Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Sensors

Feedback Methods for Vector Measurements Using an All-Optical Atomic Magnetometer

Michael Bulatowicz, Jonas Tost, Thad G Walker

Published Apr 25, 2023• 3 citations
Publisher

Abstract

In this work, we look to compare three methods of feedback for the ultimate purpose of measuring the transverse vector components of a magnetic field using a synchronous light-pulse atomic scalar magnetometer with a few tens of fT/Hz sensitivity in Earth-field-scale magnetic environments. By applying modulation in the magnetic field to orthogonal axes, the respective vector components may, in principle, be separated from the scalar measurement. Success of this technique depends in significant part on the ability to measure and respond to these perturbations with low measurement uncertainty. Using high-speed least-squares fitting, the phase response of the atomic spins relative to the first harmonic of the optical pump pulse repetition rate is monitored and correspondingly adjusted into resonance with the natural Larmor precession frequency. This paper seeks to motivate and compare three distinct methods of feedback for this purpose. As a first step toward the full development of this technique, the present work uses a simplified version with modulation applied only along the bias field. All three methods investigated herein are shown to provide results that match well with the scalar magnetometer measurements and to depend on both the applied modulation amplitude and optimal feedback response to achieve low relative uncertainty.

DOI
10.3390/s23094263

Related papers

An all-optical scalar and vector spin-exchange relaxation-free magnetometer employing on–off pump modulation

Alexander Gusarov, David Levron, Andrei Ben-Amar Baranga +2 more

It is demonstrated that a spin-exchange relaxation-free (SERF) atomic magnetometer can be used for scalar measurements with no additional hardware. Because of relaxation processes, an ensemble of alkali atoms needs a constant supply of polarized photons by a pump beam to maintain a polarized state. If the pump beam is shuttered off, the system decays to its equilibrium state. For a low enough relaxation rate and with a magnetic field present, the system will exhibit oscillations at its natural frequencies. In a SERF magnetometer, it happens at the Zeeman resonance frequency of the atoms (Larmor frequency). Thus, shuttering off the pump beam reveals oscillations at the Larmor frequency. From this frequency, one can deduce the scalar value of the applied magnetic field. As a result, all-optical scalar measurements can be performed. At the same time, either one or two vector components of the applied field can be measured by using one or two orthogonal probe beams, respectively. In a low-polarization SERF regime, the ground state can be well described by the Bloch equations for the electron spin polarization. By solving the time-dependent Bloch equations [neglecting the diffusion term and assuming that the nuclear slowing-down factor q(P) is constant], the oscillation frequency of the system is obtained. From this frequency, the scalar value of the applied magnetic field is derived. It is shown that applied fields down to 1 nT can be measured with a 0.1% relative uncertainty. Fields down to 50 pT can be measured with a 10% relative uncertainty. The time dependence acquired in the “off” periods is strongly correlated with the Zeeman sublevels population of the atomic ground state and reveals its spin dynamics.

Journal of Applied Physics•Mar 22, 2011•20 citations

Static bias magnetic field assisted optical modulation triaxial SERF atomic magnetometer

Xiaoyu Li, Bangcheng Han, Shushan Gao +4 more

Abstract High-sensitivity triaxial magnetic field measurements are crucial in various scientific and industrial applications, with spin-exchange relaxation-free (SERF) atomic magnetometers (AMs) standing out for their exceptional sensitivity. However, conventional methods for achieving triaxial measurements in SERF magnetometers typically involve multiple modulated magnetic fields, which introduce crosstalk challenges in array-based configurations. We propose a static bias magnetic field assisted optical modulation triaxial AM to address this limitation. In this configuration, the detuned circularly polarized light is utilized to achieve synchronous modulation of the fictitious magnetic field and pumping rate while incorporating a static bias magnetic field to generate a transverse projection component. We develop a comprehensive triaxial response model that fully considers the effects of the longitudinal spin polarization deflection. Building upon this model, we derive the relationship between the transverse spin component and the triaxial magnetic field and introduce parameter optimization methods to obtain optimal parameters, thus enabling triaxial measurements of 12 fT Hz −1/2 , 10 fT Hz −1/2 , and 15 fT Hz −1/2 along the x-, y -, and z -axes. Our approach offers significant advantages over existing methods, particularly in minimizing crosstalk and mitigating spin-exchange relaxation introduced by multiple modulated magnetic fields. Moreover, the effective detection of simulated magnetocardiography signals highlights the practical applicability and reliability of the proposed method in real-world scenarios.

