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Applied Physics Letters

Microwave-optical double-resonance vector magnetometry with warm Rb atoms

Bahar Babaei, Benjamin D. Smith, Andrei Tretiakov, Andal Narayanan, Lindsay J. LeBlanc

Published May 4, 2026• 1 citation
Publisher

Abstract

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.

DOI
10.1063/5.0323832

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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.
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.
Here, we describe progress toward realization of a vector magnetometer based on all-optical excitation of an atomic ensemble in a vapor cell under the conditions of electromagnetically induced transparency (EIT). The EIT resonance amplitudes depend on relative orientations of the three key vectors: laser wave-vector, polarization, and the direction of the magnetic field. By analyzing possible two-photon transitions and their combinations, we can, in principle, analytically calculate the amplitude of various EIT resonances as functions of the relative angles between the magnetic field, polarization and laser propagation vectors. By locking the polarization to one of these maxima, one can determine the plane formed by the magnetic field and the light wave vector to the accuracy better than 0.001 rad. Analysis of the relative resonance amplitude may be used to extract the full information about the magnetic field direction.
Double-resonance optically pumped magnetometry can be used to measure static magnetic fields with high sensitivity by detecting a resonant atomic spin response to a small oscillating field perturbation. Determination of the resonant frequency yields a scalar measurement of static field (B0)({B}_{0})(B0​) magnitude. We present calculations and experimental data showing that the on-resonance polarimeter signal of light transmitted through an atomic vapor in arbitrarily oriented B0{B}_{0}B0​ may be modeled by considering the evolution of alignment terms in atomic polarization. We observe that the amplitude and phase of the magnetometer signal are highly dependent upon B0{B}_{0}B0​ orientation and present precise measurements of the distribution of these parameters over the full $4\ensuremath{\pi}$ solid angle.
Quantum optical sensing is a maturing field that offers the capability to achieve extraor- dinary sensitivity. Atomic magnetometers, for example, now have the capability to detect brain signals and to precisely measure Earth’s gravity field. In optical atomic magnetome- ters, the electronic spins of the atoms in vapor form are aligned in the same direction by “pumping” the ensemble using laser light at a select frequency. Any magnetic field alters the spin states, which changes the optical properties of the vapor, such as the transmission of the laser light, providing a way to measure magnetic fields. After reviewing the theory of atomic structure and atom-light interactions relevant to the research presented here, I describe in the first part of this thesis a vector magnetometry method using microwave-assisted optical pumping, in which a microwave field resonant to the ground state hyperfine splitting of 87Rb pumps an ensemble of warm rubidium vapor, in addition to a strong optical pump beam, and a weaker optical probe beam. I present theoretical details as well as preliminary data demonstrating magnetic field measurements of a DC magnetic field. The measurements were taken when the DC field was aligned at various angles relative to the microwave magnetic field alignment. I compare theoretical and experimental differences in the measurements. With new methods for quantum devices comes the need for portability. In the second part of this thesis, we demonstrate the fabrication of millimeter-sized rubidium vapor cells using silicon micro-machining techniques. This method is relatively inexpensive compared to glass-blowing methods and allows rapid, large-scale production. I describe our process flow and demonstrate the presence of rubidium atoms inside our vapor cells. To conclude, suggestions for improvement are discussed.
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.
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.