite (Cu12Sb4S13) and famatinite (Cu3SbS4) are good candidates for green energy applications because they possess promising thermoelectric and photovoltaic properties as well as contain earth-abundant and nontoxic constituents. Herein, X-ray photoelectron spectroscopy (XPS), ultraviolet photoelectron spectroscopy (UPS), and electron paramagnetic resonance spectroscopy (EPR) methods examined inherent electronic properties and interatomic magnetic interactions of Cu-site doped tetrahedrite and famatinite nanomaterials. An energy-efficient modified polyol method was utilized for the synthesis of tetrahedrite and famatinite nanoparticles doped on the Cu-site with Zn, Fe, Ni, Mn, and Co. This is the first parallel study of tetrahedrite and famatinite nanomaterials with XPS, UPS, and EPR methods alongside a systematic analysis of dopant-dependent effects on the electronic structure and magnetic interactions for each material. XPS showed that the Cu and Sb species in tetrahedrite and famatinite possess different oxidation states, while UPS characterization reveals larger dopant-dependent shifts in the work function for tetrahedrite nanoparticles (4.21 to 4.79 eV) than for famatinite nanoparticles (4.57 to 4.77 eV). Finally, all famatinite nanoparticles display an EPR signal, indicating trace amounts of paramagnetic Cu(II) present below the detection limit of XPS. For tetrahedrite, EPR signatures were observed only for the Zn-doped and Mn-doped nanoparticles, suggesting signal broadening from Cu-Cu spin exchange or spin-lattice relaxation. This study demonstrates the complementary nature of XPS and EPR techniques for studying the oxidation states of metals in solid-state nanomaterials. Comparing the electronic and magnetic properties of tetrahedrite and famatinite while studying the impact of dopant incorporation will guide future endeavors in designing sustainable, high-performance materials for renewable energy applications.

Single-beam three-axis SERF atomic magnetometer based on coordinate system rotation

We propose what we believe to be a new single-beam three-axis spin exchange relaxation free (SERF) vector atomic magnetometer scheme based on coordinate system deflection. A theoretical model for the system response under arbitrary angle deflection was established for the first time, and the system response at different angles was simulated and analyzed. The simulation results show that the system response increases in the direction of the non-sensitive axis and decreases in the direction of the sensitive axis as the deflection angle increases, and the two responses tend to be the same when the angle is deflected to 45-degrees. Experimental measurements were carried out at a deflection angle of 45-degrees and the results showed that the sensitivity of the magnetometer was 55fT/Hz1/2 in the x1-axis, 38fT/Hz1/2 in the y1-axis and 60fT/Hz1/2 in the z1-axis. This single-beam magnetometer can be used to construct a miniaturized and low-cost weak magnetic sensor, which is expected to be used for vector measurement of biomagnetism.

Method to quickly estimate T1 value by suppressing spin exchange relaxation and magnetic field gradient relaxation in atomic sensors

The accuracy of atomic sensor is determined by the transverse nuclear spin relaxation time (T2). As the longitudinal nuclear spin relaxation time (T1) is the upper limit of T2, it becomes an important metric for evaluating the merits of alkali vapor cells. However, the conventional method for measuring T1 of pulse delay takes dozens of minutes, which will increase the effect of random errors during the testing process. In order to solve this problem, a method to quickly estimate the value of T1 is proposed by suppressing the influence of spin exchange relaxation and magnetic field gradient relaxation terms on T2. Experimental results indicate that the accuracy is maintained at above 95%, and the testing time is reduced to less than 5%.

Comprehensive analysis of the magnetic field closed-loop control system in SERF atomic magnetometer

Benefiting from the capability to measure and suppress magnetic field interferences in situ, the closed-loop magnetometer system has garnered significant attention. In this paper, the low-pass filtering link is analyzed theoretically and experimentally for the first time within the framework of the single-beam spin exchange relaxation free atomic magnetometer system (the object to be controlled). The analysis not only elucidates its impact on the closed-loop system but also establishes optimal operating parameters through a comprehensive consideration of factors such as steady-state error, bandwidth, and other metrics. A comparison and analysis of the direct output signal of the system with the controller output signal reveal the necessity of using the controller output as the closed-loop system’s output, supported by the amplitude and frequency response characteristics of the output signal. The paper introduces evaluation indicators essential for comparing the long-term measurement stability of open- and closed-loop systems, and it explores the correlation between the output signals of the open- and closed-loop systems and the cardio-magnetic input signals. Finally, the calibration methods for multi-channel closed-loop magnetometers are discussed.

