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arXiv:2310.11017 · Physical Review Applied

Correcting heading errors in optically pumped magnetometers through microwave interrogation

Christopher Kiehl, Thanmay S. Menon, D. P. Hewatt, Svenja A. Knappe, Tobias Thiele, Cindy A. Regal

Published Jul 2, 2024• 12 citations
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Abstract

We demonstrate how to measure in situ for heading errors of optically pumped magnetometers (OPMs) in the challenging parameter regime of compact vapor cells with imperfect optical pumping and high buffer gas pressure. For this, we utilize microwave-driven Ramsey and Rabi frequency spectroscopy (FS) to independently characterize scalar heading errors in free-induction-decay (FID) signals. Both of these approaches suppress 5-nT inaccuracies in geomagnetic fields caused by nonlinear Zeeman shifts in FID measurements to below 0.6 nT. For Ramsey FS, we implement short periods of microwave interrogation within a $\ensuremath{\pi}/2\text{\ensuremath{-}}{t}_{R}\text{\ensuremath{-}}3\ensuremath{\pi}/2$ Ramsey interferometry sequence, effectively circumventing systematic errors from off-resonant driving. Conversely, Rabi FS leverages an atom-microwave Hamiltonian for accurate modeling of Rabi oscillation frequencies, achieving a measurement precision down to $80\phantom{\rule{0.2em}{0ex}}\mathrm{pT}/\sqrt{\text{Hz}}$ that is limited primarily by technical microwave noise. We show that the fundamental sensitivity of Rabi FS is $30\phantom{\rule{0.2em}{0ex}}\mathrm{pT}/\sqrt{\text{Hz}}$ with our vapor cell parameters through a Cram\'er-Rao lower-bound analysis. This work paves the way for future investigations into the accuracy of hyperfine structure magnetometry and contributes to the broader applicability of OPMs in fields ranging from navigation and geophysics to space exploration and unexploded ordinance detection, where heading error mitigation is essential.

