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

Chinese Physics B

A modified analytical model of the alkali-metal atomic magnetometer employing longitudinal carrier field*

Chang Chen, Yi Zhang, Zhiguo Wang, Qiyuan Jiang, Hui Luo, Kaiyong Yang

Published Jan 4, 2021• 3 citations
Publisher

Abstract

Alkali-metal atomic magnetometers employing longitudinal carrier magnetic field have ultrahigh sensitivity to measure transverse magnetic fields and have been applied in a variety of precise-measurement science and technologies. In practice, the magnetometer response is not rigorously proportional to the measured transverse magnetic fields and the existing fundamental analytical model of this magnetometer is effective only when the amplitudes of the measured fields are very small. In this paper, we present a modified analytical model to characterize the practical performance of the magnetometer more definitely. We find out how the longitudinal magnetization of the alkali metal atoms vary with larger transverse fields. The linear-response capacity of the magnetometer is determined by these factors: the amplitude and frequency of the longitudinal carrier field, longitudinal and transverse spin relaxation time of the alkali spins and rotation frequency of the transverse fields. We give a detailed and rigorous theoretical derivation by using the perturbation-iteration method and simulation experiments are conducted to verify the validity and correctness of the proposed modified model. This model can be helpful for measuring larger fields more accurately and configuring a desirable magnetometer with proper linear range.

DOI
10.1088/1674-1056/abd7d3

Related papers

In situ determination of alkali metal density using phase-frequency analysis on atomic magnetometers

Han Yao, Hong Zhang, Danyue Ma +2 more

Abstract The alkali number density inside the sealed vapor cell restricts the fundamental sensitivity of the atomic magnetometer and may decrease in the long term, thus motivating the investigation of an in situ density determination method on atomic magnetometers. This paper presents a method to measure the alkali number density, which is proportional to the spin-exchange relaxation rate, through phase-frequency analysis. The magnetic resonance response of the atomic magnetometer was actively strengthened at low polarization by increasing the oscillating field amplitude. To downplay the side effect of the transverse field broadening, phase-frequency analysis was applied to extract the transverse relaxation time limited by spin-exchange collisions. The experimental results coincided well with the saturated vapor pressure curve ranging from 413 K to 463 K. Calculated densities were approximately 0.779–0.992 times those of predictions. The density measurement accuracy was improved compared to traditional methods.

Measurement Science and Technology•Jul 6, 2018•8 citations

The influence of longitudinal magnetic-field gradient on the transverse relaxation rate of cesium atoms

Y. Fu, Jiayue Yuan

Reducing the transverse relaxation rate of alkali atoms is crucial to improve the sensitivity of the magnetometers. In a perturbative treatment of the effects of the magnetic-field gradients, the transverse relaxation rates of alkali atoms are predicted to be proportional to the square of the longitudinal magnetic-field gradient. The theoretical predictions are confirmed in our experiments. The magnetic-field gradients in the vapor cell are measured by experiments. The magnetic-field gradient in the cell is suppressed drastically through compensating it with the compensation coils. Experimental results show that suppressing the magnetic-field gradient can reduce the transverse relaxation rate of alkali atoms significantly. This study contributes to the development of ultra-high sensitivity alkali atomic magnetometers.

AIP Advances•Nov 1, 2017•9 citations

Zero-field atomic magnetometer to extract longitudinal magnetic field

Shuying Wang, Jixi Lu, Kaixuan Zhang +3 more

Zero-field atomic ensembles enable the development of ultrahigh-sensitivity magnetometry. However, their intrinsic insensitivity to longitudinal magnetic fields along the pumping direction poses a fundamental limitation, restricting precise weak-field quantification and complex system decoupling. Herein, we propose a novel zero-field weak parametric modulation scheme capable of ultrahigh-sensitivity extraction of longitudinal magnetic fields. Transverse modulation is employed to manifest the electron spin polarization projection induced by the longitudinal fields. Based on the perturbation model established, first-order parametric resonance associated with the longitudinal magnetic field yields significant signal enhancement under low-frequency and weak modulation conditions, while simultaneously suppressing spin-exchange relaxation caused by magnetic field modulation. We experimentally achieved a longitudinal measurement sensitivity of 16 fT / Hz 1 / 2 , more than an order of magnitude improved over traditional schemes, with a bandwidth of 70 Hz. Benefiting from low spin relaxation, the noise floor of the transverse magnetic field measurement is preserved at 4 fT / Hz 1 / 2 . The proposed scheme pushes the boundaries of existing weak magnetic field measurement, providing critical capabilities for state-of-the-art precision experiments including new physical quantity detection.

