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arXiv:2409.20446 · EPJ Quantum Technology

Phase projection errors in rf-driven optically pumped magnetometers

Z. D. Grujić, M. M. Ćurčić, Aleksandra Kocić, Antoine Weis, Theo Scholtes

Published May 8, 2026• 0 citations
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Abstract

Abstract We investigate the phase relationship between the oscillating (rf) excitation field and the detected (light) power modulation in scalar rf-driven optically pumped magnetometers (OPMs), in particular in the $M_{x}$ M x configuration. While the static dependence of the demodulation phase on the direction of the external static magnetic field vector can be largely mitigated by aligning the oscillating rf field along the light propagation direction, we demonstrate that a dynamic (transient) phase response arises under magnetic field tilts. We analytically solve the corresponding modified Bloch equation and confirm agreement with experimental observations obtained using an $M_{x}$ M x magnetometer incorporating a paraffin-coated Cs vapor cell. The results reveal fundamental limitations of $M_{x}$ M x magnetometers regarding response time and accuracy, in particular when employed with active electronic feedback, such as a phase-locked loop. Therefore, this work is highly relevant to important magnetometry applications where the direction of the quasi-static magnetic field of interest is unknown a priori or varies over time, or in measurements requiring a large detection bandwidth. Such conditions are encountered in applications such as geomagnetic surveying, particularly with mobile platforms.

DOI
10.1140/epjqt/s40507-026-00517-8

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Abstract We investigate the phase relationship between the oscillating (rf) excitation field and the detected (light) power modulation in scalar rf-driven optically pumped magnetometers (OPMs), in particular in the MxM_{x}Mx​ M x configuration. While the static dependence of the demodulation phase on the direction of the external static magnetic field vector can be largely mitigated by aligning the oscillating rf field along the light propagation direction, we demonstrate that a dynamic (transient) phase response arises under magnetic field tilts. We analytically solve the corresponding modified Bloch equation and confirm agreement with experimental observations obtained using an MxM_{x}Mx​ M x magnetometer incorporating a paraffin-coated Cs vapor cell. The results reveal fundamental limitations of MxM_{x}Mx​ M x magnetometers regarding response time and accuracy, in particular when employed with active electronic feedback, such as a phase-locked loop. Therefore, this work is highly relevant to important magnetometry applications where the direction of the quasi-static magnetic field of interest is unknown a priori or varies over time, or in measurements requiring a large detection bandwidth. Such conditions are encountered in applications such as geomagnetic surveying, particularly with mobile platforms.
Optically pumped magnetometers (OPMs) have demonstrated significant potential in weak magnetic field detection due to their high sensitivity. In this study, we developed an Mz-type optically pumped rubidium magnetometer using a paraffin-coated anti-relaxation vapor cell. The system optimization and performance characterization were conducted inside a magnetic shield. Specifically, the pump light intensity and radio-frequency (RF) magnetic field were jointly optimized by using the linewidth-amplitude ratio as the core metric. Based on the frequency-domain noise spectrum, the sensitivity in open-loop mode was measured to be approximately 30.8 pT/Hz^{1/2}. Furthermore, a closed-loop feedback locking technique was applied, reducing the measured noise floor under the tested conditions and improving the sensitivity to 22.9 pT/Hz^{1/2}, with a measured -3 dB bandwidth of 123 Hz. The dynamic characteristics were evaluated via magnetic-field step response, showing that the system could track magnetic-field changes stably under closed-loop operation. Finally, by using tri-axial modulation and frequency-domain demodulation, we overcame the scalar measurement limitation of traditional Mz magnetometers. This work realizes vector magnetic field detection and provides a technical basis for applications such as geomagnetic navigation and magnetic anomaly detection.
Abstract We have investigated the dependence of lock-in-demodulated Mx {M}_x Mx​ M x -magnetometer signals on the orientation of the static magnetic field B0 {\mathbf{B}}_0 B0​ B 0 of interest. Magnetic resonance spectra for 2400 discrete orientations of B0 {\mathbf{B}}_0 B0​ B 0 covering a 4π 4\pi 4π 4 π solid angle have been recorded by a PC-controlled steering and data acquisition system. Off-line fits by previously derived lineshape functions allow us to extract the relevant resonance parameters (shape, amplitude, width, and phase) and to represent their dependence on the orientation of B0 {\mathbf{B}}_0 B0​ B 0 with respect to the laser beam propagation direction. We have performed this study for two distinct Mx {M}_x Mx​ M x -magnetometer configurations, in which the rf-field is either parallel or perpendicular to the light propagation direction. The results confirm well the algebraic theoretical model functions. We suggest that small discrepancies are related to hitherto uninvestigated atomic alignment contributions.
Optically pumped magnetometers (OPMs) have demonstrated significant potential in weak magnetic field detection due to their high sensitivity. In this study, we developed an Mz-type optically pumped rubidium magnetometer using a paraffin-coated anti-relaxation vapor cell. The system optimization and performance characterization were conducted inside a magnetic shield. Specifically, the pump light intensity and radio-frequency (RF) magnetic field were jointly optimized by using the linewidth-amplitude ratio as the core metric. Based on the frequency-domain noise spectrum, the sensitivity in open-loop mode was measured to be approximately 30.8pT/Hz 1/2 . Furthermore, a closed-loop feedback locking technique was applied, reducing the measured noise floor under the tested conditions and improving the sensitivity to 22.9pT/Hz 1/2 , with a measured −3dB bandwidth of 123 Hz. The dynamic characteristics were evaluated via magnetic-field step response, showing that the system could track magnetic-field changes stably under closed-loop operation. Finally, by using tri-axial modulation and frequency-domain demodulation, we overcame the scalar measurement limitation of traditional Mz magnetometers. This work realizes vector magnetic field detection and provides a technical basis for applications such as geomagnetic navigation and magnetic anomaly detection.
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.
We have investigated the dependence of lock-in-demodulated MxM_xMx​ -magnetometer signals on the orientation of the static magnetic field B0\mathbf {B}_{0}B0​ of interest. Magnetic resonance spectra for 2400 discrete orientations of B0\mathbf {B}_{0}B0​ covering a 4π4\pi4π solid angle have been recorded by a PC-controlled steering and data acquisition system. Off-line fits by previously derived lineshape functions allow us to extract the relevant resonance parameters (shape, amplitude, width, and phase) and to represent their dependence on the orientation of B0\mathbf {B}_{0}B0​ with respect to the laser beam propagation direction. We have performed this study for two distinct MxM_xMx​ -magnetometer configurations, in which the rf-field is either parallel or perpendicular to the light propagation direction. The results confirm well the algebraic theoretical model functions. We suggest that small discrepancies are related to hitherto uninvestigated atomic alignment contributions.
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.