Quantification and suppression of optical non-orthogonality and light intensity noise in all-optical hot atomic sensing systems

All-optical hot atomic sensing systems such as optical pumping magnetometers (OPM) and comagnetometers, nuclear magnetic resonance (NMR) magnetometers and gyroscopes, have the ability to sense magnetic field, anomalous field and inertial rotation, thus having a wide potential for applications in precision measurement, fundamental physics research and inertial navigation. System noise limits the minimum value of the signal that can be measured and there is coupling effect between the noises. Therefore, the quantification and suppression of various noise are challenging and should be investigated. As one of the major noises, the light intensity fluctuation of the probe light and the pump light affects the sensitivity of the all-optical hot atomic sensing systems. However, there has been no in-depth research on the quantification of the light intensity noise. In this paper, a method of measuring the light intensity noise is proposed, which can be applied to kinds of all-optical hot atomic sensing systems. For verification, the effects of probe and pump light intensity fluctuations on system noise are simulated and experimentally verified in a spin exchange relaxation free (SERF) comagnetometer. Besides, it is found that the optical non-orthogonality amplifies the probe light intensity noise by more than 3.4 times and a quantification method of optical non-orthogonality is proposed. Finally, a suppression method of the light intensity noise is presented by suppressing the optical non-orthogonality and the noise is suppressed by 59%. A universal light intensity noise quantification method is proposed for all-optical hot atomic sensing systems, and a light intensity noise suppression method is proposed for SERF comagnetometers, which can be applied to the suppression of noises coupled with atomic polarization.

Response optimization of a three-axis sensitive SERF magnetometer for closed-loop operation

Most triaxial-vectorial magnetic field measurements with spin-exchange relaxation free (SERF) atomic magnetometer (AM) are based on the quasi-steady-state solution of the Bloch equation. However, the responding speed of these methods is greatly limited because the frequency of the modulation signal should be slow enough to ensure the validity of the quasi-steady-state solution. In this work, a new model to describe the response of the three-axis sensitive SERF AM with high modulation frequency is presented and verified. The response of alkali-atomic spin to high-frequency modulation field is further investigated by solving the Bloch equation in a modulation-frequency-dependence manner. This solution is well verified by our experiments and can offer a reference for selection of modulation frequencies. The result shows a potential to achieve a SERF AM operating in a geomagnetic field without heavy aluminum shielding when the modulation frequencies are selected properly.

SERF-like magnetometry in room-temperature environment.

We demonstrate an atomic magnetometry using amplitude-modulated pumping and hyperfine repumping techniques in a paraffin-coated cell. By exploiting the constructive interference between spins polarized by the pump beam and an additional repump beam, we observe a three-fold increase in the amplitude of magnetic resonance, along with a reduction in linewidth by approximately two times. The implementation of the repump beam effectively narrows the linewidth, demonstrating successful suppression of spin-exchange relaxation. This reduction in relaxation rate, combined with the enhanced signal, significantly improves the sensitivity of the magnetometer. Consequently, our technique offers a promising approach for achieving SERF-like magnetometry with sub-fT-level sensitivity in Earth-field range and room-temperature environment.

Light-narrowed parametric resonance magnetometer with the fundamental sensitivity beyond the spin-exchange limit.

In the field of biomagnetic measurements, one of the most important recent challenges is to perform measurements in a magnetically unshielded environment. This first requires that atomic magnetometers can operate in a finite magnetic field, and have enough high sensitivity. To meet these requirements, we develop a light-narrowed parametric resonance (LPR) magnetometer. By adding a modulation magnetic field to the large longitudinal magnetic field, our LPR magnetometer can measure small transverse magnetic fields with an intrinsic sensitivity of 3.5 fT/Hz1/2 in a longitudinal magnetic field of μT range. Moreover, we have also demonstrated that in contrast to the previous light-narrowed scalar magnetometers, our LPR magnetometer has the potential to achieve higher sensitivity. Because in our case spin-exchange relaxation suppression by using light narrowing can lead to an improvement of fundamental sensitivity limit regardless of which quantum noise is dominant, and hence the fundamental sensitivity is no longer limited by spin-exchange, and approaches the fundamental limit set by the spin-exchange and spin-destruction cross sections.