Physical Review Research•Jul 18, 2025•5 citations

Three-Axis Atomic Magnetometer Employing Longitudinal Field Modulation

Zhichao Ding, Jie Yuan, Guangfeng Lu +2 more

A three-axis atomic magnetometer employing longitudinal field modulation is demonstrated theoretically and experimentally. The operational condition of this magnetometer is that the longitudinal z-component of the external magnetic field is dominant, which is achieved by applying a bias magnetic field. The longitudinal z-component of the external magnetic field is extracted from the modulation frequency, which tracks the resonance frequency, and the transversex- andy- components are, respectively, obtained from the quadrature and the in-phase signals of a lock-in amplifier. Through feedback control, the magnitude and direction of an external magnetic field can be measured in real time, and an excellent orthogonality of the three-axis magnetometer response is obtained. By optimizing the parameters of this three-axis magnetometer, a longitudinal field sensitivity of 0.3${\rm{pT}/ \rm{Hz}}^{1/ 2}$and a transverse field sensitivity of 2${\rm{pT}/ \rm{Hz}}^{1/ 2}$are achieved.

IEEE photonics journal•Aug 24, 2017•32 citations

Nuclear slowing-down factors in alkali-metal vapors

Vasiliki Koutrouli, Georgios Vasilakis, Kostas Mouloudakis

Nuclear slowing-down factors account for the sharing of angular momentum between the electron and the nucleus in the effective Bloch description of alkali-metal spin dynamics in the spin-exchange-relaxation-free (SERF) regime. For collinear optical pumping and magnetic field, we find that longitudinal and transverse spin dynamics are characterized by different polarization-dependent slowing-down factors. Transverse dynamics are governed by the conventional factor $q(p)$, with $p$ the electron spin polarization, whereas longitudinal relaxation is governed by $q(p)+p\,dq(p)/dp$. The two factors coincide at zero polarization but differ substantially at high polarization, where the single-factor description overestimates the underlying pumping and relaxation rates inferred from longitudinal transients by factors approaching two to four, depending on the nuclear spin. We further derive closed-form expressions, valid at arbitrary polarization, for the residual spin-exchange relaxation of the transverse spin components at finite magnetic field along the pumping axis. This contribution is quadratic in the magnetic field and can become comparable to the zero-field linewidth at fields well within the SERF regime. The results are obtained by perturbation theory on the density-matrix dynamics linearized around the stationary state and are verified by numerical solutions of the microscopic density-matrix equation. These findings refine the effective Bloch description of alkali-metal spin dynamics and are directly relevant to atomic magnetometers and alkali-metal--noble-gas comagnetometers, including those used in precision searches for physics beyond the Standard Model.

physics.atom-phCross-listedarXiv:2609.08261•Sep 9, 2026•0 citations

Tunable Atomic Magnetometer for Detection of Radio-Frequency Magnetic Fields

Igor Savukov, Scott J. Seltzer, Michael V. Romalis +1 more

We describe an alkali-metal magnetometer for detection of weak magnetic fields in the radio-frequency (rf) range. High sensitivity is achieved by tuning the Zeeman resonance of alkali atoms to the rf frequency and partially suppressing spin-exchange collisions in the alkali-metal vapor. We demonstrate magnetic field sensitivity of 2 fT/Hz(1/2) at a frequency of 99 kHz with a resonance width of 400 Hz. We also derive a simple analytic expression for the fundamental limit on the sensitivity of the rf magnetometer and show that a sensitivity of about 0.01 fT/Hz(1/2) can be achieved in a practical system with a measurement volume of 200 cm3.

