The coupling between the coil and the cylindrical magnetic shield (CMS) in atomic sensors not only results in the inconsistency of the coil constant with the theory but also deteriorates the uniformity, which affects the sensor performance. To solve the abovementioned deficiencies, a design method of highly uniform field coils inside the CMS based on the coupling model with finite permeability and thickness and particle swarm optimization (PSO) with dynamic inertia weights is proposed for the first time. The coupling model of the coil inside the CMS is established by Green’s function method (GFM). Then, it is combined with the nonlinear optimization method, and the coil configuration is optimized by the dynamic inertia weight PSO (DW-PSO) to obtain the optimal parameters. It not only reduces the calculation error of the model, but also improves the uniformity. Comparing this work with the Lee-Whiting coil inside a CMS, the theoretical uniformity is further improved by two orders of magnitude, and measured uniformity errors in the target region reach $1.404\times {10^{-4}}$ , and $2.317\times {10^{-4}}$ , respectively. The correctness and effectiveness are proved by finite-element simulation and experimental results. The accuracy and uniformity of coils can be considerably improved, which is beneficial to further improve the measurement sensitivity of instruments related to magnetic field uniformity.

This paper investigates the atomic spin polarization controllability of spin-exchange relaxation-free co-magnetometers (SERFCMs). This is the first work in the field of controllability analysis for the atomic spin ensembles systems, whose dynamic behaviors of spin polarization are described by the Bloch equations. Based on the Bloch equations, a state-space model of the atomic spin polarization for SERFCM is first established, which belongs to a particular class of nonlinear systems. For this class of nonlinear systems, a novel determination method for the global state controllability is proposed and proved. Then, this method is implemented in the process of controllability analysis on the atomic spin polarization of an actual SERFCM. Moreover, a theoretically feasible and reasonable solution of the control input is proposed under some physical constraints, with whose limitation of realistic conditions, the controller design can be accomplished more practically and more exactly. Finally, the simulation results demonstrate the feasibility and validation of the proposed controllability determination method.

The transverse light-shift can induce non-negligible polarization error in the output signal of spin-exchange relaxation-free (SERF) co-magnetometer. In this paper, a novel method for rapid measurement of transverse light-shift based on the error of steady-state response of co-magnetometer is proposed firstly, then the sources of transverse light-shift in a compact SERF co-magnetometer is modeled and analyzed from three aspects: the non-ideal linear polarization of probe laser, the circular dichroism of the atomic spin ensembles, and the stress-induced birefringence effect of the cell wall. Furthermore, the decoupling and suppression methods of transverse light-shift based on a degree of circular polarization (DOCP) regulation scheme is presented, to realize the decoupling measurement of the transverse light-shift introduced by the whole co-magnetometer cell, and cancel it out with the non-ideal linear polarization of the probe laser. Eventually, the DOCP regulation scheme suggested in this paper achieves more than a 67% suppression ratio in transverse light-shift, and the short- and long-term performance of SERF co-magnetometer are improved due to the reduction of the coupling effect between the probe laser power and transverse field. Moreover, the measurement, decoupling and suppression methods provided in this paper also have the potential to be applied to other atomic sensors, such as the SERF magnetometers and nuclear spin co-magnetometers.

This article is the first work to propose a series of control strategies for the longitudinal electron spin polarization of the spin-exchange relaxation-free comagnetometer system to ensure its ultrastable measurement. Two types of finite-time control strategies are presented for a nonlinear system with affine input. The first control strategy is finite-time fractional exponential feedback control (FEFC), which ensures that the trajectories of an autonomous system converge to an equilibrium state in a finite time that can be specified. The second control strategy is finite-time robust FEFC, which provides a finite-time stability of a nonautonomous system with unknown structures under disturbance and perturbations, and its upper bound of the settling time can be estimated. The theoretical results are supported by numerical simulations.

In this article, a highly sensitive in situ magnetic field fluctuation measurement method is proposed based on nuclear-spin depolarization in a spin-exchange relaxation-free (SERF) atomic comagnetometer (ACM). The steady-state model of the hybrid atomic spin ensemble is systematically studied. According to the theoretical model, two different states of nuclear-spin polarization and unpolarization lead to different sensitivities of the system to rotation and magnetic fields. The gradient magnetic field (GMF) is employed to change the state of nuclear-spin polarization of the noble gas, transforming the ACM into an atomic magnetometer (AM). The polarization and relaxation rates of the electron spin and nuclear spin under the two measurement modes are measured and compared by the magnetic resonance method and transient response method. At the same time, the performances in the ACM and AM are tested. Detailed experiments verify that the AM can achieve sensitivity for the magnetic field measurement with an average value of $53.6~\mathbf {fT/Hz^{1/2}}$ in the frequency range of $10\sim 30$ Hz. The Allan variance method is adopted to evaluate the $x$ - and $y$ -axis magnetic field stabilities of the ACM, and the magnitudes are 61.6 and 55.9 fT at 100 s, contributing about 4.9 $\times 10\mathbf {^{-3}}\,\,\mathbf {^{\circ }/h}$ and 2.6 $\times 10\mathbf {^{-4}}\,\,\mathbf {^{\circ }/h}$ to the long-term stability of the ACM. This method can not only realize the high-sensitivity in situ measurement of the close-to-zero magnetic field and its fluctuation but also realize the switching of the two measurement modes of rotation and magnetic field measurements, which is essential for the evaluation of magnetic field error.

This work is the first to solve the 3-D spin polarization control (3DSPC) problem of atomic ensembles, which controls the spin polarization to achieve arbitrary states with the cooperation of multiphysics fields. First, a novel adaptive dynamic programming (ADP) structure is proposed based on the developed multicritic multiaction neural network (MCMANN) structure with nonquadratic performance functions, as a way to solve the multiplayer nonzero-sum game (MP-NZSG) problem in 3DSPC under the constraints of asymmetric saturation inputs. Then, we utilize the MCMANNs to implement the multicritic multiaction ADP (MCMA-ADP) algorithm, whose convergence is proven by the compression mapping principle. Finally, the MCMA-ADP is deployed in the spin-exchange relaxation-free (SERF) system to provide a set of control laws in 3DSPC that fully exploits the multiphysics fields to achieve arbitrary spin polarization states. Numerical simulations support the theoretical results.