Application of kernel principal component analysis for optical vector atomic magnetometry

Abstract

Vector atomic magnetometers that incorporate electromagnetically induced transparency (EIT) allow for precision measurements of magnetic fields that are sensitive to the directionality of the observed field by virtue of fundamental physics. However, a practical methodology of accurately recovering the longitudinal angle of the local field through observations of EIT spectra has not been established. In this work, we address this problem of angle determination with an unsupervised machine learning algorithm utilizing nonlinear dimensionality reduction. The proposed algorithm was developed to interface with spectroscopic measurements from an EIT-based atomic rubidium magnetometer and uses kernel principal component analysis (KPCA) as an unsupervised feature extraction tool. The resulting KPCA features allow each EIT spectrum measurement to be represented by a single coordinate in a new reduced dimensional feature space, thereby streamlining the process of angle determination. A supervised support vector regression (SVR) machine was implemented to model the resulting relationship between the KPCA projections and field direction. If the magnetometer is configured so that the azimuthal angle of the field is defined with a polarization lock, the KPCA-SVR algorithm is capable of predicting the longitudinal angle of the local magnetic field within 1 degree of accuracy and the magnitude of the absolute field with a resolution of 70 nT. The combined scalar and angular sensitivity of this method make the KPCA-enabled EIT magnetometer competitive with conventional vector magnetometry methods. © 2023. All rights reserved.

Sensitivity of a vector atomic magnetometer based on electromagnetically induced transparency

“…However, the theory is less accurate when one utilized atomic cells containing an optimal amount of a buffer gas. Machine learning algorithms allow determining the parameters of the magnetic field by analyzing the relative amplitudes of all possible EIT resonances without theoretical evaluation of their evolution [28,29].…”

“…It is possible to avoid blind spots, like one around 𝜃 ≈ 40 • , by evaluating multiple EIT resonances and incorporating machine learning (ML) algorithms. Principal component analysis (PCA), an unsupervised ML method, can be utilized as a feature extraction tool to represent different manifestations of the 87 Rb EIT spectrum with a minimal number of scalar features [29]. These features can be paired with supervised learning algorithms to make measurements of 𝜙, 𝜃, and |𝐵|.…”

“…For angular measurements with the magnetometer, a tailored basis was obtained from the principal axes calculated using PCA on a data set of EIT spectra with variations in 𝜙 and 𝜃 (with a fixed magnitude of |𝐵| = 50 𝜇𝑇). The principal directions correspond to eigenvectors of the EIT data set covariance matrix [29]. QR factorization with column pivoting was performed on the tailored basis matrix, resulting in a permutation array that identified the optimal placements of 𝑚 sensors corresponding to 𝑚 principal axes (with each sensor placement corresponding with a specific detuning frequency of the probe field for the EIT spectrum).…”