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This 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. [ABSTRACT FROM AUTHOR]

Inside a spin-exchange relaxation-free (SERF) co-magnetometer with a high-pressure buffer gas atomic cell, the magnetic field gradient causes the decoherence of atomic spins to produce magnetic-field gradient relaxation. This paper presents a new method for the accurate measurement of magnetic field gradient relaxation of alkali metal atoms and inert atoms of strongly coupled spin systems under triaxial magnetic field gradients in the K-Rb-21Ne co-magnetometer. The magnetic field gradient relaxation of alkali metal atoms is measured using a step magnetic field modulation method, and the magnetic field gradient relaxation of inert atoms is measured using a combined free induction decay and spin growth method. The method does not require the use of large background magnetic fields and RF fields to maintain the atoms in the SERF state, does not require additional optics, and is not affected by the pumping or detecting of optical power. A kinetic model that considers a large electron-equivalent magnetic field was designed and a gradient relaxation model was developed. The quadratic coefficients of the experimentally measured gradient relaxation curves fit the theoretical model well over the range of the applied magnetic field gradients, confirming the validity of the proposed method. [ABSTRACT FROM AUTHOR]

We disclose a method to obtain the transverse light-shift along the probe light of a single-axis alkali metal-noble gas co-magnetometer. The relationship between transverse compensating field and light-shift is deduced through the steady-state solution of Bloch equations. The variety of probe light intensity is used to obtain the residual magnetic field, and step modulation tests are applied to acquire the total spin-relaxation rate of electron spins and self-compensation point. The transverse light-shift can be calculated by these parameters, and it is reduced from − 0.115 to − 0.039 nT by optimizing the probe light wavelength. Finally, long-term static test for a K-Rb-21Ne co-magnetometer has been performed. The bias instability of about 0.009 deg/h and rate ramp coefficient of 0.096 (deg/h)/h have been achieved to prove the improvement of stability. [ABSTRACT FROM AUTHOR]

We describe a dual-axis atomic spin comagnetometer for rotation sensing using a single laser beam. A circularly polarized laser is used to pump the co-located atomic ensembles of alkali metal and noble gas and probe their gyroscopic precession at the same time, which is different from the traditional two-beam orthogonal pump-probe configuration. Combined with magnetic field modulations perpendicular to the laser propagating direction, the comagnetometer could measure dual-axis rotation rates simultaneously. This system is demonstrated theoretically and experimentally. A rotation sensitivity of 5.1 × 10–7 rad s−1 Hz−1∕2 and a bias instability of 0.016 °/h have been achieved. The theory and method presented here shed light on the way to miniaturize the comagnetometer with high precision for practical applications. [ABSTRACT FROM AUTHOR]

This paper investigates a novel method for the in-situ evaluation of the low-frequency magnetic field fluctuation in an atomic comagnetometer (ACM). An in-situ magnetic field measurement model is first established for the hybrid atomic spin ensembles in the ACM based on the simplified Bloch equations. Then, the ACM is transformed into an in-situ magnetometer by employing a large longitudinal magnetic field and a transversal alternating current (AC) magnetic field, respectively. This in-situ magnetometer is sensitive to the magnetic field fluctuation along the detection laser direction according to the established measurement model and can realize the magnetic field measurement sensitivity of 88fT/Hz1/2 at 0.1Hz. Finally, the low-frequency magnetic field fluctuation is evaluated with this in-situ magnetometer, whose influence on the stability of the ACM is also analyzed by the Allan variance method. The experimental results show that the contribution of the magnetic field fluctuation along the detection laser direction to the stability of the ACM is about 0.0068 deg/h, which means that the magnetic field error still has a non-negligible effect on the stability of the system. This new in-situ magnetic field measurement method has the advantages of simple operation and no need to replace the atomic vapor cell, which provides an effective means of the magnetic field error evaluation for the ACM. [ABSTRACT FROM AUTHOR]

Alkali metal-noble gas comagnetometers operated in the regime of spin-exchange relaxation-free (SERF) have been widely used in fundamental physics tests and rotation sensing as gyroscope. Spin-exchange relaxation is an important systematic bias of the comagnetometer, which could limit sensitivity significantly. However, the suppression effect of the spin-exchange relaxation has not been examined quantitatively so far. Herein, we systematically investigate the relaxation of the alkali metal atoms and find that the spin-exchange relaxation is not completely eliminated under the normal operating condition of the K-Rb-21Ne comagnetometer. In addition to the optical pumping rate, the spin-exchange relaxation still plays a dominant role in the broadening of electron Zeeman resonances due to the large electron magnetic field. This is the first demonstration that the alkali metal atoms are operated in the near-SERF regime in the alkali metal-noble gas comagnetometer with a large election magnetic field, which will shed light on the way to reduce the relaxation of the alkali metal atoms and enhance the sensitivity of the comagnetometer. [ABSTRACT FROM AUTHOR]

