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Optics Express

Refined analysis and representation of atomic polarization in NMOR atomic magnetometers

Yanchao Chai, Liwei Jiang, Jiali Liu, Mengnan Tian, Xin Hui Zhao, Zhenglong Lu, Zhuo Wang, Xusheng Lei

Published Jul 15, 2025• 1 citation
Publisher

Abstract

The nonlinear magneto-optical rotation (NMOR) atomic magnetometer is a highly sensitive total-field device with significant applications in fundamental physics, geophysics, and biomedical monitoring. The atomic polarization, which is optically induced through resonant light pumping, plays a pivotal role in determining the sensitivity and stability of the magnetometer. In this paper, refined analysis and representation of atomic polarization in NMOR atomic magnetometers are presented through the establishment of a three-dimensional polarization distribution model based on the rate equation. The polarization characteristics of the single-beam pump and repump modes are compared, and the scale factors of both modes are experimentally measured. Both simulation and experimental results demonstrate that the proposed model accurately captures the spatial distribution of optically induced polarization, which is essential for improving the performance and extending the application potential of NMOR magnetometers in high-sensitivity optical sensing systems.

DOI
10.1364/oe.565257

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The nonlinear magneto-optical rotation (NMOR) atomic magnetometer is a highly sensitive total-field device with significant applications in fundamental physics, geophysics, and biomedical monitoring. The atomic polarization, which is optically induced through resonant light pumping, plays a pivotal role in determining the sensitivity and stability of the magnetometer. In this paper, refined analysis and representation of atomic polarization in NMOR atomic magnetometers are presented through the establishment of a three-dimensional polarization distribution model based on the rate equation. The polarization characteristics of the single-beam pump and repump modes are compared, and the scale factors of both modes are experimentally measured. Both simulation and experimental results demonstrate that the proposed model accurately captures the spatial distribution of optically induced polarization, which is essential for improving the performance and extending the application potential of NMOR magnetometers in high-sensitivity optical sensing systems.
Abstract Polarization moments play a crucial role in measuring magnetic fields for nonlinear magneto‐optical rotation (NMOR) atomic magnetometers. However, it is challenging to distinguish between each polarization moment and evaluate its effect on the magnetic resonance response signal in an alkali vapor cell with buffer gas. To address this issue, a method is proposed to identify different polarization moments through the frequency shift of the magnetic resonance response signal. The proportion of each polarization moment is determined, and it is demonstrated that the magnetic resonance response signal is affected by the hexadecapole moment, resulting in a frequency shift and a decrease in signal amplitude. To mitigate this effect, an approach is investigated to manipulate the polarization moments by flipping the phase of the pump light. Ultimately, a 15.19% increase in response amplitude is achieved in the simulated geomagnetic environment within the magnetic shield barrel. The theory and method presented here provide strong support for the study of the polarization moments in an alkali vapor cell with buffer gas, which potentially enhance the performance of NMOR atomic magnetometers.
We show theoretically the presence of an optical field polarization rotation blocking mechanism in single-probe-based magnetic field sensing schemes, revealing the root cause for extremely small nonlinear magneto-optical rotation (NMOR) signal in single-probe-based atomic magnetometers. We present a colliding-probe atomic magnetometer theory, analytically describing the principle of the first nonlinear-optical atomic magnetometer. This new atomic magnetometry technique breaks the NMOR blockade in single-probe atomic magnetometers, enabling an energy circulation that results in larger than 20-dB enhancement in NMOR signal as well as better than 6-dB improvement of magnetic field detection sensitivity. Remarkably, all experimental observations reported to date can be qualitatively well-explained using this colliding-probe atomic magnetometry theory without numerical computations. This colliding-probe atomic magnetometry technique may have broad applications in scientific and technological fields ranging from micro-Tesla magnetic resonance imaging to cosmic particle detection.
Abstract In NMOR magnetometers, we choose the linear polarized light to pump atoms, and the polarization state is the key factor affecting the evolution of alkali metal atoms. However, polarization errors are introduced due to the refraction of the glass surfaces of the cell and the imperfection of optical devices, which causes the actual laser light to be elliptically polarized. In this paper, the optical ellipticity for this system is accurately measured by the π transition principle first. Then, the magnetic resonance signals under different ellipticity are investigated theoretically and experimentally, and the atomic polarization state is visualized. The results show that the optical ellipticity error introduced by the system will reduce the measurement accuracy and sensitivity of the system, and it is meaningful to use high extinction ratio optical devices and introduce the quarter-wave plate to offset the circularly polarized components.
A self-oscillating magnetometer based on nonlinear magneto-optical rotation using amplitude-modulated pump light and unmodulated probe light (AM-NMOR) in 87Rb has been constructed and tested towards a goal of airborne detection of magnetic anomalies. In AM-NMOR, stroboscopic optical pumping via amplitude modulation of the pump beam creates alignment of the ground electronic state of the rubidium atoms. The Larmor precession causes an ac rotation of the polarization of a separate probe beam; the polarization rotation frequency provides a measure of the magnetic field. An anti-relaxation coating on the walls of the atomic vapor cell results in a long lifetime of 56 ms for the alignment, which enables precise measurement of the precession frequency. Light is delivered to the magnetometer by polarization-maintaining optical fibers. Tests of the sensitivity include directly measuring the beat frequency between the magnetometer and a commercial instrument and measurements of Earth's field under magnetically quiet conditions, indicating a sensitivity of at least 5 pT/νHz. Rotating the sensor indicates a heading error of less than 1 nT, limited in part by residual magnetism of the sensor.
The high-precision and portable nonlinear magneto-optical rotation (NMOR) atomic magnetometer has significant potential in the direction of magnetic field measurement under a geomagnetic environment. Here, we propose a single-beam NMOR atomic magnetometer with amplitude modulation based on a fiberized electro-optic modulator (EOM) for the first time, to the best of our knowledge, which provides a feasible scheme for the integrated design. A theoretical model of the system response signal as a function of the modulation amplitude is established by a Jones matrix. Based on the theoretical model, the influence mechanism of the modulation amplitude on the system response signal is further analyzed and the optimal modulation parameters can be determined. Finally, a sensitivity of 42.67 fT/Hz1/2 at 50-µT magnetic field is achieved. The proposed scheme is also applicable to other magnetometers under a geomagnetic environment.
We experimentally demonstrate that a squeezed probe optical field can improve the sensitivity of magnetic field measurements based on nonlinear magneto-optical rotation (NMOR) with an amplitude-modulated pump when compared to a coherent probe field under identical conditions. To realize an all-atomic magnetometer prototype, we utilize a nonlinear atomic interaction, known as polarization self-rotation, to produce a squeezed probe field. An independent pump field, amplitude-modulated at the Larmor frequency of the bias magnetic field, allows us to extend the range of most sensitive NMOR measurements to sub-Gauss magnetic fields. While the overall sensitivity of the magnetometer is rather low ( > 250 p T / H z ), we clearly observe a 15 % sensitivity improvement when the squeezed probe is used. Our observations confirm the recently reported quantum enhancement in a modulated atomic magnetometer [ Phys. Rev. