Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Optical Engineering

In situ simultaneous measurement of magnetic coil constants and nonorthogonal angles using atomic magnetometers

Lin Li, Junjian Tang, Baodong Chen, Binbin Zhao, Binquan Zhou, Yueyang Zhai

Published Feb 15, 2023• 6 citations
Publisher

Abstract

An in situ simultaneous measurement of magnetic coil constants and nonorthogonal angles method is proposed using the atomic magnetometer. Based on the transient response of the atomic spin polarization under the different magnetic fields, we establish the corresponding measurement model of magnetic coil constants and nonorthogonal angles through the relationship between the Larmor precession frequency and the external magnetic field. By this model, we experimentally obtained the coil constants of x , y, and z axes are, respectively, 9.04 ± 0.10, 8.94 ± 0.07, and 4.34 ± 0.02 nT / V in our system. The nonorthogonal angles are 89.04 deg between x axis and y axis, 88.60 deg between y axis and z axis, and 91.15 deg between z axis and x axis. This method can be used to simultaneously measure magnetic coil constants and nonorthogonal angles without relying on external instruments, which provides a basic guarantee for the accurate calculation sensitivity of spin-exchange-relaxation-free atomic magnetometers, especially for miniaturized atomic magnetometers.

DOI
10.1117/1.oe.62.2.024106

Related papers

Triaxial Coils In Situ Calibration Method Based on Measuring the Alternating Magnetic Field-Induced Dynamic Response of the SERF Magnetometer

Kun Wang, Danyue Ma, Siran Li +4 more

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 the${x}$-,${y}$-, and${z}$-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.

IEEE Sensors Journal•Jul 7, 2023•15 citations

A Coil Constant Calibration Method Based on the Phase-Frequency Response of Alkali Atomic Magnetometer

Han Yao, Danyue Ma, Junpeng Zhao +2 more

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.

Photonic Sensors•Jan 18, 2019•9 citations

Ingenious Method for Measuring the Non-Orthogonal Angle of the Saddle-Shaped Coils of an SERF Atomic Magnetometer System

Hong Zhang, Sheng Zou, Xiyuan Chen

The spin exchange relaxation free (SERF) atomic magnetometer has been a research hotspot due to its ultra-high sensitivity. The SERF atomic magnetometer's sensitivity is subject to the accuracy of its compensating magnetic field and the calibration signal. These two processes need a tri-axial coil system to generate the required magnetic fields, which are directly affected by the non-orthogonality of the tri-axial coil system, especially the non-orthogonality between the x- and y-axes coils. In order to solve this problem, an ingenious and effective method for measuring the non-orthogonal angle between the x- and y-axes in a magnetic coil system has been demonstrated in this paper for the first time. This measurement method was only based on the dynamics of the SERF atomic magnetometer and did not need any additional calibration equipment. A large dc magnetic field Bywas applied to the y-axis, such that the magnetic field Byxprojected from Byon to the x-axis could be measured. By then solving the relevant trigonometric function, we could obtain the non-orthogonal angle. Using this method, we experimentally obtained the non-orthogonal angle of about 84.08° between the x- and y-axes saddle-shaped coils, with a variance of about 0.14°. Finally, the correctness of this method for calculating the non-orthogonal angle was analyzed.

IEEE Transactions on Magnetics•Jun 30, 2016•16 citations

Effect of Optical Nonorthogonality on Dynamic Response in Dual-Beam Atomic Magnetometer

Bozheng Xing, Siran Li, Xiujie Fang +2 more

In this article, we analyze the amplitude-frequency and phase-frequency responses of a spin-exchange relaxation-free (SERF) atomic magnetometer with the nonorthogonal angle between the pump and probe beam. The optical nonorthogonality leads to a change in the photon spin direction of circularly polarized pump light, which decides the polarization direction of the atomic ensemble, causing significant differences in dynamic responses to the magnetic field. We theoretically analyze relationships between dynamic response solutions of the Bloch equation with different pump lights and magnetic field directions based on which the equations are linearized. The equations are solved with the Fourier transform method, and three-axis dynamic responses are obtained under the influences of optical nonorthogonality and residual static magnetic field. In the experiment, we verify the linear superposition characteristics between different response components. According to the results, we propose a novel method to quickly calibrate the nonorthogonal angle, which could reduce the optical nonorthogonal angle by 20 times, reaching 0.54°, and effectively enhance the dynamic magnetic field response signal in atomic magnetometers.

IEEE Transactions on Instrumentation and Measurement•Nov 25, 2024•7 citations

A Novel Measurement Method for Spin Polarization Three Axis Spatial Distribution in Spin-Exchange Relaxation Free Atomic Magnetometer

Xiujie Fang, Jin Chun Li, Yanning Ma +5 more

The measurement of atomic spin polarization distribution in spin-exchange relaxation free (SERF) magnetometer is an important topic for improving the sensitivity and consistency of multi-channel magnetic field measurement applications. A novel spin polarization spatial distribution measurement method is presented based on the transient response of the magnetometer after modulating the pumped light with a chopper. Polarization is obtained by a slow-down factor based on the fast spin-exchange interaction effects. Longitudinal and transverse polarization distributions are measured simultaneously without interrupting the operation of the SERF status. Under different oscillating magnetic fields, the spin polarization is measured at the cell centroid. Residual magnetic field inside the magnetometer is obtained from the linear relationship between the precession frequency and the oscillating magnetic field. The one-dimensional polarization distributions in the x, y, and z axes are measured using a digital micromirror device with a resolution of 0.25 cm. The measurement results conform to the Lambert-Bier absorption law and the Gaussian distribution law. Furthermore, 7 × 7 two-dimensional spatial distribution measurements of polarization on the xy and yz planes are performed. Nonuniformity of 1.04 in the xy plane and 1.82 in the yz plane in the built magnetometer. Compared with other measurement methods, the distribution measurement method proposed is independent of optical depth and suitable for low polarization and high polarization applications. Based on the results of the proposed measurement method of spin polarization spatial distribution, further compensation can improve the application consistency of multi-channel magnetic field measurements and improve the sensitivity of single-channel differential measurements.