Water evaporation is essential for various applications, including seawater desalination and evaporative cooling system. If the water evaporation rate becomes fast through water treatment technology, satisfactory efficiency can be achieved in these applications. In this study, the potential of enhancing water evaporation by combining dynamic and static treatment of magnetic field was explored. Water was firstly treated by dynamic treatment of the magnetic field. Then the treated water was exposed to the static magnetic field and its evaporation amount was measured. The effect of magnetic field strength on water evaporation was investigated. The surface tension of water was determined to explain the mechanism behind variation of water evaporation. Results show that the single dynamic magnetic treatment can promote the evaporation rate of water. The combination of dynamic and static magnetic treatment generates a synergistic effect and significantly improves the water evaporation, and a maximum enhancement of 14.3% is obtained in this study. The behind mechanism is magnetic field treatments decrease the surface tension of water and induce water molecule to escape from water to air interface easily. This study presents an effective and economical approach to improve water evaporation rate with simple operation and low energy consumption, and contributes to the high efficiency in applications involves water evaporation. [ABSTRACT FROM AUTHOR]

An on-site and fast synchronous measurement of coil constant and nonorthogonal angle, using an all-optical atomic magnetometer, was reported in this article. Based on the spectrum analysis of electron paramagnetic resonance of spin-polarized potassium under different magnetic fields, the measurement models of coil constant and nonorthogonal angle were established, according to which we experimentally obtained the weighted average results with related estimated uncertainties: the coil constants in the $x$ -, $y$ -, and $z$ -axes were (145.9 ± 0.3) nT/mA, (149.5 ± 0.3) nT/mA, and (129.6 ± 0.1) nT/mA, respectively; the nonorthogonal angles existing in the $x z$ and $y z$ axes were (0.11 ± 0.02)° and (0.23 ± 0.02)°, respectively. The determination results of the residual magnetic field in the $z$ -axis, with two comparative experiments, demonstrated the validity of this on-site synchronous measurement method. The present method can be easily used in calibrating coil constant and nonorthogonal angle for all-optical atomic magnetometers, especially for miniaturized ones. [ABSTRACT FROM AUTHOR]

The performance of a multilayer magnetic shield directly affects and limits the sensitivity improvement of an atomic magnetometer. To better meet the requirements of spin-exchange relaxation free atomic magnetometer for the environmental magnetic field, the magnetic shield should be optimized. At present, the optimizations have focused only on a single objective, such as the axial shielding factor. However, the importance of other goals should not be neglected. In this paper, multiobjective optimization of the shield is carried out to obtain a better comprehensive performance. First, according to the structural characteristics of the multilayer shield, a multiobjective optimization model is established. Then, a multiobjective genetic algorithm is utilized to optimize the shield. After optimization, a Pareto optimal solution set is obtained. Furthermore, depending on the desired design requirements, two sets of optimal combinations of target values and variable parameters are selected, based on the fuzzy comprehensive evaluation method and the lowest magnetic noise. This method can obtain a balance between different optimization objectives and effectively improve the comprehensive performance of the shield. [ABSTRACT FROM AUTHOR]

This paper has studied the barium spectra in external magnetic and electric fields on the recently-built system based on a super-conducting solenoid with high stability of better than 1 Gauss. Firstly, we compared the spectra in a high pure magnetic field of B = 4.00000 T for different polarized laser, s+ and s-. We prove that after a proper shift, the s+ and s- spectra are completely identical. We also investigated the dependence of the spectral feature in the high magnetic field on an additionally applied crossing electric field. Along with the increase of the electric field, there is an energy shift for every spectral line. Based on a transformative Hamiltonian, we explained this energy shift well. [ABSTRACT FROM AUTHOR]

With time-of-flight and electric field ionization detection technique, we investigate the motional Stark effect for highly excited Rydberg barium in high magnetic field and its active cancellation experimentally. In the experiment, the atom beam is aligned at a small angle of 15deg with respect to the magnetic field. The motional Stark effect cancellation is demonstrated on two sets of circularly polarized spectra in static magnetic field B = 1.00000 Tesla and B = 1.70000 Tesla, respectively, although the effect is very small (~3.5 Vcm[?]1) in our apparatus configuration. [ABSTRACT FROM AUTHOR]

