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Magnetic field shields are important for electronic equipment, ultrahigh-sensitivity sensors, and electrical instruments. For ultrahigh-sensitivity atomic sensors, in particular, ferrite shields with low intrinsic magnetic noise are widely used. In this article, the calculation methods of longitudinal and transverse magnetic noise, which are calculated by loss, are analyzed. The experimental results confirm the feasibility of the model. Using the loss separation method, it is proved that the loss of ferrite magnetic shielding is mainly hysteresis loss, which is below 100 Hz. To effectively reduce the magnetic noise, we analyze the effect of structure parameters on the longitudinal and transverse magnetic noise, and the optimized parameters are obtained. The results show that the longitudinal magnetic noise decreases with the increasing aspect ratio and stabilize eventually. When the aspect ratio exceeds 1, the transverse magnetic noise remains practically unchanged. When the external diameter is fixed, by optimizing the thickness of the magnetic shield, the optimal solution for the longitudinal and transverse magnetic noise is obtained.

A novel method to determine the spin polarization and its distribution for a spin-exchange relaxation-free (SERF) atomic magnetometer are proposed in this paper. The Larmor precession frequency is measured using the fast Fourier transform (FFT) analysis result of the transient response of the magnetometer under the excitation of a series of the step-changed magnetic field. The spin polarization is extracted from the slow-down factor of the precession frequency. The variation of the spin polarization with different pump light intensities and the distribution of the spin polarization along the direction of the pump light are analyzed, and the experimental results are well consistent with the theoretical predictions. The expanded uncertainties of the experimental results vary from 2% to 11% with the increase of the spin polarization and the reason for this variation is analyzed. The advantage of this method is that it allows the accurate measurement of the spin polarization in the pump beam direction within the SERF regime operating state, and it is unaffected by the large optical depth of the vapor cell.

Ferrites are promising nonmetallic materials used for the fabrication of low-noise magnetic shields because they possess high permeability and high electrical resistivity. However, large-sized ferrite components are difficult to fabricate or machine. In this study, we develop a cylindrical ferrite shield that consists of five annuli and two lids with an inner volume of φ11.2 cm × 22.5 cm. Although this structure contains gaps between different components, it eases considerably the fabrication and machining process as compared to the entire module. The magnetic noise is measured by a spin-exchange relaxation-free atomic magnetometer, and the detrimental effects of the gaps are analyzed quantificationally using the finite element method. Our research results indicate that compared with the ferrite shield without gaps, the magnetization noise increases by 34.1%. Nonetheless, the magnetic noise at the center of the ferrite shield achieves 5.5f -1/2 fT, which is much lower than that of μ-metal shields with a similar size. If the gap width can be reduced to be smaller than 0.01 mm, the increase of the magnetization noise will be less than 4.9%, which can be negligible in practical applications. Our study provides a low-cost, readily available, and low-noise ferrite shield structure.

The magnetic field gradient within optical pumping magnetometers (OPMs) suppresses sensitivity improvement. We investigated the effects of the magnetic field gradient along the x-, y-, and z-axes on the limiting factors of magnetometers under extremely low magnetic field conditions. We modified the magnetic field gradient relaxation model such that it can be applied to atoms in the spin exchange relaxation free (SERF) regime. The gradient relaxation time and spin polarizations, combined with fast spin-exchange interaction, were determined simultaneously using the oscillating cosine magnetic field excitation and amplitude spectrum analysis method. During the experiments, we eliminated the errors caused by the temperature and pumping power, and considered different isotope spin exchange collisions in naturally abundant Rb during the data analysis to improve the fitting accuracy. The experimental results agreed well with those of theoretical calculations and confirmed the accuracy of the improved model. The contribution of the transverse magnetic field gradient to the relaxation of the magnetic field gradient cannot be ignored in the case of small static magnetic fields. Our study provides a theoretical and experimental basis for eliminating magnetic gradient relaxation in atomic sensors in the SERF region.

The magnetic noise generated by the ferrite magnetic shield affects the performance of ultra-sensitive atomic sensors. Differential measurement can effectively suppress the influence of common-mode (CM) magnetic noise, but the limit of suppression capability is not clear at present. In this paper, a finite element analysis model using power loss to calculate differential-mode (DM) magnetic noise under a ferrite magnetic shield is proposed. The experimental results confirm the feasibility of the model. An ultrahigh-sensitive magnetometer was built, the single channel magnetic noise measured and the differential-mode (DM) magnetic noise are 0.70 fT/Hz1/2 and 0.10 fT/Hz1/2 @30 Hz. The DM magnetic noise calculated by the proposed model is less than 5% different from the actual measured value. To effectively reduce DM magnetic noise, we analyze and optimize the structure parameters of the shield on the DM magnetic noise. When the outer diameter is fixed, the model is used to analyze the influence of the ratio of ferrite magnetic shielding thickness to outer diameter, the ratio of length to outer diameter, and the air gap between magnetic annuli on DM magnetic noise. The results show that the axial DM magnetic noise and radial DM magnetic noise reach the optimal values when the thickness to outer diameter ratio is 0.08 and 0.1. The ratio of length to outer diameter is negatively correlated with DM magnetic noise, and the air gap (0.1–1 mm) is independent of DM magnetic noise. The axial DM magnetic noise is less than that of radial DM magnetic noise. These results are useful for suppressing magnetic noise and breaking through the sensitivity of the magnetometer.

