Qian Cao

High-uniformity magnetic compensation coils are essential for establishing a near-zero and spatially stable magnetic-field environment in spin-exchange relaxation-free (SERF) atomic magnetometers. However, conventional Taylor-expansion-based coil objectives mainly suppress local high-order field terms near the centre and do not directly constrain the usable uniform-field length, regional field error or configuration repeatability. This paper presents a stable design method for circular magnetic compensation coils by combining a two-stage gated objective function with a gated multi-archive reliability-guided success-history adaptive differential evolution algorithm. The gated objective first enforces the basic central-field uniformity through a Taylor residual criterion and then optimizes the axial uniform-field length, root-mean-square relative error and geometric regularity. The optimization algorithm adaptively coordinates exploration and refinement using population-state gating, archive-assisted search and reliability-guided strategy selection. Finite-element simulations and prototype magnetic-field measurements are used to evaluate the designed coil. The results show that the proposed design achieves an effective uniform region of ±0.8R under a relative-uniformity threshold of 0.01, with a root-mean-square relative error on the order of 10−3. Repeated optimization tests further show that the gated objective reduces the axial uniform-region fluctuation by approximately one order of magnitude and the configuration dispersion by more than two orders of magnitude. The method provides a reproducible optimization route for compact high-uniformity compensation coils in weak magnetic-field measurement systems.

Weak measurement techniques have been extensively applied in the field of quantum precision measurement to detect ultra-small signals due to the amplification effect. In this work, we propose an optical detection system for a spin-exchange relaxation-free (SERF) magnetometer based on the inverse weak measurement (IWM) framework. By using the spatial pattern of a probe laser as the measurement pointer, we successfully detect ultra-weak magnetic fields. In our model, the spatial pattern of the probe laser is weakly coupled to its polarization, which is sensitive to external magnetic fields. Through post-selection on the optical polarization, the ultra-small magnetic field is significantly amplified with the amplification factor inversely proportional to the coupling strength, as reflected in the measured displacement of the final spatial pattern. By analyzing the response curve of the probe laser displacement to the magnetic field, we identify the point of maximum sensitivity, achieving a magnetic field sensitivity of 182.8 fT / Hz ^1/2 . Furthermore, in the IWM scheme, the detected signals depend only on the internal degrees of freedom of the probe laser, making the system robust against the fluctuations in laser power. To demonstrate this advantage, we compute the Allan standard deviation of the output signals for both conventional and IWM detection methods. The results indicate that the IWM-based method improves stability of detection by one to two orders of magnitude. This work presents, to our knowledge, a novel detection approach that integrates weak measurement techniques, offering a significant enhancement in the performance of SERF magnetometers.

Atomic magnetometers (AMs), recognized for their ultra-high magnetic sensitivity, demand highly uniform pump light fields to maximize measurement accuracy. In this paper, a phase modulation-based method using convolutional neural networks (CNN) and the Gerchberg–Saxton (GS) algorithm is proposed to generate the pumping light field, and the model was trained using a supervised learning approach with a custom dataset. The specific training settings are as follows: the backpropagation algorithm was adopted as the training algorithm, and the Adam optimization method was used for network training, with a learning rate of 0.001 and a total of 100 training epochs, utilizing a liquid crystal spatial light modulator (LCSLM) to regulate the light field phase distribution dynamically. By transforming Gaussian beams into flat-top beams, the method significantly enhances polarization uniformity within vapor cells, leading to improved magnetometric sensitivity. The proposed hybrid algorithm reduces the mean square error from 35% to 19% and peak non-uniformity from 21% to 7.6%. A reflective LCSLM-based optical setup is implemented to produce circular and square flat-top beams with a measured non-uniformity of 5.1%, resulting in an enhancement of magnetic sensitivity from 14.54 fT/Hz^1/2 to 7.80 fT/Hz^1/2.

In this study, an in situ measurement method of spin polarization in single‐beam atomic magnetometer is presented. Modeling magnetic linewidth by incorporating nonlinear attenuation along the propagation direction of light and employing the output response equation of magnetometers at zero‐field resonance. Utilizing the model for fitting to extract relaxation rate information, the photon absorption cross‐sections at three temperatures are estimated to be , , and , respectively. Further, the spin polarization curves are obtained by introducing the spin polarization equations. Given the diminishing marginal utility resulting from the enhancement of performance through increased spin polarization, long‐term sensitivity is employed to determine optimal spin polarization range. The optimal long‐term sensitivity for four displayed states is (@31.5Hz), while the ultimate minimum sensitivity is 10.7 (@31.5Hz). The optimal spin polarization ranges at three temperatures are 78.9%–87.1%, 82.3%–88.5%, and 84.5%–88.4%, respectively. The measurement method applied to single‐beam magnetometer can be easily extended to multi‐axis vector magnetometer. The determination of optimal spin polarization range is of great significance for the performance and stability of the magnetometer system, improving the sensitivity of magnetic field measurement, and ensuring its widespread application in bio‐magnetic measurement.

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.

Optical rotation detection system (ORDS) utilizing quantum nondemolition measurement methods is widely applied in the field of quantum metrology and quantum information. However, the sensitivity of ORDS is limited by the uncertainty from optical-couple noise during the measurement of the atomic spin ensemble. In this study, we specifically analyze the mechanism of optical-couple noise caused by the fluctuations of probe light’s polarization in the modulated ORDS with a new model established to describe atomic spin precession in this particular condition. It is discovered that transverse electron-spin polarization errors are generated by the residual probe photon spin polarization in the ORDS, which results in extra coupling magnetic noise. In order to suppress this noise, a novel in-situ method is proposed that the resultant electron-spin errors are reduced by a specifically designed closed-loop system. The results are verified through the ORDS in a co-magnetometer. After zeroing the extra probe photon spin polarization, an angular sensitivity better than 1×10 ^-8 rad/Hz ^1/2 is achieved for frequencies higher than 5 Hz, demonstrating a probe background noise of 0.26 fT/Hz ^1/2 @14.5 Hz, approaching electronic noise and photon shot noise. With closed-loop control, the optical rotation bias instability is promoted by 4.2 times (from 107.9 to 25.7 μrad/h), and the angular noise of the ORDS is reduced by 2.4 times at 1-100 Hz. The measurement uncertainty of the realized ORDS nears the standard quantum limit, paving the road for long-term ultrasensitive measurements for new physics explorations.

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

In this study, a method to design highly uniform magnetic field cylinder coils based on the grey wolf optimizer (GWO) algorithm is proposed. For the first time, this method is applied to the magnetic field design area. In this way, the uniform magnetic field region was expended, and the newly designed coils could be utilized in atomic sensors. Compared with other types of coil, namely the Genetic Algorithm (GA) coils and Lee–Whiting coils, the GWO coils exhibit the highest degree of uniformity. The uniform region of the GWO coils is in the range of [−0.53R, 0.53R] along the z-axis and exhibits a relative uniformity of less than 0.1%, as confirmed by experiments. This indicates that the newly designed coils display a huge superiority in the size of the uniform region, thus being able to provide a more uniform magnetic field. With the aim of enhancing the performance of the magnetic field compensation system of SERF atomic sensors, the proposed method also serves as an effective optimized algorithm to design highly uniform magnetic field coils coupled with magnetic shielding layers.