Electrical heating elements, which are widely used to heat the vapor cell of ultrasensitive atomic magnetometers, inevitably produce a magnetic field interference. In this paper, we propose a novel measurement method of the amplitude of electrical-heating-induced magnetic field for an atomic magnetometer. In contrast to conventional methods, this method can be implemented in the atomic magnetometer itself without the need for extra magnetometers. It can distinguish between different sources of magnetic fields sensed by the atomic magnetometer, and measure the three-axis components of the magnetic field generated by the electrical heater and the temperature sensor. The experimental results demonstrate that the measurement uncertainty of the heater's magnetic field is less than 0.2 nT along the x-axis, 1.0 nT along the y-axis, and 0.4 nT along the z-axis. The measurement uncertainty of the temperature sensor's magnetic field is less than 0.02 nT along all three axes. This method has the advantage of measuring the in-situ magnetic field, so it is especially suitable for miniaturized and chip-scale atomic magnetometers, where the cell is extremely small and in close proximity to the heater and the temperature sensor. [ABSTRACT FROM AUTHOR]

The atomic number densities of 87Rb vapor and surrounding gas 3He in a sealed cubic cell were measured by sweeping the absorption line and fitting the experimental data with a Lorentzian profile. The absorption was carried out around the D1 transition at different temperatures. We compare our results for the number density for 87Rb with the previous methods and calculate the fractional error to be less than 5% as well as the error for 3He between this work and the density obtained from the filling procedure to be no more than 4.2% at 370K. In addition, we discuss the factors that contribute to the error, among which the cell temperature plays the most important role. [ABSTRACT FROM AUTHOR]

In the spin-exchange relaxation-free (SERF) comagnetometer, the atomic polarization gradient caused by light absorption can cause significant but unexpected nuclear spin transverse relaxation, which affects the system's accuracy and sensitivity. This paper proposes the SERF comagnetometer configuration based on optical compensation to suppress polarization gradient in the vapor cell. The influence of polarization gradient on the system's magnetic field suppression ability is analyzed by the state-space method. In addition, the atomic polarization distribution simulation and the performance testing between the traditional SERF comagnetometer and the proposed configuration are conducted. Compared to traditional configuration, the polarization gradient relaxation of the proposed configuration is effectively suppressed by 62%, the magnetic field suppression ability of the system is improved by 51%, and the rotation sensitivity is increased by 25.4%. This work investigates the influence of polarization gradient on system characteristics and proposes a comagnetometer configuration to suppress polarization gradient, enhancing the system's magnetic field suppression ability and improving sensitivity. The demonstration of the polarization gradient suppression method is of significance for improving the performance of other inertial measurement devices such as nuclear magnetic resonance gyroscopes. [Display omitted] • A uniform atomic comagnetometer based on optical compensation is proposed. • The influence of polarization gradient on the system is analyzed. • The atomic spatial distribution model of the proposed configuration is established. • The polarization gradient relaxation is suppressed by 62%. • A rapid polarization confirmation method is proposed for performance comparison. [ABSTRACT FROM AUTHOR]

Spin Exchange Relaxation-Free Co-Magnetometer (SERFCM) possesses ultra-sensitive rotation measurement capabilities, offering broad application prospects in inertial navigation and fundamental physics research. Precision of SERFCM in rotation measurements is directly influenced by its ability to suppress magnetic noise. In this study, a state-space method is used to establish a SERFCM response model, considering the effect of pump light wavelength. An analysis is conducted to assess the effect of pump light wavelength detuning on the ability to suppress magnetic noise of SERFCM. Theoretical results indicate that detuned pump light wavelength can effectively reduce the magnetic field gradient generated by atomic polarization, thereby improving overall system performance. Experimental validation demonstrates that a slight detuning of the pump light wavelength results in a 21% improvement in the ability to suppress low-frequency magnetic fields. [Display omitted] • Establish a SERFCM response model considering the effect of pump light wavelength. • Effect of pump light wavelength on magnetic field gradient is analyzed and proved. • The low-frequency magnetic field suppression ability improves by 21%. [ABSTRACT FROM AUTHOR]