Measurement Science and Technology•Nov 7, 2025•2 citations

Pulsed vector atomic magnetometer using an alternating fast-rotating field

Tao Wang, Wonjae Lee, Mark E. Limes +3 more

Abstract We introduce a vector atomic magnetometer that employs a fast-rotating magnetic field applied to a pulsed 87Rb scalar atomic magnetometer. This approach enables simultaneous measurements of the total magnetic field and its two polar angles relative to the rotation plane. Operating in gradiometer mode, the magnetometer achieves a total field gradient sensitivity of 35 $${{{\rm{fT}}}}/\sqrt{{{{\rm{Hz}}}}}$$ fT / Hz (0.7 parts per billion) and angular resolutions of 6 $${{{\rm{nrad}}}}/\sqrt{{{{\rm{Hz}}}}}$$ nrad / Hz at a 50 μT Earth field strength. The noise spectra remain flat down to 1 Hz and 0.1 Hz, respectively. Here we show that this method overcomes several metrological challenges commonly faced by vector magnetometers and gradiometers. We propose a unique peak-altering modulation technique to mitigate systematic effects, including a newly identified dynamic heading error. Additionally, we establish the fundamental sensitivity limits of the sensor, demonstrating that its vector sensitivity approaches scalar sensitivity while preserving the inherent accuracy and calibration benefits of scalar sensors. This high-dynamic-range, ultrahigh-resolution magnetometer offers exceptional versatility for diverse applications.

arXiv:2304.00214•Nature Communications•Feb 5, 2025•29 citations

Three-axis atomic magnetometer based on spin precession modulation

Hao Huang, Hai Feng Dong, Xiaofei Hu +2 more

We demonstrate a three-axis atomic magnetometer with one intensity-modulated pump beam and one orthogonal probe beam. The main field component is measured using the resonance of the pumping light, while the transverse field components are measured simultaneously using the optical rotation of the probe beam modulated by the spin precession. It is an all-optical magnetometer without using any modulation field or radio frequency field. Magnetic field sensitivity of 0.8 pT/Hz1∕2 is achieved under a bias field of 2 μT.

Applied Physics Letters•Nov 2, 2015•60 citations

Vector measurements using all optical scalar atomic magnetometers

Rui Zhang, Rahul Mhaskar, Ken Smith +2 more

Vector field measurement is demonstrated with an all-optical scalar atomic magnetometer using intrinsic parameters related to its scalar operation. The Bell-Bloom type atomic magnetometer measures the Larmor precession of cesium atoms through on-resonant absorption of a probe beam. While the AC component of the probe signal is used for the field magnitude measurement, the probe DC signal contains information about the polar angle, defined as the angle between the magnetic field and the probe beam. Additional polar angle information is obtained from the light-shift-induced magnetic field caused by the frequency modulation of the probe beam. With a measurement time of 100 ms, better than 0.02° sensitivity has been achieved using a commercial miniaturized sensor at the optimal sensor orientation. The angle measurement accuracy is checked against an optical encoder over the entire polar angle range of 0°–180°. Better than 1° error is recorded over most set polar angles. Azimuthal angle measurement is also exhibited with two orthogonally oriented sensors.

arXiv:2011.08943•Journal of Applied Physics•Jan 28, 2021•17 citations

All Optical Scalar Atomic Magnetometer Capable of Vector Measurement

Rui Zhang, Rahul R. Mhaskar, Ken A. Smith +2 more

Vector field measurement is demonstrated with an all-optical scalar atomic magnetometer using intrinsic parameters related to its scalar operation. The Bell-Bloom type atomic magnetometer measures the Larmor precession of cesium atoms through on-resonant absorption of a probe beam. While the AC component of the probe signal is used for the field magnitude measurement, the probe DC signal contains information about the polar angle, defined as the angle between the magnetic field and the probe beam. Additional polar angle information is obtained from the light-shift-induced magnetic field caused by the frequency modulation of the probe beam. With a measurement time of 100 milliseconds, better than 0.02 degree sensitivity has been achieved using a commercial miniaturized sensor at the optimal sensor orientation. The angle measurement accuracy is checked against an optical encoder over the entire polar angle range of 0 to 180 degrees. Better than 1 degree error is recorded over most set polar angles. Azimuthal angle measurement is also exhibited with an additional orthogonally oriented sensor.

•Nov 17, 2020•0 citations
In this work, we look to compare three methods of feedback for the ultimate purpose of measuring the transverse vector components of a magnetic field using a synchronous light-pulse atomic scalar magnetometer with a few tens of fT/Hz sensitivity in Earth-field-scale magnetic environments. By applying modulation in the magnetic field to orthogonal axes, the respective vector components may, in principle, be separated from the scalar measurement. Success of this technique depends in significant part on the ability to measure and respond to these perturbations with low measurement uncertainty. Using high-speed least-squares fitting, the phase response of the atomic spins relative to the first harmonic of the optical pump pulse repetition rate is monitored and correspondingly adjusted into resonance with the natural Larmor precession frequency. This paper seeks to motivate and compare three distinct methods of feedback for this purpose. As a first step toward the full development of this technique, the present work uses a simplified version with modulation applied only along the bias field. All three methods investigated herein are shown to provide results that match well with the scalar magnetometer measurements and to depend on both the applied modulation amplitude and optimal feedback response to achieve low relative uncertainty.
It is demonstrated that a spin-exchange relaxation-free (SERF) atomic magnetometer can be used for scalar measurements with no additional hardware. Because of relaxation processes, an ensemble of alkali atoms needs a constant supply of polarized photons by a pump beam to maintain a polarized state. If the pump beam is shuttered off, the system decays to its equilibrium state. For a low enough relaxation rate and with a magnetic field present, the system will exhibit oscillations at its natural frequencies. In a SERF magnetometer, it happens at the Zeeman resonance frequency of the atoms (Larmor frequency). Thus, shuttering off the pump beam reveals oscillations at the Larmor frequency. From this frequency, one can deduce the scalar value of the applied magnetic field. As a result, all-optical scalar measurements can be performed. At the same time, either one or two vector components of the applied field can be measured by using one or two orthogonal probe beams, respectively. In a low-polarization SERF regime, the ground state can be well described by the Bloch equations for the electron spin polarization. By solving the time-dependent Bloch equations [neglecting the diffusion term and assuming that the nuclear slowing-down factor q(P) is constant], the oscillation frequency of the system is obtained. From this frequency, the scalar value of the applied magnetic field is derived. It is shown that applied fields down to 1 nT can be measured with a 0.1% relative uncertainty. Fields down to 50 pT can be measured with a 10% relative uncertainty. The time dependence acquired in the “off” periods is strongly correlated with the Zeeman sublevels population of the atomic ground state and reveals its spin dynamics.