The existence of an approximately uniform and unsaturated electron spin polarization distribution within a high-density alkali-metal vapor is considered of great importance for significantly improving the response amplitude and sensitivity properties of an atomic magnetometer. However, when a high-density alkali-metal vapor is formed, the optical depth is much larger than the value of one, resulting in the electron spin polarization gradient. In this work, it was demonstrated from both numerical simulations and experimental points of view, that by replacing the resonant pumping light with two off-resonant pumping light sources, the signal amplitude of the magnetometer can be doubled. By using this approach, the electron spin polarization gradient can be significantly suppressed and the sensitivity can be improved by more than 10%. The proposed scheme is generally applicable to various optical pumping high-density alkali-metal vapor systems, where a uniform electron spin polarization distribution is required, such as optical pumping co-magnetometers and atomic gyroscopes.

Rb optically pumped magnetometer (OPM) based on electron paramagnetic resonance (EPR) show advantages to measure the nuclear magnetization and have succeeded in fundamental physics and rotation sensing, etc. The magnetometry sensitivity is a key performance of these Rb OPMs which should be improved. In this study, a high sensitivity Rb OPM is demonstrated theoretically and experimentally. To improve the sensitivity, acousto-optic modulation based on balanced detection is applied to suppress the probe noises. Compared with the conventional optical rotation detection for this OPM configuration, the probe noise shows a significant suppression especially in low frequencies. Eventually, a simultaneous dual-axis transverse measurement with 30 fT/Hz1/2 sensitivity is achieved in a 200 Hz bandwidth and a 250nT linear working range. In addition, we utilize a closed-loop feedback to improve the stability and enlarge the transverse measurement range to 10µT order of magnitude while maintain the open-loop performances. A quasi-static magnetic field measurement can also be achieved in the longitudinal direction in the closed-loop mode. This OPM can serve for the nuclear magnetization measurement with a high sensitivity especially in environments with a large magnitude of the external magnetic field.

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.

A stable magnetic field environment is one of the key factors to realize the ultrasensitive magnetic field detection. Ferrite materials, which possess both high electrical resistivity and high permeability, are ideal magnetic shielding materials. Gaps and holes usually exist in the large size magnetic shield which effects shielding effectiveness. In this paper, the variation of the DC magnetic shielding ratio, for different gaps and access hole dimensions, is quantificationally investigated using the finite element method. The shielding ratio in the simulation is close to the theoretical calculation for the closed shield when the thickness of gaps is very small. Our study indicates that gaps and holes separately reduced the shielding effectiveness, and the coexistence of gaps and holes aggravated the reduction of shielding effectiveness. Compared with the shielding ratio of the ferrite enclosure without gaps and holes for the known size shield, the transverse and longitudinal direction of the shielding ratio increase by 9% and 274% with gaps (thickness = 0.1 mm) and holes (diameter = 25 mm), respectively. The simulation results are partially verified with experimentally using a cylindrical ferrite shield made of Zn0.17Mn0.74Fe2.06O4 and Zn0.33Mn0.58Fe2.06O4. The difference between the experimental and simulation results is less than 10%.

We propose an in-situ method to calibrate the coil constants of the optical atomic magnetometer. This method is based on measuring the Larmor precession of spin polarized alkali metal atoms and has been demonstrated on a K-Rb hybrid atomic magnetometer. Oscillation fields of different frequencies are swept on the transverse coil. By extracting the resonance frequency through phase-frequency analysis of electron spin projection, the coil constants are calibrated to be 323.1 ± 0.28 nT/mA, 108 ± 0.04 nT/Ma, and 185.8 ± 1.03 nT/mA along the X, Y, and Z directions, respectively.

In this study, we demonstrate a non-modulated triaxial magnetic field compensation method for spin-exchange relaxation-free (SERF) atomic magnetometers. We realize simultaneous compensation of the magnetic field along the pump and probe directions by maximizing the first order differential value of the zero-field resonance signal. The magnetic field perpendicular to the pump-probe plane is compensated by zeroing the DC response of the magnetometer. The zero-field resonance is obtained by applying a linearly changed magnetic field along the direction perpendicular to that of the pump-probe plane. The first order differential of the zero-field resonance is acquired using the second order central difference method in real time. Compared with the conventional compensation methods, this method does not involve modulation and demodulation. Therefore, it requires no lock-in amplifier, thus making it more applicable in miniature atomic devices. Moreover, this method compensates the magnetic field along the pump and probe directions using only one criterion. It avoids the cross-talk effect between the pump and probe directions in the presence of non-orthogonal coils. The experiment results show that the compensation resolution is 9 pT, 7 pT and 0.05 pT for the probe, pump, and direction perpendicular to the pump-probe plane, respectively.