Magnetic field gradients affect the signal-to-noise ratio of the spin-exchange relaxation-free gyroscopes (SERFG), thereby affecting sensitivity and long-term stability. A novel method to in situ measure, decouple and suppress the effect of magnetic field gradient on relaxation rate of SERFG is studied. The total magnetic field gradient is in situ measured by fitting the relationship between magnetic field gradient (applied by magnetic field coil) and relaxation rate method, and the effects of magnetic field gradients generated by electron spin polarization and those generated by inhomogeneous distribution of the residual magnetic field on the relaxation rate of SERFG are separated by turning the pump light on and off. The experimental study demonstrates that the magnetic field gradient in the atomic vapor cell is compensated by a self-developed magnetic field gradient coil to reduce the effect on the nucleon spin relaxation rate, and that the sensitivity and bias instability of SERFG are improved due to the in situ measurement, decoupling and compensation of the magnetic field gradient. This study lays the path for effectively improving the performance index and practical application potential of SERFG. [Display omitted] • The experimental demonstrates that the magnetic field gradient is compensated by coils to reduce the effect on the nucleon spin relaxation rate • Our experiments show that the shorter the time to pump the laser through the atomic vapor cell, the closer the measured T 2 is to T 1 • The measurement, decoupling and suppression methods have the potential to be applied to other atomic sensors. [ABSTRACT FROM AUTHOR]

Magnetic field interference poses a major challenge to the proper functioning of electronic equipment, electronic instruments and ultra-sensitive sensors, so magnetic field shield is a vital component. Particularly for ultra-sensitive atomic sensors, there is a pressing need for magnetic shields with superior performance and reduced magnetic noise. This paper introduces the application of nanocrystalline alloy magnetic shields in ultra-sensitive atomic sensors. We have analyzed the calculation of the longitudinal and transverse magnetic noise of nanocrystalline magnetic shields using a loss separation based approach and establish a magnetic noise model for nanocrystalline alloy magnetic shields. Meanwhile, we investigate the impact of structural parameters on longitudinal and transverse magnetic noise to effectively minimize magnetic noise in the shield. Additionally, we present an error model for magnetic noise, providing valuable theoretical support for mitigating magnetic noise errors in K-Rb- 21 Ne SERF co-magnetometers. This study contributes to the advancement of magnetic shield technology for ultra-sensitive atomic sensors, improving their overall performance and accuracy. • Innovative application of nanocrystals in high-precision atomic sensors as low noise magnetic shielding. • A noise model of nanocrystalline magnetic shielding was established and analyzed, and it was determined that hysteresis loss dominates at 100 Hz, especially at around 1 Hz, which is much greater than other losses. • The longitudinal and transverse magnetic noise effects of cylindrical nanocrystalline shield parameters with different thickness, aspect ratio and aperture diameter were also analyzed using FEM. • We present an error model for magnetic noise, providing valuable theoretical support for mitigating magnetic noise errors in K-Rb-21Ne SERF co-magnetometers. • This study provides a new research direction for reducing system magnetic noise and miniaturization in the future. Under the same noise level, the volume of nanocrystals is much smaller than that of ferrite. [ABSTRACT FROM AUTHOR]

[Display omitted] • A novel method for simultaneous measurement of spin polarizability of Rb atoms and 21Ne atoms in the spin-exchange relaxation-free (SERF) co-magnetometer. • The method is based on the frequency response model of K-Rb-21Ne spin strongly coupled ensemble. • Measurements have little influence on the atomic ensemble compared with the traditional method. • The method is more accurate, stabilized and faster than previous methods. • In the presence of interference input rotation and magnetic fields, this method is more suitable for measuring the spin polarizability of atomic ensemble. Accurate and fast measurement of the spin polarizability of alkali-metal and noble-gas atoms in co-magnetometer is essential to improve the sensitivity of ultra-sensitive inertial measurements. We establish a frequency response model of K-Rb-21Ne spin strongly coupled ensembles, based on this we present a method for simultaneously measuring the spin polarization of 21Ne and Rb atoms. By applying magnetic field in y -direction oscillating at a fixed frequency, the z -axis main magnetic field value is changed linearly at the same time, the polarizability of Rb and 21Ne spins can be simultaneously obtained. The experimental results were highly consistent with analytical results. By applying a gradient magnetic field to amplify the effect of atomics depolarization, the self-compensating magnetic field points and atomic ensemble polarizability were measured three times continuously using our method and another method. The results proved that this method has fast measurement speed, high accuracy, and low influence on spin polarisation. [ABSTRACT FROM AUTHOR]