Photonics•Mar 20, 2023•2 citations

In Situ Measurement of the Non‐Orthogonal Angles of Magnetic Field Coils Based on Single‐Beam Magnetic Resonance

Zhi Liu, Lihong Dong, Zhe Qi +3 more

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.

Advanced Quantum Technologies•Aug 1, 2024•1 citation
An in situ simultaneous measurement of magnetic coil constants and nonorthogonal angles method is proposed using the atomic magnetometer. Based on the transient response of the atomic spin polarization under the different magnetic fields, we establish the corresponding measurement model of magnetic coil constants and nonorthogonal angles through the relationship between the Larmor precession frequency and the external magnetic field. By this model, we experimentally obtained the coil constants of x , y, and z axes are, respectively, 9.04 ± 0.10, 8.94 ± 0.07, and 4.34 ± 0.02 nT / V in our system. The nonorthogonal angles are 89.04 deg between x axis and y axis, 88.60 deg between y axis and z axis, and 91.15 deg between z axis and x axis. This method can be used to simultaneously measure magnetic coil constants and nonorthogonal angles without relying on external instruments, which provides a basic guarantee for the accurate calculation sensitivity of spin-exchange-relaxation-free atomic magnetometers, especially for miniaturized atomic magnetometers.
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.
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.
The spin exchange relaxation free (SERF) atomic magnetometer has been a research hotspot due to its ultra-high sensitivity. The SERF atomic magnetometer's sensitivity is subject to the accuracy of its compensating magnetic field and the calibration signal. These two processes need a tri-axial coil system to generate the required magnetic fields, which are directly affected by the non-orthogonality of the tri-axial coil system, especially the non-orthogonality between the x- and y-axes coils. In order to solve this problem, an ingenious and effective method for measuring the non-orthogonal angle between the x- and y-axes in a magnetic coil system has been demonstrated in this paper for the first time. This measurement method was only based on the dynamics of the SERF atomic magnetometer and did not need any additional calibration equipment. A large dc magnetic field Bywas applied to the y-axis, such that the magnetic field Byxprojected from Byon to the x-axis could be measured. By then solving the relevant trigonometric function, we could obtain the non-orthogonal angle. Using this method, we experimentally obtained the non-orthogonal angle of about 84.08° between the x- and y-axes saddle-shaped coils, with a variance of about 0.14°. Finally, the correctness of this method for calculating the non-orthogonal angle was analyzed.
In this article, we analyze the amplitude-frequency and phase-frequency responses of a spin-exchange relaxation-free (SERF) atomic magnetometer with the nonorthogonal angle between the pump and probe beam. The optical nonorthogonality leads to a change in the photon spin direction of circularly polarized pump light, which decides the polarization direction of the atomic ensemble, causing significant differences in dynamic responses to the magnetic field. We theoretically analyze relationships between dynamic response solutions of the Bloch equation with different pump lights and magnetic field directions based on which the equations are linearized. The equations are solved with the Fourier transform method, and three-axis dynamic responses are obtained under the influences of optical nonorthogonality and residual static magnetic field. In the experiment, we verify the linear superposition characteristics between different response components. According to the results, we propose a novel method to quickly calibrate the nonorthogonal angle, which could reduce the optical nonorthogonal angle by 20 times, reaching 0.54°, and effectively enhance the dynamic magnetic field response signal in atomic magnetometers.
The measurement of atomic spin polarization distribution in spin-exchange relaxation free (SERF) magnetometer is an important topic for improving the sensitivity and consistency of multi-channel magnetic field measurement applications. A novel spin polarization spatial distribution measurement method is presented based on the transient response of the magnetometer after modulating the pumped light with a chopper. Polarization is obtained by a slow-down factor based on the fast spin-exchange interaction effects. Longitudinal and transverse polarization distributions are measured simultaneously without interrupting the operation of the SERF status. Under different oscillating magnetic fields, the spin polarization is measured at the cell centroid. Residual magnetic field inside the magnetometer is obtained from the linear relationship between the precession frequency and the oscillating magnetic field. The one-dimensional polarization distributions in the x, y, and z axes are measured using a digital micromirror device with a resolution of 0.25 cm. The measurement results conform to the Lambert-Bier absorption law and the Gaussian distribution law. Furthermore, 7 × 7 two-dimensional spatial distribution measurements of polarization on the xy and yz planes are performed. Nonuniformity of 1.04 in the xy plane and 1.82 in the yz plane in the built magnetometer. Compared with other measurement methods, the distribution measurement method proposed is independent of optical depth and suitable for low polarization and high polarization applications. Based on the results of the proposed measurement method of spin polarization spatial distribution, further compensation can improve the application consistency of multi-channel magnetic field measurements and improve the sensitivity of single-channel differential measurements.
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.