Fast measurement of spin-exchange relaxation in the range of earth-scale magnetic field

The spin-exchange relaxation of electron spins directly affects the sensitivity of the atomic magnetometers. Rapid determination of the spin-exchange relaxation is essential. In this work, we propose a novel method for measuring the spin-exchange relaxation that allows being operated in the range of zero to earth-scale magnetic field. The longitudinal and transverse relaxation are synchronously extracted from the magnetic resonance linewidth and radio-frequency field amplitude corresponding to the maximum slope of the dispersive resonance curve. The spin-exchange relaxation is further obtained from the difference. The experimental results are consistent with the conventional linewidth fitting method in near-zero magnetic field and with the theoretical expectation in earth-scale magnetic field. This method not only improves authenticity compared to the conventional linewidth fitting method by considering the effect of rf field on relaxation, but also provides a fast and reliable measurement of the spin-exchange relaxation in earth-scale field.

Measurement and analysis of an optimized Jiles–Atherton model considering the influence of temperature applied in magnetic shielding devices

Magnetic shielding devices work at different temperatures due to the influence of gas chamber and environmental temperature in the application of ultra-highly sensitive spin exchange relaxation free (SERF) magnetometers. To accurately evaluate the residual magnetic field (MF) of a magnetic shielding device at different temperatures, it is necessary to build a magnetization model considering temperature. However, the modeling of permalloy’s magnetization properties and the measurement of residual MF in magnetic shielding devices at different temperatures have not been considered. In this paper, an optimized Jiles–Atherton (JA) model of permalloy considering temperature is constructed, in which parameters are extracted using a particle swarm optimization algorithm. To further verify the effectiveness of the model in the magnetic shielding device, it is applied to the residual MF simulation of magnetic shielding devices and verified by measurement. The optimized JA model considering temperature improves the calculation accuracy of magnetic shielding devices, which is of great significance for the application of ultra-highly sensitive SERF magnetometers.

The suppression of the probe laser pumping effect in SERF atomic magnetometer

Introduction: A spin exchange relaxation free atomic magnetometer, as an ultra-highly sensitive magnetic field sensor, is limited by the performance of the probe laser system. The probe laser pumping effect (PLPE) hinders the increase in the performance of probe laser system.Methods: This study investigated the PLPE and proposed a method for suppressing the same. Through changes to the angle of a quarter wave plate and the addition of a triangular modulated magnetic field to the alkali atoms, the suppression point was determined.Results and discussion: Further, related parameters were measured for different degree of polarizations of the probe laser, which confirmed that the influence of PLPE on the magnetic field was the least at the suppressed point.

Automated Machine Learning Strategies for Multi-Parameter Optimisation of a Caesium-Based Portable Zero-Field Magnetometer.

Machine learning (ML) is an effective tool to interrogate complex systems to find optimal parameters more efficiently than through manual methods. This efficiency is particularly important for systems with complex dynamics between multiple parameters and a subsequent high number of parameter configurations, where an exhaustive optimisation search would be impractical. Here we present a number of automated machine learning strategies utilised for optimisation of a single-beam caesium (Cs) spin exchange relaxation free (SERF) optically pumped magnetometer (OPM). The sensitivity of the OPM (T/Hz), is optimised through direct measurement of the noise floor, and indirectly through measurement of the on-resonance demodulated gradient (mV/nT) of the zero-field resonance. Both methods provide a viable strategy for the optimisation of sensitivity through effective control of the OPM's operational parameters. Ultimately, this machine learning approach increased the optimal sensitivity from 500 fT/Hz to <109fT/Hz. The flexibility and efficiency of the ML approaches can be utilised to benchmark SERF OPM sensor hardware improvements, such as cell geometry, alkali species and sensor topologies.

