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Nature Communications

Machine learning assisted vector atomic magnetometry

Xin Meng, Youwei Zhang, Xichang Zhang, Shenchao Jin, Tingran Wang, Liang Jiang, Liantuan Xiao, Suotang Jia, Yanhong Xiao

Published Sep 29, 2023• 43 citations
Publisher

Abstract

Multiparameter sensing such as vector magnetometry often involves complex setups due to various external fields needed in explicitly connecting one measured signal to one parameter. Here, we propose a paradigm of indirect encoding for vector atomic magnetometry based on machine learning. We encode the three-dimensional magnetic-field information in the set of four simultaneously acquired signals associated with the optical rotation of a laser beam traversing the atomic sample. The map between the recorded signals and the vectorial field information is established through a pre-trained deep neural network. We demonstrate experimentally a single-shot all optical vector atomic magnetometer, with a simple scalar-magnetometer design employing only one elliptically-polarized laser beam and no additional coils. Magnetic field amplitude sensitivities of about 100 [Formula: see text] and angular sensitivities of about [Formula: see text] (for a magnetic field of around 140 nT) are derived from the neural network. Our approach can reduce the complexity of the architecture of vector magnetometers, and may shed light on the general design of multiparameter sensing.

DOI
10.1038/s41467-023-41676-x

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Multiparameter sensing such as vector magnetometry often involves complex setups due to various external fields needed in explicitly connecting one measured signal to one parameter. Here, we propose a paradigm of indirect encoding for vector atomic magnetometry based on machine learning. We encode the three-dimensional magnetic-field information in the set of four simultaneously acquired signals associated with the optical rotation of a laser beam traversing the atomic sample. The map between the recorded signals and the vectorial field information is established through a pre-trained deep neural network. We demonstrate experimentally a single-shot all optical vector atomic magnetometer, with a simple scalar-magnetometer design employing only one elliptically-polarized laser beam and no additional coils. Magnetic field amplitude sensitivities of about 100 [Formula: see text] and angular sensitivities of about [Formula: see text] (for a magnetic field of around 140 nT) are derived from the neural network. Our approach can reduce the complexity of the architecture of vector magnetometers, and may shed light on the general design of multiparameter sensing.
Multiparameter sensing such as vector magnetometry often involves complex setups due to various external fields needed in explicitly connecting one measured signal to one parameter. Here, we propose a paradigm of indirect encoding for vector atomic magnetometry based on machine learning. We encode the three-dimensional magnetic-field information in the set of four simultaneously acquired signals associated with the optical rotation of a laser beam traversing the atomic sample. The map between the recorded signals and the vectorial field information is established through a pre-trained deep neural network. We demonstrate experimentally a single-shot all optical vector atomic magnetometer, with a simple scalar-magnetometer design employing only one elliptically-polarized laser beam and no additional coils. Magnetic field amplitude sensitivities of about 100 fT/√Hz and angular sensitivities of about 100∼200μrad/√Hz (for a magnetic field of around 140 nT) are derived from the neural network. Our approach can reduce the complexity of the architecture of vector magnetometers, and may shed light on the general design of multiparameter sensing.
Quantum magnetometry provides remarkable sensitivity and miniaturization potential for precision measurement, yet conventional vector magnetic field detection often suffers from hardware complexity and directional dead zones. Here we present a deep learning-based, single-beam all-optical vector magnetometer that enables end-to-end neural network modeling for omnidirectional magnetic field sensing without dead zones. By exploiting the nonlinear relationship between coherent population trapping (CPT) spectra of 87Rb D1 line and field orientation, we construct a one-dimensional deep residual network to directly decode single-pass spectral signals into azimuth angles, fully resolving the φ/φ+180° ambiguity inherent in traditional approaches. The experimental results demonstrate that the proposed scheme has a good effect on eliminating degeneracy problems, and the system performance is tested that pitch angular sensitivity of 0.01°/Hz1/2, and azimuth angular sensitivity of 0.01rad without additional modulation coils or multi-beam configurations. This work establishes a general framework for intelligent spectral inversion of complex physical quantities and offers a single-beam architecture suitable for highly integrated quantum sensors.
This paper reports an all-optical vector magnetometer enhanced by a machine learning model. Using a dual probing beam setup, spin projections in both probe directions are simultaneously detected. Vector information is directly obtained from the measured phases of spin projection signals. To enhance the measurement accuracy and mitigate the dead zone effect, we introduce an artificial neural network (ANN) to link the phase signals to the field direction. With the addition of amplitude information to the ANN input, the average angle error is reduced to less than 0.3° within a hemisphere. Furthermore, this configuration demonstrates a field angle sensitivity of better than 30 μ rad/Hz1/2.
The precise measurement of magnetic fields is a fundamental tool of remote sensing. However, accurately measuring the direction of magnetic fields is challenging with atomic magnetometers. In this work, we discuss progress on the development of an all-optical vector atomic magnetometer that uses electromagnetically induced transparency (EIT) on87Rb vapor. The magnitude of the magnetic field is evaluated by measuring the separation of the laser transmission peaks of the Zeeman-resolved EIT spectra, and the direction is measured by evaluating the relative peak contrast using a lightweight machine learning algorithm involving principal component analysis (PCA). We have demonstrated a scalar sensitivity of $ < 10pT/\sqrt {Hz} $ in the 1–100 Hz band and an angular accuracy of < 1°. This approach for vector magnetometry does not require an array of sensors or calibration coils, ultimately setting the groundwork for the design of a new magnetometer that is lighter and more accurate than conventional vector magnetometer configurations.
Vector field measurement is demonstrated with an all-optical scalar atomic magnetometer using intrinsic parameters related to its scalar operation. The Bell-Bloom type atomic magnetometer measures the Larmor precession of cesium atoms through on-resonant absorption of a probe beam. While the AC component of the probe signal is used for the field magnitude measurement, the probe DC signal contains information about the polar angle, defined as the angle between the magnetic field and the probe beam. Additional polar angle information is obtained from the light-shift-induced magnetic field caused by the frequency modulation of the probe beam. With a measurement time of 100 milliseconds, better than 0.02 degree sensitivity has been achieved using a commercial miniaturized sensor at the optimal sensor orientation. The angle measurement accuracy is checked against an optical encoder over the entire polar angle range of 0 to 180 degrees. Better than 1 degree error is recorded over most set polar angles. Azimuthal angle measurement is also exhibited with an additional orthogonally oriented sensor.
Vector field measurement is demonstrated with an all-optical scalar atomic magnetometer using intrinsic parameters related to its scalar operation. The Bell-Bloom type atomic magnetometer measures the Larmor precession of cesium atoms through on-resonant absorption of a probe beam. While the AC component of the probe signal is used for the field magnitude measurement, the probe DC signal contains information about the polar angle, defined as the angle between the magnetic field and the probe beam. Additional polar angle information is obtained from the light-shift-induced magnetic field caused by the frequency modulation of the probe beam. With a measurement time of 100 ms, better than 0.02° sensitivity has been achieved using a commercial miniaturized sensor at the optimal sensor orientation. The angle measurement accuracy is checked against an optical encoder over the entire polar angle range of 0°–180°. Better than 1° error is recorded over most set polar angles. Azimuthal angle measurement is also exhibited with two orthogonally oriented sensors.