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Joint Conference of the European Frequency and Time Forum and IEEE International Frequency Control Symposium (EFTF/IFCS)

In Situ Calibration of Magnetic Field Coils Using Parametric Resonance in Optically-pumped Magnetometers

Wei Xiao, He Wang, Xiangzhi Zhang, Yulong Wu, Teng Wu, Jingbiao Chen, Xiang Peng, Hong Mei Guo

Published Jul 7, 2021• 4 citations
Publisher

Abstract

In this article, we propose an in situ method to calibrate the magnetic-field coil systems in optically-pumped magnetometers. The method is based on parametric resonance induced by nonresonant radio-frequency (RF) fields, and is especially suitable for microfabricated single-beam zero-field atomic magnetometers. We have experimentally and theoretically demonstrated this method with a single-beam spin-exchange-relaxation-free (SERF) magnetometer, and the experiment results are in line with theoretical expectations.

DOI
10.1109/eftf/ifcs52194.2021.9604246

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In this article, we propose an in situ method to calibrate the magnetic-field coil systems in optically-pumped magnetometers. The method is based on parametric resonance induced by nonresonant radio-frequency (RF) fields, and is especially suitable for microfabricated single-beam zero-field atomic magnetometers. We have experimentally and theoretically demonstrated this method with a single-beam spin-exchange-relaxation-free (SERF) magnetometer, and the experiment results are in line with theoretical expectations.
Zero-field optically pumped magnetometers operating in the spin-exchange relaxation-free (SERF) regime have been extensively studied, and usually depend on zeroth-order parametric resonance to measure the magnetic field. However, the studies conducted on this topic lack thorough analyses and in-depth discussion of nonzero-order magnetic resonances in single-beam SERF magnetometers. In this paper, we analyzed the nonzero-order resonance, especially the first-order resonance, based on a single-beam SERF magnetometer, and discussed its various applications. A comprehensive theoretical analysis and experiments were conducted with respect to multiple functions, including nonzero finite magnetic field measurements, spin polarization measurement, and in situ coil constant calibration. The results showed that first-order resonance can be utilized for nonzerofinite magnetic field measurements, and the spin polarization of alkali-metal atoms can be determined by measuring the slowing-down factor using the resonance condition. Furthermore, acquiring the first-order resonance point at an equivalent zero pump light power through fitting offers an approach for quick and precise in situ coil constant calibration. This study contributes to the applications of SERF magnetometers in nonzero finite magnetic fields.
The electronic spin polarization of alkali-metal-vapor atoms is a pivotal parameter for atomic magnetometers. Herein, a novel method is presented for determining the spin polarization with a miniaturized single-beam spin-exchange-relaxation-free (SERF) magnetometer on the basis of zero-field cross-over resonance. Two separate laser beams are utilized to heat the cell and interrogate the vapor atoms, respectively. Spin polarization can be extracted by measuring the resonance response signal of the magnetometer to the transverse magnetic field under different irradiances. Results of these experiments are consistent well with the theoretical predictions with the maximum deviation less than 4%. The proposed method has the integrated advantages of possessing a simple configuration and in-situ measurement. Furthermore, combined with a homemade optical differential detection system with a factor of approximately three of the power noise suppression, the developed single-beam SERF atomic magnetometer with a measuring sensitivity of 32 fT/Hz 1/2 has been achieved. This demonstrated approach can help guide the development of chip-scale atomic magnetometers for bio-magnetic field imaging applications.
The calibration results of the triaxial coils affect the atomic magnetometer’s measurement sensitivity. For precise in situ calibration, we first studied the transient atomic dynamics of a dual-beam spin-exchange relaxation free (SERF) atomic magnetometer under alternating magnetic fields. We obtained the corresponding dynamic free-induction-decay (FID) curves by alternately applying square wave signals to thex{x}x-,y{y}y-, andz{z}z-axis coil, and then extracted the precession frequencies by fast Fourier transform (FFT) to achieve a decoupled calibration of the triaxial coil constants. Our calibration results were in better agreement under different experimental conditions than traditional parameter fitting methods with a relative error of less than 1.5% compared to conventional fluxgate calibration methods. Furthermore, we simultaneously measured nonorthogonal angles between each pair of axes: x–y, y–z, and z–x, respectively, which are used to correct the magnetic fields error. This method is suitable for coil calibration and nonorthogonal correction of integrated and miniaturized dual beam magnetometers.
Spin-exchange relaxation-free (SERF) magnetometers enable femtotesla-level bio-magnetic imaging, yet their scalability into high-density arrays is impeded by inter-sensor crosstalk arising from conventional magnetic-field modulation. While optical amplitude modulation offers a crosstalk-free alternative, its resonance mechanisms within the SERF regime remain unexplored. Here, we report a dual-resonance mechanism induced by amplitude-modulated light in a SERF magnetometer. Our theoretical model characterizes this behavior as the coexistence of a central zero-field resonance and symmetric parametric resonances at high atomic densities, in excellent agreement with experimental measurements. Systematic temperature and pump-power sweeps reveal the evolution of the dual-resonance profile, demonstrating that high alkali density sharpens and amplifies the zero-field resonance, whereas strong optical pumping restores the dominance of parametric resonances. Exploiting these distinct resonances, we utilize the parametric component to extract the slowing-down factor and spin polarization, which allows in situ coil calibration in both probe and pump channels with errors below 0.5%. In contrast, operation on the zero-field resonance significantly suppresses long-term drifts compared with DC detection and yields a sensitivity of 4.96 fT/Hz 1/2 . Ultimately, these findings elucidate the modulation physics within the SERF regime and establish a crosstalk-free framework that paves the way for high-precision bio-magnetic arrays.
We demonstrate an optically pumped (87)Rb magnetometer in a microfabricated vapor cell based on a zero-field dispersive resonance generated by optical modulation of the (87)Rb ground state energy levels. The magnetometer is operated in the spin-exchange relaxation-free regime where high magnetic field sensitivities can be achieved. This device can be useful in applications requiring array-based magnetometers where radio frequency magnetic fields can induce cross-talk among adjacent sensors or affect the source of the magnetic field being measured.
Abstract This work proposes a novel method for in situ measurement of the non‐orthogonal angles of magnetic field coils based on single‐beam magnetic resonance. The orthogonality of magnetic field coils is crucial for ensuring the accuracy of atomic magnetometers. The theoretical principles are derived to establish a measurement method for the non‐orthogonal angles. The proposed method requires only one single beam of light to perform in situ measurements of non‐orthogonal angles in the YZ and XZ directions. The experimental results demonstrate that the angle between the Y and Z coils is 89.3001 ± 0.0045°, a value that remains stable despite variations in experimental parameters such as temperature and light power, thereby confirming the robustness of the method. Additionally, the measured gyromagnetic ratio is 6.9963 ± 0.0005 Hz nT −1 , which closely matches the theoretical value of 6.9958 Hz nT −1 , further validating the method's accuracy. The proposed method provides a more straightforward approach and has significant potential for widespread application across various atomic magnetometers, especially in miniaturized configurations. Furthermore, this method may be extended to the field of atomic gyroscopes.