Physical Review Letters•Aug 3, 2005•312 citations
Alkali-metal atomic magnetometers employing longitudinal carrier magnetic field have ultrahigh sensitivity to measure transverse magnetic fields and have been applied in a variety of precise-measurement science and technologies. In practice, the magnetometer response is not rigorously proportional to the measured transverse magnetic fields and the existing fundamental analytical model of this magnetometer is effective only when the amplitudes of the measured fields are very small. In this paper, we present a modified analytical model to characterize the practical performance of the magnetometer more definitely. We find out how the longitudinal magnetization of the alkali metal atoms vary with larger transverse fields. The linear-response capacity of the magnetometer is determined by these factors: the amplitude and frequency of the longitudinal carrier field, longitudinal and transverse spin relaxation time of the alkali spins and rotation frequency of the transverse fields. We give a detailed and rigorous theoretical derivation by using the perturbation-iteration method and simulation experiments are conducted to verify the validity and correctness of the proposed modified model. This model can be helpful for measuring larger fields more accurately and configuring a desirable magnetometer with proper linear range.
Abstract The alkali number density inside the sealed vapor cell restricts the fundamental sensitivity of the atomic magnetometer and may decrease in the long term, thus motivating the investigation of an in situ density determination method on atomic magnetometers. This paper presents a method to measure the alkali number density, which is proportional to the spin-exchange relaxation rate, through phase-frequency analysis. The magnetic resonance response of the atomic magnetometer was actively strengthened at low polarization by increasing the oscillating field amplitude. To downplay the side effect of the transverse field broadening, phase-frequency analysis was applied to extract the transverse relaxation time limited by spin-exchange collisions. The experimental results coincided well with the saturated vapor pressure curve ranging from 413 K to 463 K. Calculated densities were approximately 0.779–0.992 times those of predictions. The density measurement accuracy was improved compared to traditional methods.
Reducing the transverse relaxation rate of alkali atoms is crucial to improve the sensitivity of the magnetometers. In a perturbative treatment of the effects of the magnetic-field gradients, the transverse relaxation rates of alkali atoms are predicted to be proportional to the square of the longitudinal magnetic-field gradient. The theoretical predictions are confirmed in our experiments. The magnetic-field gradients in the vapor cell are measured by experiments. The magnetic-field gradient in the cell is suppressed drastically through compensating it with the compensation coils. Experimental results show that suppressing the magnetic-field gradient can reduce the transverse relaxation rate of alkali atoms significantly. This study contributes to the development of ultra-high sensitivity alkali atomic magnetometers.
Zero-field atomic ensembles enable the development of ultrahigh-sensitivity magnetometry. However, their intrinsic insensitivity to longitudinal magnetic fields along the pumping direction poses a fundamental limitation, restricting precise weak-field quantification and complex system decoupling. Herein, we propose a novel zero-field weak parametric modulation scheme capable of ultrahigh-sensitivity extraction of longitudinal magnetic fields. Transverse modulation is employed to manifest the electron spin polarization projection induced by the longitudinal fields. Based on the perturbation model established, first-order parametric resonance associated with the longitudinal magnetic field yields significant signal enhancement under low-frequency and weak modulation conditions, while simultaneously suppressing spin-exchange relaxation caused by magnetic field modulation. We experimentally achieved a longitudinal measurement sensitivity of 16 fT / Hz 1 / 2 , more than an order of magnitude improved over traditional schemes, with a bandwidth of 70 Hz. Benefiting from low spin relaxation, the noise floor of the transverse magnetic field measurement is preserved at 4 fT / Hz 1 / 2 . The proposed scheme pushes the boundaries of existing weak magnetic field measurement, providing critical capabilities for state-of-the-art precision experiments including new physical quantity detection.
A three-axis atomic magnetometer employing longitudinal field modulation is demonstrated theoretically and experimentally. The operational condition of this magnetometer is that the longitudinal z-component of the external magnetic field is dominant, which is achieved by applying a bias magnetic field. The longitudinal z-component of the external magnetic field is extracted from the modulation frequency, which tracks the resonance frequency, and the transversex- andy- components are, respectively, obtained from the quadrature and the in-phase signals of a lock-in amplifier. Through feedback control, the magnitude and direction of an external magnetic field can be measured in real time, and an excellent orthogonality of the three-axis magnetometer response is obtained. By optimizing the parameters of this three-axis magnetometer, a longitudinal field sensitivity of 0.3pT/Hz1/2{\rm{pT}/ \rm{Hz}}^{1/ 2}pT/Hz1/2and a transverse field sensitivity of 2pT/Hz1/2{\rm{pT}/ \rm{Hz}}^{1/ 2}pT/Hz1/2are achieved.
Nuclear slowing-down factors account for the sharing of angular momentum between the electron and the nucleus in the effective Bloch description of alkali-metal spin dynamics in the spin-exchange-relaxation-free (SERF) regime. For collinear optical pumping and magnetic field, we find that longitudinal and transverse spin dynamics are characterized by different polarization-dependent slowing-down factors. Transverse dynamics are governed by the conventional factor q(p)q(p)q(p), with ppp the electron spin polarization, whereas longitudinal relaxation is governed by q(p)+p dq(p)/dpq(p)+p\,dq(p)/dpq(p)+pdq(p)/dp. The two factors coincide at zero polarization but differ substantially at high polarization, where the single-factor description overestimates the underlying pumping and relaxation rates inferred from longitudinal transients by factors approaching two to four, depending on the nuclear spin. We further derive closed-form expressions, valid at arbitrary polarization, for the residual spin-exchange relaxation of the transverse spin components at finite magnetic field along the pumping axis. This contribution is quadratic in the magnetic field and can become comparable to the zero-field linewidth at fields well within the SERF regime. The results are obtained by perturbation theory on the density-matrix dynamics linearized around the stationary state and are verified by numerical solutions of the microscopic density-matrix equation. These findings refine the effective Bloch description of alkali-metal spin dynamics and are directly relevant to atomic magnetometers and alkali-metal--noble-gas comagnetometers, including those used in precision searches for physics beyond the Standard Model.
We describe an alkali-metal magnetometer for detection of weak magnetic fields in the radio-frequency (rf) range. High sensitivity is achieved by tuning the Zeeman resonance of alkali atoms to the rf frequency and partially suppressing spin-exchange collisions in the alkali-metal vapor. We demonstrate magnetic field sensitivity of 2 fT/Hz(1/2) at a frequency of 99 kHz with a resonance width of 400 Hz. We also derive a simple analytic expression for the fundamental limit on the sensitivity of the rf magnetometer and show that a sensitivity of about 0.01 fT/Hz(1/2) can be achieved in a practical system with a measurement volume of 200 cm3.