Ultra-sensitive multi-channel optically pumped atomic magnetometers based on the spin-exchange relaxation-free (SERF) effect are powerful tools for applications in the field of magnetic imaging. To simultaneously achieve ultra-high spatial resolution and ultra-high magnetic field sensitivity, we proposed a high-resolution multi-channel SERF atomic magnetometer for two-dimensional magnetic field measurements based on a digital micro-mirror device (DMD) as the spatial light modulator for a single vapor cell. Under the optimal experimental conditions obtained via spatial and temporal modulation of the probe light, we first demonstrated that the average sensitivity of the proposed 25-channel magnetometer was approximately 25fT/Hz1/2 with a spatial resolution of 216µm. Then, we measured the magnetic field distribution generated by a gradient coil and compared the experimentally obtained distributions with those calculated via finite element simulation. The obtained g value of 99.2% indicated good agreement between our experimental results and the theoretical calculations, thereby confirming that our proposed multi-channel SERF magnetometer was effective at measuring magnetic field distributions with an ultra-high spatial resolution.

This study proposes an approach to generate a uniform flat-top beam with a liquid crystal spatial light modulator (LC-SLM) to optimize ultrasensitive inertial measurement. The random incomplete Gaussian beam is modulated into a flat-top beam by uploading a beam shaping optimization algorithm on an LC-SLM. Simulation results verify the effectiveness of the proposed method. The beam obtained from the experimental results with the 4f filter system optimization also conforms to the properties of the generated flat-top beam. Compared to existing beam shaping algorithms for simulation and experimental analysis, the beam shaping design based on the LC-SLM to optimize the ultrasensitive inertial measurement is realized. This method has also been verified to be effective in beam shaping in various beam situations. The application of this method in ultrahigh-sensitivity inertial measurement should prove significant.

Triaxial uniform coils housed in magnetic shields are extensively used in atomic sensors. The coil constant can be affected by the magnetic shield that imposes a ferromagnetic boundary. This study numerically and experimentally analyzes the coil constant dependence on the Mn–Zn ferrite magnetic shield thickness, aspect ratio, air gaps between the magnetic annuli, and the distance from the coils. Results show that the radial coil constant (saddle-shaped coil) only depends upon the distance between the coil and the magnetic shield. The axial coil constant (Lee–Whiting coil) depends on the aspect ratio, distance between the coil and the magnetic shield, and air gap width between the magnetic annuli. The axial coil constant is linearly related to the air gap. When the thickness of the magnetic shield is greater than 2 mm, the radial and axial coil constants are independent of the shield thickness. The difference between the simulated and measured values is only 3.9%. The numerical calculation accuracy was verified by experimental measurements. This study can aid in the design and research of coils in the ferrite magnetic shield in atomic sensors.

In an optically pumped alkali vapor cell with a high density of atoms, the attenuation of the pump light generates a spatially non-uniform distribution of the electronic spin polarization of alkali atoms, which is detrimental to biomagnetism applications of magnetometers as well as the hyperpolarization of noble gas atoms. Therefore, in this study, we propose a new scheme to generate a nearly uniform, unsaturated spin polarization region based on counter-propagating pump beams and atomic diffusion. A finite element method-based simulation is used to demonstrate the three-dimensional distribution of the spin polarization in a spherical cell. The effects of cell temperature and pump light power on the homogeneity of the spin polarization are studied. The distribution of spin polarization near the center of the cell is experimentally measured and a 1 cm uniform spin polarization region is achieved in the center of the cell. The uniformity of spin polarization in the center region of the cell increased by 50% compared with single beam pumping. The advantage of our proposed scheme is that it can generate an unsaturated uniform region of spin polarization in the center of a cell using a single species of alkali atoms.

Mu-metal shields are widely used in atomic devices, but their magnetic noise related to loss is the key performance limit. The magnetic noise can be calculated by using complex permeability and the magnetic field intensity in the shield. In this study, Bertotti loss separation is used for the first time to accurately calculate the changes of complex permeability due to the hysteresis loss in different frequencies and magnetic field intensities, and we further consider the change in magnetic field intensity due to the induced eddy current, which also increases the accuracy of the magnetic noise calculation. For extremely low frequencies below 20 Hz, the improved noise simulation model differs from the measured results by less than 11%. If the loss separation is not considered, the difference between the measured value and the simulated value would be as high as 54%. The high agreement between the calculation and the experimental results proves the accuracy of the proposed method. Our method can be used in the design and optimization of low-noise magnetic shields to improve the sensitivity of atomic devices

The photoelastic modulator (PEM) is an optical modulation device which is widely used in optical detections. In this paper, we propose a high-precision and large-scale method for calibrating the peak retardations of PEM based on compound Bessel function. By applying compound Bessel function instead of the single Bessel function, the uncertainty of peak retardation calibration result decreases more than two times and the calibration scale expands nearly two times. Further, the second harmonic component is substituted for the DC component to reduce the random errors. In the experiment, a PEM is calibrated and the calibration result obtained for peak retardation is linear to the setting value in scale 0.15–2.5 rad. A dead zone appears in region 0 to 0.15 rad with value 0.233 rad. The experiment demonstrates that the relative uncertainty of peak retardation decreases from 2.5 % to less than 1 %.