DOI
10.1103/physrevapplied.22.014005

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We demonstrate how to measure in situ for heading errors of optically pumped magnetometers (OPMs) in the challenging parameter regime of compact vapor cells with imperfect optical pumping and high buffer gas pressure. For this, we utilize microwave-driven Ramsey and Rabi frequency spectroscopy (FS) to independently characterize scalar heading errors in free-induction-decay (FID) signals. Both of these approaches suppress 5-nT inaccuracies in geomagnetic fields caused by nonlinear Zeeman shifts in FID measurements to below 0.6 nT. For Ramsey FS, we implement short periods of microwave interrogation within a \ensuremathπ/2\ensuremath-tR\ensuremath-3\ensuremathπ/2\ensuremath{\pi}/2\text{\ensuremath{-}}{t}_{R}\text{\ensuremath{-}}3\ensuremath{\pi}/2\ensuremathπ/2\ensuremath-tR​\ensuremath-3\ensuremathπ/2 Ramsey interferometry sequence, effectively circumventing systematic errors from off-resonant driving. Conversely, Rabi FS leverages an atom-microwave Hamiltonian for accurate modeling of Rabi oscillation frequencies, achieving a measurement precision down to 80pT/Hz80\phantom{\rule{0.2em}{0ex}}\mathrm{pT}/\sqrt{\text{Hz}}80pT/Hz​ that is limited primarily by technical microwave noise. We show that the fundamental sensitivity of Rabi FS is 30pT/Hz30\phantom{\rule{0.2em}{0ex}}\mathrm{pT}/\sqrt{\text{Hz}}30pT/Hz​ with our vapor cell parameters through a Cram'er-Rao lower-bound analysis. This work paves the way for future investigations into the accuracy of hyperfine structure magnetometry and contributes to the broader applicability of OPMs in fields ranging from navigation and geophysics to space exploration and unexploded ordinance detection, where heading error mitigation is essential.
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.
Light-atom interactions during spin preparation and readout in optically pumped magnetometers can lead to inaccuracies. We demonstrate a novel, to the best of our knowledge, detection strategy that exploits an interrogation sequence in the pulsed free-induction-decay modality to suppress these systematic errors. The technique is predicated on monitoring the dynamics of preoriented atomic spins as they evolve unperturbed during a dark interval, by subsequently applying a time-delayed optical pulse to infer the spin state's phase. This detection mode reduced light shift inaccuracies to within 0.6 nT, and could be employed in a wide variety of high-precision atomic magnetometry experiments.
Abstract Heading error is a major limitation for resonance-based atomic magnetometers operating in the geomagnetic-field range, where the magnetic-field direction often changes with respect to the sensor. Here, we investigate the physical origin of heading error in a single-beam amplitude-modulated nonlinear magneto-optical rotation magnetometer based on the hyperfine alignment resonances of the 87 Rb D1 line in a buffer-gas vapor cell. Unlike orientation-based magnetometers, where nonlinear Zeeman effects usually constitute a major source of heading error, the F = 2 alignment resonance spectrum maintains a stable center frequency under different magnetic-field orientations when the individual resonance components are unresolved. In practical single-beam measurements, the observed heading error is associated with an orientation-dependent residual spectral background, which breaks the apparent symmetry of the alignment-resonance profile and biases the extracted center frequency. To suppress this background-induced bias, we propose a multi-point frequency extraction method that retrieves the resonance center from distorted single-beam spectra. In unshielded geomagnetic-field measurements, the equal-weight pooled peak-to-peak heading-error estimate for the F = 2 manifold is reduced to 0.32 nT, with a one-sided 95% upper coverage limit of 0.90 nT. Separately, an estimated photon-shot-noise-limited sensitivity of about 23 fT / Hz 1 / 2 is obtained. These results provide a compact route to low-heading-error and high-sensitivity atomic magnetometry for practical geomagnetic-field quantum sensing.
Alkali-metal optically-pumped magnetometers are prone to inaccuracies arising from the overlap of the average F = I + 1/2 and F = I - 1/2 ground-state Zeeman resonances. We employ density-matrix simulations and experiments to investigate how this hyperfine systematic error varies with spin polarization in a 87^{87}87Rb free-induction-decay (FID) magnetometer. At low spin polarizations, (P≤0.5P \leq 0.5P≤0.5), this effect causes single-frequency magnetic-field extraction techniques to exhibit inaccuracies up to approximately 3.5 nT. Density-matrix simulations reveal that this bias can be traced to the relative amplitude and phase between the F = I ±\pm± 1/2 hyperfine ground-state manifolds in the FID spin precession signal. We show that this systematic error can be mitigated using either a double-frequency fitting model that accounts for the relative amplitude and phase or synchronous-pulse pumping, that minimizes the F = 1 contribution to the FID signal. Theoretical simulations predict accuracies within 0.5 nT for both techniques across a wide range of spin polarizations, suggesting a sevenfold enhancement over single-frequency extraction methods. Our experiments validate this, showcasing a variation in the extracted field below 1 nT, a 3.5-fold improvement compared to single-frequency extraction methods. Furthermore, the mitigation techniques demonstrate agreement of the extracted magnetic field within 1.5 nT.
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.
We demonstrate an optically pumped magnetometer (OPM) operated in a free-induction-decay (FID) configuration that is capable of tracking oscillating magnetic signals in the presence of a 50 μT static field. Excellent waveform reconstruction is demonstrated for low frequency modulations with respect to the Nyquist limited bandwidth. A 100 pT oscillation was successfully reconstructed using signal averaging, and an optimum sensitivity of 3.9 pT/Hz was measured from the spectrum of the residuals relative to the sinusoidal fit. The impact of the pump-probe repetition rate and spin depolarization on the frequency response of the sensor is investigated in detail using miniaturized vapor cell technology, with the (-3 dB) bandwidths residing beyond the Nyquist limit in each case. We also discuss technical limitations associated with the magnetometer when exposed to oscillating fields of sufficiently high amplitude or frequency. This is discussed in the context of potential distortions arising in the reproduced signals, induced by frequency modulation (FM) and aliasing artefacts.