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. • A novel measurement of spin-exchange relaxation applicable in earth-scale field. • The transverse and longitudinal relaxation can be synchronously extracted. • Provide a way to evaluate the effect of spin-exchange relaxation suppression method. [ABSTRACT FROM AUTHOR]

A novel strategy for designing uniform magnetic field and gradient magnetic field coils considering the boundary effect of magnetic shielding is proposed in this study. This strategy uses intelligent optimization algorithm to skillfully transform the complex coil design problem into the spatial optimization problem of individual population. The mirror method is combined with Green's function to accurately calculate the magnetic field, and the target field method (TFM) is combined with the whale optimization algorithm to optimize the stream functions using adaptive ridge regression. The minimum fitness function is defined as the real-time magnetic field relative error, and the optimal ridge coefficient is continuously obtained by determining the current density coefficient. The proposed method significantly reduces the magnetic field deviation in the target area compared to the conventional TFM, with reductions ranging from 12.2 % to 0.11 % (B x coil), 0.3 % to 0.02 % (B z coil), 20 % to 10 % (d B x / d z coil) and 2.9 % to 2.4 % (d B z / d z coil). The strategy has been effectively validated by analytical simulations and experimental results, and is expected to be applied to the design of uniform field coils and gradient coils for ultra-high precision atomic sensors. [Display omitted] • The coupling problem between the magnetic shielding system and the designed magnetic field coil is greatly reduced. • This method determines the fitness evaluation function according to the real-time actual current density. • The magnetic field coil designed by the hybrid optimization method proposed in this paper reduces the magnetic field deviation by nearly one to two orders of magnitude compared to the conventional TFM. • The proposed method significantly reduces the magnetic field deviation in the target area compared to the conventional TFM. [ABSTRACT FROM AUTHOR]

The magnetic field performance of the uniform coils will be affected by magnetic shields and produce errors in the atomic magnetometer. It is necessary to analyze the influencing factors and guide the coil design. Aiming at the above shortcomings, this paper analyzes the coupling effect of magnetic shield and coil and proposed a Lee-Whiting coil design method based on the linearly decreasing inertia weight particle swarm optimization (LDW-PSO) algorithm. Firstly, the magnetic field model under the ferromagnetic boundary is established, and the effects of the size, thickness and permeability of the magnetic shield on the magnitude and uniformity of the Lee-Whiting coil magnetic field are analyzed. The results show that the coupling coefficient of the coil changes monotonically with the change of the size of the magnetic shield, while the uniformity error has a minimum value with the change of the size of the shield. In addition, an improved Lee-Whiting coil is designed by combining the LDW-PSO algorithm, which improves the uniformity of the coil. Compared with the original coil, the measured uniformity error of the improved coil is reduced from 8. 39 × 1 0 − 4 to 2. 81 × 1 0 − 4 . The accuracy of the theoretical analysis is verified by experiments. This paper is of great significance to study the coupling and optimization design of the coil based on the magnetic shields in atomic magnetometers. [Display omitted] • The influence of magnetic shield parameters on coil uniformity is analyzed. • The optimal coil size for the uniformity in magnetic shield is given by analysis and testing. • The improved Lee-Whiting coil is designed by intelligent optimization algorithm. • Improved Lee-Whiting coil overcomes the coupling effect between coil and magnetic shield. • The correctness of the analysis and the effectiveness of the design are proved by experiments. [ABSTRACT FROM AUTHOR]

Spin-exchange relaxation-free (SERF) co-magnetometer is expected to be a high-precision gyroscope, but the slow response speed severely restricts its practicality. In this paper, a transient response analysis is proposed to give comprehensively quantify the dynamic characteristic of the SERF co-magnetometer. A compensation magnetic field configuration is proposed for the fastest response speed the system can achieve. The results show that the system gets the fastest response speed at the dynamic compensation point we proposed and the response speed of the system at that point is 19.36 times faster than that at the traditional magnetic compensation point. In addition, derived from experimental data, the spin-exchange relaxation induced by magnetic fields is observed and quantified, which decreases the sensitivity of inertia and magnetic measurement. This research supports improving the response speed of SERF co-magnetometer and expanding its application range, such as platform inertial navigation systems. • Transient response analysis based on system's eigenvalues is proposed to describe the coupling dynamic in electron-nuclear spin regime and measure the Spin-Exchange relaxation. • Dynamic compensation point is analyzed comprehensively which has the fastest system response. [ABSTRACT FROM AUTHOR]