Quantum‐Based Magnetic Field Sensors for Biosensing

AbstractThe accurate detection of very weak biomagnetic signals with a sensitivity of fT levels and mapping nanoscale magnetic field variations are two of the most significant challenges for biosensing. Compared to the limited sensitivity and spatial resolution of traditional magnetic field sensors, quantum‐based magnetic field sensors are emerging as a promising solution. In this review, the latest developments of three representative quantum‐based magnetic field sensors, including superconducting quantum interference device (SQUID) magnetometers, spin exchange relaxation free (SERF) atomic magnetometers, and nitrogen‐vacancy centers in diamond, are summarized. Both virtues and limitations of these sensors are analyzed systematically, and typical applications in magnetocardiography, magnetoencephalography, detection of neuronal action potentials, magnetic imaging of living cells, biomedical diagnosis, etc., are presented. Furthermore, SQUIDs combined with microfluidics for magnetic immunoassay diagnostics, the chip‐scale SERF atomic magnetometers fabricated by microelectromechanical systems that offer wearable flexibility, and nanodiamonds functionalized with magnetic nanoparticles to improve the sensitivity of nanothermometers are discussed.

A Novel Measurement Method for Spin Polarization Three Axis Spatial Distribution in Spin-Exchange Relaxation Free Atomic Magnetometer

The measurement of atomic spin polarization distribution in spin-exchange relaxation free (SERF) magnetometer is an important topic for improving the sensitivity and consistency of multi-channel magnetic field measurement applications. A novel spin polarization spatial distribution measurement method is presented based on the transient response of the magnetometer after modulating the pumped light with a chopper. Polarization is obtained by a slow-down factor based on the fast spin-exchange interaction effects. Longitudinal and transverse polarization distributions are measured simultaneously without interrupting the operation of the SERF status. Under different oscillating magnetic fields, the spin polarization is measured at the cell centroid. Residual magnetic field inside the magnetometer is obtained from the linear relationship between the precession frequency and the oscillating magnetic field. The one-dimensional polarization distributions in the x, y, and z axes are measured using a digital micromirror device with a resolution of 0.25 cm. The measurement results conform to the Lambert-Bier absorption law and the Gaussian distribution law. Furthermore, 7 × 7 two-dimensional spatial distribution measurements of polarization on the xy and yz planes are performed. Nonuniformity of 1.04 in the xy plane and 1.82 in the yz plane in the built magnetometer. Compared with other measurement methods, the distribution measurement method proposed is independent of optical depth and suitable for low polarization and high polarization applications. Based on the results of the proposed measurement method of spin polarization spatial distribution, further compensation can improve the application consistency of multi-channel magnetic field measurements and improve the sensitivity of single-channel differential measurements.

Accurate Determination of Spin-Exchange Relaxation in a Self-Compensated Atomic Comagnetometer

The spin-exchange (SE) relaxation of the electron spins limits the sensitivity of the self-compensated atomic co-magnetometer. In this paper, a novel method for measuring the SE relaxation based on the pulse response of the comagnetometer is proposed. The SE relaxation is measured from the difference between the transverse and longitudinal relaxation of the electron spins, which are synchronously extracted from the responses along the probe and pump laser directions to a series of pulsed magnetic fields. Furthermore, we investigate the variation of the SE relaxation with different pump laser power densities and cell temperatures based on this method. The results indicate that there is a maximum of the SE relaxation with the increase of the pump laser power density, and the pump laser power density corresponding to the maximum increases with the cell temperature. The theory and method presented here not only shed light on the way to suppress the SE relaxation in the self-compensated comagnetometer, but also have the potential to be applied to other optically pumped atomic sensors.

Structure optimization of non-magnetic electric heating film for spin exchange relaxation free magnetometer

Spin exchange relaxation free (SERF) atomic magnetometer is one of the most sensitive magnetometers. High temperature and a non-magnetic environment are two key conditions to achieve ultra-high sensitivity. In this paper, a non-magnetic heating film with magnetic field self-suppression is optimized by the genetic algorithm method. Four structural parameters of the non-magnetic heating film including the wire spacing, wire width, wire thickness, and layer distance are optimized to minimize the magnetic field in the heated space. The simulation result based on the finite element analysis method shows that the magnetic field and the temperature field produced by a pair of heating films at the vapour cell are uniform. Finally, the magnetic field experiment proved that when the current is 10 ​mA, the magnetic field is 3.0520 ​nT. The temperature control experiment indicates that the temperature could be stabilized at 180 ​± ​0.2 ​°C. This study is significant for electric heating with a lower magnetic field and contributes to further improving the performance of atomic sensors.