This paper investigates the performance optimization of optically pumped magnetometers under zero-field parametric modulation. Based on the analytical solutions of the Bloch equation, both longitudinal and transverse modulations are studied experimentally. To estimate the nonuniform polarization distribution of alkali-metal atoms in the vapor cell, an average pumping rate model is proposed. Furthermore, the accuracy of this model and the measurement of the transverse relaxation rate are verified via the agreement between experimental and theoretical values. The results indicate that optimal performance can be achieved by employing a suitable modulation field, the selection of which is related to the modulation index $u$ in the Bessel series and the pump-light intensity. Although both operating modes show similar responses to weak magnetic fields, their effects on pump-light intensity are different due to the means of detecting atomic polarization. An optimal value of the pump-light intensity on the response strength exists in longitudinal modulation. However, with regard to transverse modulation, the sensitivity under weak pump-light intensity is better. This research has far-reaching significance for cases when the parametric modulation is manipulated.

Atomic magnetometers operated in spin-exchange relaxation-free (SERF) have the potential to replace superconducting quantum interference devices (SQUIDs) in the field of biomagnetism. Here, we demonstrate the dual-axis closed-loop control of a single-beam SERF magnetometer that allows sensing of two orthogonal magnetic fields simultaneously and independently with suppressed crosstalk effect, achieved by applying a rotating modulation field and using the negative feedback. Operating in the dual-axis closed-loop mode with a miniature 4 $\times $ 4 $\times $ 4 mm ⁸⁷ Rb cell, we achieve the magnetic field sensitivity of 20 fT/Hz ^1/2 and a bandwidth of 1.8 kHz. In addition to the experimental study of the sensitivity and bandwidth, we perform a theoretical analysis of the dual-axis response and develop an effective decoupling method. The implementation of closed-loop control enables the magnetometer to be robust against the disturbance of the ambient field, which could enlarge the dynamic range, enhance the systematic stability, and suppress the crosstalk effect. Such a simple, yet high-performance SERF magnetometer could be suitable as a promising candidate in the field of biomagnetism, allowing for a denser sensor array and opening up new possibilities for noninvasive biomagnetic imaging.

This paper presents a modified pigeon-inspired optimization method for designing self-shielded uniform magnetic field coils that offers an innovation in miniature atomic sensors. The proposed coil system consists of circular coil pairs distributed on two coaxial cylinder surfaces, which can provide a highly uniform magnetic field at the coil center and rapidly attenuate the external field. This design is transformed into a nonlinear objective optimization problem with constraints, so that the coil geometric parameters can be obtained by the proposed algorithm, instead of solving closed-form equations by pure numerical method. Parallel competition and hierarchical search strategy are firstly introduced to accelerate the convergence speed and avoid falling into the local optimal value. Comparative experiments of several algorithms demonstrate the accuracy, effectiveness, convergence stability of the proposed method. Compared with traditional design methods, this method can automatically find the optimal parameters of the coil according to any constraints. Theoretical contrast shows that compared with the Lee-Whiting coil, the uniformity of proposed coil is improved by about 2 to 3 orders of magnitude and has a significant self-shielded effect. This work is beneficial to the miniaturization of atomic sensors.

In this paper, an optimization method that uses the derivatives and the target field information of the magnetic field simultaneously is proposed to suppress the coupling between the coil and the magnetic shielding in miniature atomic sensors. The coupling between the coil and the magnetic shielding varies with the material magnetic permeability, which causes the magnetic field to fluctuate with the temperature as the material permeability. The magnetic field fluctuations will cause the measurement errors and drifts of the sensors. The proposed method can effectively suppress the magnetization of the magnetic shielding caused by the coil magnetic field. A shielded coil outside the main coil is used to efficiently attenuate the magnetic field outside the main coil to suppress the coupling between the coil and the magnetic shielding. A coil system consisting of pairs of circular coils distributed on two coaxial cylinder surfaces is proposed in this paper. The Taylor expansion is used to ensure the uniformity of the internal magnetic field, while the target field information is used to ensure the attenuation of the external magnetic field. A particle swarm optimization (PSO) algorithm is used to optimize the parameters of the main and shielded coils. The theoretical calculations and the finite element analysis prove that the proposed approach is an effective design method for the self-shielded coils.