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Stochastic magnetic field noise has a non‐negligible negative impact on the performance of quantum precision measurement instruments such as spin‐exchange relaxation‐free (SERF) co‐magnetometer in terms of sensitivity and stability. Conventional magnetic field error analysis and suppression methods are not applicable to stochastic magnetic field noise. In this paper, a stochastic model of the SERF co‐magnetometer is proposed to analyze the mechanism of stochastic magnetic field noise. The mean and covariance propagation model of the SERF co‐magnetometer is given based on the stochasticity model and statistical principles. The analysis of simulation experiments reveals that reducing the longitudinal electron spin polarization can somewhat reduce the standard deviation of the system output caused by stochastic magnetic field noise. And the atomic ensembles are most resistant to stochastic magnetic field noise when the electron spin polarization strongly couples with the nuclear spin polarization. Finally, the experiments verified the above conclusions. In conclusion, this paper provides theoretical and experimental support for analyzing and suppressing the effect of stochastic magnetic field noise on the SERF co‐magnetometer, which is of great significance for improving the sensitivity and stability of the measurement. [ABSTRACT FROM AUTHOR]

With the widespread use of magneto-sensitive elements, magnetic shields are an important part of electronic equipment, ultra-sensitive atomic sensors, and in basic physics experiments. Particularly in Spin-exchange relaxation-free (SERF) co-magnetometers, the magnetic shield is an important component for maintaining the SERF state. However, the inherent noise of magnetic shield materials is an important factor limiting the measurement sensitivity and accuracy of SERF co-magnetometers. In this paper, both amorphous and nanocrystalline materials were designed and applied as the innermost magnetic shield of an SERF co-magnetometer. Magnetic noise characteristics of different amorphous and nanocrystalline materials used as the internal magnetic shielding layer of the magnetic shielding system were analyzed. In addition, the effects on magnetic noise due to adding aluminum to amorphous and nanocrystalline materials were studied. The experimental results show that compared with an amorphous material, a nanocrystalline material as the inner magnetic shield layer can effectively reduce the magnetic noise and improve the sensitivity and precision of the rotation measurement. Nanocrystalline material is very promising for inner shield composition in SERF co-magnetometers. Furthermore, its ultra-thin structure and low cost have significant application value in the miniaturization of SERF co-magnetometers. [ABSTRACT FROM AUTHOR]

The ferrite magnetic shield is widely used in ultra-high-sensitivity atomic sensors because of its low noise characteristics. However, its noise level varies with temperature and affects the performance of the spin-exchange relaxation-free (SERF) co-magnetometer. Therefore, it is necessary to analyze and suppress the thermal magnetic noise. In this paper, the thermal magnetic noise model of a ferrite magnetic shield is established, and the thermal magnetic noise of ferrite is calculated more accurately by testing the low-frequency complex permeability at different temperatures. A temperature suppression method based on the improved heat dissipation efficiency of the ferrite magnetic shield is also proposed. The magnetic noise of the ferrite is reduced by 46.7%. The experiment is basically consistent with the theory. The sensitivity of the co-magnetometer is decreased significantly, from 1.21 × 10 − 5 ° /s/Hz 1 / 2 to 7.02 × 10 − 6 ° /s/Hz 1 / 2 at 1 Hz. The experimental results demonstrate the effectiveness of the proposed method. In addition, the study is also helpful for evaluating the thermal magnetic noise of other materials. [ABSTRACT FROM AUTHOR]

This study proposes a high-performance magnetic shielding structure composed of MnZn ferrite and mu-metal film. The use of the mu-metal film with a high magnetic permeability restrains the decrease in the magnetic shielding coefficient caused by the magnetic leakage between the gap of magnetic annuli. The 0.1–0.5 mm thickness of mu-metal film prevents the increase of magnetic noise of composite structure. The finite element simulation results show that the magnetic shielding coefficient and magnetic noise are almost unchanged with the increase in the gap width. Compared with conventional ferrite magnetic shields with multiple annuli structures under the gap width of 0.5 mm, the radial shielding coefficient increases by 13.2%, and the magnetic noise decreases by 21%. The axial shielding coefficient increases by 22.3 times. Experiments verify the simulation results of the shielding coefficient of the combined magnetic shield. The shielding coefficient of the combined magnetic shield is 16.5%. It is 91.3% higher than the conventional ferrite magnetic shield. The main difference is observed between the actual and simulated relative permeability of mu-metal films. The combined magnetic shielding proposed in this study is of great significance to further promote the performance of atomic sensors sensitive to magnetic field. [ABSTRACT FROM AUTHOR]

