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arXiv:2603.08594

An Accurate Vector Magnetometer via Zeeman Rabi Oscillations

Thanmay S. Menon, D. P. Hewatt, Christopher Kiehl, Michaela Ellmeier, Svenja A. Knappe, Cindy A. Regal

Published Mar 9, 2026• 0 citations
arXivHTMLPDF

Abstract

Accurate magnetic field direction sensing in compact platforms is critical in applications spanning magnetic navigation, space science, and biomedical imaging. We demonstrate a single-optical-axis vector optically pumped magnetometer based on Rabi oscillations between Zeeman sublevels driven by a series of resonant radiofrequency (RF) polarization ellipses (PEs). A calibration protocol based on controlled rotations of the DC magnetic field determines the spatial orientation of each PE. We develop a detailed theoretical model describing the angular dependence of the Rabi frequencies, incorporating key systematics including RF Stark shifts and Bloch-Siegert shifts. We also account for an RF-based heading-error systematic affecting Rabi-frequency measurements arising from the nonlinear Zeeman effect. Simultaneous Larmor measurements yield the magnitude of the magnetic field, enabling integrated vector-scalar measurements. The magnetometer achieves deadzone-free vector operation with 80 $μ$rad mean angular accuracy and angular noise densities as low as 8 $μ$rad$/\sqrt{\mathrm{Hz}}$, offering a pathway towards miniaturized sensors without requiring 3D optical access or sensor rotations.

DOI
10.48550/arxiv.2603.08594

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Accurate magnetic field direction sensing in compact platforms is critical in applications spanning magnetic navigation, space science, and biomedical imaging. We demonstrate a single-optical-axis vector optically pumped magnetometer based on Rabi oscillations between Zeeman sublevels driven by a series of resonant radiofrequency (RF) polarization ellipses (PEs). A calibration protocol based on controlled rotations of the DC magnetic field determines the spatial orientation of each PE. We develop a detailed theoretical model describing the angular dependence of the Rabi frequencies, incorporating key systematics including RF Stark shifts and Bloch-Siegert shifts. We also account for an RF-based heading-error systematic affecting Rabi-frequency measurements arising from the nonlinear Zeeman effect. Simultaneous Larmor measurements yield the magnitude of the magnetic field, enabling integrated vector-scalar measurements. The magnetometer achieves deadzone-free vector operation with 80 μμμrad mean angular accuracy and angular noise densities as low as 8 μμμrad/Hz/\sqrt{\mathrm{Hz}}/Hz​, offering a pathway towards miniaturized sensors without requiring 3D optical access or sensor rotations.
Robust calibration of vector optically pumped magnetometers (OPMs) is a nontrivial task, but increasingly important for applications requiring high-accuracy such as magnetic navigation, geophysics research, and space exploration. Here, we showcase a vector OPM that utilizes Rabi oscillations driven between the hyperfine manifolds of 87 Rb to measure the direction of a DC magnetic field against the polarization ellipse structure of a microwave field. By relying solely on atomic measurements—free-induction decay (FID) signals and Rabi measurements across multiple atomic transitions—this sensor can detect drift in the microwave vector reference and compensate for systematic shifts caused by off-resonant driving, nonlinear Zeeman (NLZ) effects, and buffer gas collisions. To facilitate deadzone-free operation, we also introduce a Rabi measurement that utilizes dressed-state resonances that appear during simultaneous Larmor precession and Rabi driving (SPaR). These measurements, performed within a microfabricated vapor cell platform, achieve an average vector accuracy of 0.46 mrad and vector sensitivities down to 11µrad/Hz for geomagnetic field strengths near 50 µT. This performance surpasses the challenging 1-deg (17 mrad) accuracy threshold of several contemporary OPM methods utilizing atomic vapors with an electromagnetic vector reference.
When optically pumped magnetometers are aimed for use in the Earth's magnetic field, the orientation of the sensor to the field direction is of special importance to achieve accurate measurement results. Measurement errors and inaccuracies related to the heading of the sensor can be an even more severe problem in the case of special operational configurations, such as the use of strong off-resonant pumping. We systematically study the main contributions to the heading error in systems that promise high magnetic field resolutions at the Earth's magnetic field strengths, namely the nonlinear Zeeman splitting and the orientation-dependent light shift. The good correspondence of our theoretical analysis to experimental data demonstrates that both of these effects are related to a heading-dependent modification of the interaction between the laser light and the dipole moment of the atoms. Also, our results promise a compensation of both effects using a combination of clockwise and counterclockwise circular polarization.
Precession frequencies measured by optically pumped scalar magnetometers are dependent on the relative angle between the sensor and the external magnetic field. This dependence is known to be induced mainly by the nonlinear Zeeman effect and the orientation-dependent light shift, resulting in the so-called heading errors if the magnetic field orientation is not well known or is not stable. In this work, we find that the linear nuclear Zeeman effect has also a significant impact on the heading errors. It not only shifts the precession frequency but causes asymmetry: the heading error for sensors orienting in the upper-half plane with respect to the external field is different from the case when the sensors work in the lower-half plane. This heading error also depends on the relative direction of the probe laser to the driving magnetic field. With a left-handed circularly-polarized pump laser, when the probe laser is parallel to the driving field, the angular dependence of the precession frequency is smaller when the sensor is in the upper plane. Otherwise, when they are perpendicular to each other, the heading error is smaller when the sensor is in the lower plane. Furthermore, to suppress the heading error, we propose to utilize a small magnetic field along the propagation direction of the pump laser. By tuning the magnitude of this auxiliary field, the heading-error curve is flattened around different angles, which can increase the accuracy in practice when the magnetometer works around a certain orientation angle.
We demonstrate an all-optical magnetometer capable of measuring the magnitude and direction of a magnetic field using nonlinear magneto-optical rotation in a cesium vapor. Vector capability is added by effective modulation of the field along orthogonal axes and subsequent demodulation of the magnetic-resonance frequency. This modulation is provided by the AC Stark shift induced by circularly polarized laser beams. The sensor exhibits a demonstrated rms noise floor of 50 fT/ √ Hz in measurement of the field magnitude and 0.5 mrad/ √ Hz in the field direction; elimination of technical noise would improve these sensitivities to 12 fT/ √ Hz and 5 μrad/ √ Hz, respectively. Applications for a precise all-optical vector magnetometer would include magnetically sensitive fundamental physics experiments, such as the search for a permanent electric dipole moment of the neutron.
Atomic systems offer opportunities for noninvasive, accurate vector magnetometers that operate at ambient temperature and are conducive to miniaturization. Here, we demonstrate an unshielded three-axis vector magnetometer whose operation is based on the angle-dependent relative amplitude of cavity-enhanced magneto-optical double-resonance features in a room-temperature atomic ensemble. We determine the vector magnetic field value by sweeping the microwave frequency across all Zeeman sublevels and measuring optical transmission at seven double-resonance features, whose amplitudes vary as the orientation of the external static magnetic field (B→ext) changes with respect to the optical and microwave field polarization directions. Due to the complex dynamics of optical pumping and broadening mechanisms in the Doppler-broadened ensemble, we use a convolutional neural network model to account for details in our measurement spectra; this analysis determines the magnetic field direction with an accuracy of 1° and its amplitude with an accuracy of 56 nT measured at the near-Earth-field value of 50 μT.
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.