Abstract High-sensitivity triaxial magnetic field measurements are crucial in various scientific and industrial applications, with spin-exchange relaxation-free (SERF) atomic magnetometers (AMs) standing out for their exceptional sensitivity. However, conventional methods for achieving triaxial measurements in SERF magnetometers typically involve multiple modulated magnetic fields, which introduce crosstalk challenges in array-based configurations. We propose a static bias magnetic field assisted optical modulation triaxial AM to address this limitation. In this configuration, the detuned circularly polarized light is utilized to achieve synchronous modulation of the fictitious magnetic field and pumping rate while incorporating a static bias magnetic field to generate a transverse projection component. We develop a comprehensive triaxial response model that fully considers the effects of the longitudinal spin polarization deflection. Building upon this model, we derive the relationship between the transverse spin component and the triaxial magnetic field and introduce parameter optimization methods to obtain optimal parameters, thus enabling triaxial measurements of 12 fT Hz −1/2 , 10 fT Hz −1/2 , and 15 fT Hz −1/2 along the x-, y -, and z -axes. Our approach offers significant advantages over existing methods, particularly in minimizing crosstalk and mitigating spin-exchange relaxation introduced by multiple modulated magnetic fields. Moreover, the effective detection of simulated magnetocardiography signals highlights the practical applicability and reliability of the proposed method in real-world scenarios.
Abstract We introduce a vector atomic magnetometer that employs a fast-rotating magnetic field applied to a pulsed 87Rb scalar atomic magnetometer. This approach enables simultaneous measurements of the total magnetic field and its two polar angles relative to the rotation plane. Operating in gradiometer mode, the magnetometer achieves a total field gradient sensitivity of 35 fT/Hz{{{\rm{fT}}}}/\sqrt{{{{\rm{Hz}}}}}fT/Hz​ fT / Hz (0.7 parts per billion) and angular resolutions of 6 nrad/Hz{{{\rm{nrad}}}}/\sqrt{{{{\rm{Hz}}}}}nrad/Hz​ nrad / Hz at a 50 μT Earth field strength. The noise spectra remain flat down to 1 Hz and 0.1 Hz, respectively. Here we show that this method overcomes several metrological challenges commonly faced by vector magnetometers and gradiometers. We propose a unique peak-altering modulation technique to mitigate systematic effects, including a newly identified dynamic heading error. Additionally, we establish the fundamental sensitivity limits of the sensor, demonstrating that its vector sensitivity approaches scalar sensitivity while preserving the inherent accuracy and calibration benefits of scalar sensors. This high-dynamic-range, ultrahigh-resolution magnetometer offers exceptional versatility for diverse applications.
We demonstrate a three-axis atomic magnetometer with one intensity-modulated pump beam and one orthogonal probe beam. The main field component is measured using the resonance of the pumping light, while the transverse field components are measured simultaneously using the optical rotation of the probe beam modulated by the spin precession. It is an all-optical magnetometer without using any modulation field or radio frequency field. Magnetic field sensitivity of 0.8 pT/Hz1∕2 is achieved under a bias field of 2 μT.
Vector field measurement is demonstrated with an all-optical scalar atomic magnetometer using intrinsic parameters related to its scalar operation. The Bell-Bloom type atomic magnetometer measures the Larmor precession of cesium atoms through on-resonant absorption of a probe beam. While the AC component of the probe signal is used for the field magnitude measurement, the probe DC signal contains information about the polar angle, defined as the angle between the magnetic field and the probe beam. Additional polar angle information is obtained from the light-shift-induced magnetic field caused by the frequency modulation of the probe beam. With a measurement time of 100 ms, better than 0.02° sensitivity has been achieved using a commercial miniaturized sensor at the optimal sensor orientation. The angle measurement accuracy is checked against an optical encoder over the entire polar angle range of 0°–180°. Better than 1° error is recorded over most set polar angles. Azimuthal angle measurement is also exhibited with two orthogonally oriented sensors.
Vector field measurement is demonstrated with an all-optical scalar atomic magnetometer using intrinsic parameters related to its scalar operation. The Bell-Bloom type atomic magnetometer measures the Larmor precession of cesium atoms through on-resonant absorption of a probe beam. While the AC component of the probe signal is used for the field magnitude measurement, the probe DC signal contains information about the polar angle, defined as the angle between the magnetic field and the probe beam. Additional polar angle information is obtained from the light-shift-induced magnetic field caused by the frequency modulation of the probe beam. With a measurement time of 100 milliseconds, better than 0.02 degree sensitivity has been achieved using a commercial miniaturized sensor at the optimal sensor orientation. The angle measurement accuracy is checked against an optical encoder over the entire polar angle range of 0 to 180 degrees. Better than 1 degree error is recorded over most set polar angles. Azimuthal angle measurement is also exhibited with an additional orthogonally oriented sensor.