Cylindrical ferrite shields consisting of multiple annuli can provide low-magnetic-noise environments. However, the gaps between different parts of the shield adversely affect the shielding performance. In this study, we numerically study the influence of the gaps on both the axial and radial magnetic noise of the multi-annular ferrite shield with different gap widths, permeabilities, and aspect ratios using the generalized Nyquist relation and the finite element method. Our study indicates that as the gap width increases, the axial magnetic noise decreases, while the radial magnetic noise increases. For the shield with a gap width of 0.10 mm and an aspect ratio of one in our study, the axial magnetic noise decreases by 5.2%, and the radial magnetic noise increases by 8.3%–33.5%. The difference in the increase is related to the permeability, and gaps have smaller effect on the radial magnetic noise of the shield with lower permeabilities. Therefore, compared with the no-gap shield, the multi-annular ferrite shield can provide an even better low-magnetic-noise environment along the axial direction. Although the gaps can induce an increase of the radial magnetic noise, this detrimental effect can be suppressed significantly by using a ferrite material with lower permeability and reducing the gap width. Our findings can aid in the application and optimization of low-noise ferrite shields. [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]

Spin-exchange relaxation-free (SERF) co-magnetometer is considered to be a promising nuclear spin gyroscope due to its ultrahigh rotation measurement sensitivity and magnetic field disturbance cancellation ability. Recent experiments indicate that the relaxation of the noble-gas spins would result in reduction of the magnetic field disturbance cancellation ability, which means that magnetic noise from the passive magnetic shield in a SERF co-magnetometer can cause rotation rate measurement error. In this paper, the magnetic field frequency response of a SERF atomic magnetometer is derived based on state space method and the magnetic noise of different shield materials are measured. The magnetic noise error model in a SERF co-magnetometer is then derived and the magnetic noise induced rotation rate measurement error is quantitatively evaluated. The superiority of ferrite shield is shown by the performance of a K-Rb-21Ne co-magnetometer. Experimental results show that ferrite shield with lower magnetic noise and better temperature stability is a more favorable choice for the inner shield of the co-magnetometer. [ABSTRACT FROM AUTHOR]

A set of five-layer cylindrical magnetic shields is designed and constructed to attenuate external geomagnetic field to less than 10 nT (ideally zero). We aim to achieve a shield design having high shielding factor, low magnetic noise, and small volume. However, magnetic noise is incompatible with shielding factor and volume. Thus, there is a compromise. This paper presents an optimization method to acquire a sufficiently effective, low-noise, and lightweight multi-layer shield. The optimization objective and constraints are provided in the form of analytic expressions. The mathematical model is constructed in MATLAB. The optimization is executed in iSIGHT software integrated MATLAB. By optimizing the nonlinear programming quadratic line (NLPQL) algorithm, theoretically the axial shielding factor ${\sf\textit {S}}_{\text {tot}}^{\sf\textit {A}}$ can be increased by a factor of about 390.3, on the premise that the magnetic noise and volume have increased negligibly. Apart from better shielding performance, a combination of optimum parameters is obtained. This optimization method has good universality. As long as certain shielding requirements are determined, the corresponding optimum parameters can be acquired accurately. This method is of great significance for future improvements to shield design. [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]

Spin-exchange relaxation-free gyroscope (SERFG) is a promising rotation sensor, and the bias error is one of its most important characteristics. It is identified that rotation measurement noise induced by thermal magnetization fluctuations inherent in the ferrite shield in a SERFG limits its bias stability. The root cause of this error lies in the low-frequency magnetic field sensitivity dominated by the nuclear spin relaxation rate. In this paper, the steady state response model of the SERFG is modified considering the non-negligible nuclear relaxation rate and the pressure-dependent magnetic field sensitivity is experimentally studied. Our results show that reducing nuclear spin relaxation is an effective method to suppress the bias error induced by thermal magnetization fluctuations. Finally, in case of $Pneon=1$ atm, it is estimated that a bias stability limit of $5 \times {10^{ - 4}}$ deg/h is set by the lowest thermal magnetization noise of $4.4f^{-1/2}\,\,{\text {fT}} $ ever reported in a ferrite shield. [ABSTRACT FROM AUTHOR]

The light shift is an important error source for atomic magnetometers. It would vanish if the frequency of the circularly polarized light is tuned to the optical resonance center. For high-density alkali-metal atomic magnetometers, the vapor cell has a large optical depth near the resonance, resulting in the difficulty in obtaining the exact resonance center by measuring the optical absorption line. In order to solve this problem, we propose a method to tune the pump light to a frequency where the shift is minimum based on the magnetic field zeroing technique. In addition, we also compare our results with the fitting center of the optical absorption line based on the measurement data far detuned from the resonance. The experimental results show that our method achieves a better suppression result of the light shift. [ABSTRACT FROM AUTHOR]

This paper aims to review the technology, developments, and applications of spin exchange relaxation free (SERF) atomic magnetometers. The generalized comparisons between the SERF magnetometer and the other types of weak magnetic sensors are elaborated. Further, the fundamental composition and operational principle of the SERF atomic magnetometer are elucidated. The development history and recent technological developments with respect to several aspects, including the alkali metal vapor source, atom heating method, pump and probe lasers, and magnetic shielding system, are presented. The classification and respective advantages and disadvantages of these technologies are described in detail. Finally, the existing and potential applications, as well as the prospective future development trends are presented. [ABSTRACT FROM AUTHOR]

Many sensitive atomic devices require magnetic shield to reduce external magnetic field interference. Mn–Zn ferrites are optimistic candidates for shielding because they provide a high shielding factor and a low magnetic noise. This study evaluated the magnetic noise of Mn–Zn ferrite magnetic shield based on its grain size. The morphologies of Mn–Zn ferrite samples were characterized to establish a correlation between their grain sizes and magnetic permeability, which can be used to calculate magnetic noises. The correlation was then used to evaluate the shielding performance of another Mn–Zn ferrite, where the magnetic noise of the magnetic shield made from the ferrite was calculated to be 2.53 f −1/2fT. The magnetic noise of the magnetic shield was also measured experimentally using a spin-exchange relaxation-free atomic magnetometer. The measured magnetic noise of ferrite shield was 2.61 f −1/2fT, while the white noise of the atomic magnetometer was 0.71 fT/Hz1/2 below 100 Hz. The consistency between the experimental results and predicted values suggests the viability of the proposed approach, providing a convenient, efficient, and precise method for developing ferrite ceramics materials for low-noise magnetic shields. [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 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 in-situ method to measure complex magnetic permeability (CMP) based on the magnetic shielding mechanism is presented. • By measuring the magnetic field at the center of shielding, the effective CMP of a large dimensional ferrite shielding can be determined. • The addition of Co significantly improved the thermal stability of CMP by 6.62 times and reduce the magnetic noise. • This method ensures a real-time observation of CMP and magnetic noise under different temperatures. Magnetic shielding made of low noise ferrite materials is used in many ultra-sensitive measurements. The complex magnetic permeability (CMP) of ferrites directly affects the magnetic shielding performance, so the measurement of CMP is particularly important. Conventional measurements omit the effects of temperature on ferrites' magnetic properties and can only measure samples with specific shapes. Here a novel measurement method of CMP based on the magnetic shielding mechanism is presented. By in-situ measuring the magnetic field, the effective CMP of large dimensional ferrite shielding can be determined. Also, the intrinsic magnetic noise of a MnZn ferrite shielding was observed using the proposed method. Using the finite elements method (FEM), we identified the influencing factors of air gap in the CMP measurements. We also analyzed the influence of element doping on the thermal stability of CMP. This study ensures a real-time observation of CMP and magnetic noise under different temperatures. [ABSTRACT FROM AUTHOR]

Spin-exchange relaxation-free (SERF) co-magnetometer presents promising applications in both inertial navigation and basic physical experiments because of its ultrahigh rotation measurement sensitivity and magnetic field disturbance cancellation capacity. Magnetic shielding system is an essential part of the co-magnetometer, and the intrinsic magnetic noise of shielding material is one of the main factors limiting the sensitivity of co-magnetometer. This paper presents a low-noise nanocrystalline magnetic shield for SERF co-magnetometer. The transfer function model of SERF co-magnetometer to transverse magnetic noise was established based on Bloch equation. The amplitude and frequency band of the co-magnetometer signal noise caused by transverse magnetic noise were quantitatively obtained, and the magnetic noise characteristics of nanocrystalline and other shielding materials were analyzed by theoretical calculation and experimental measurement in the obtained frequency band. The superiority of nanocrystalline in low magnetic noise was verified. Experimental results show that the signal noise and bias instability of the SERF co-magnetometer can be considerably decreased by using the nanocrystalline shield as the inner shield. [Display omitted] • A low-noise nanocrystalline shield for atomic co-magnetometer is proposed. • The transfer function model of the co-magnetometer to biaxial magnetic noise is established based on Bloch equation. • The advantages of nanocrystalline shield in magnetic noise characteristics are confirmed. • The signal noise and bias instability of the co-magnetometer are significantly reduced. [ABSTRACT FROM AUTHOR]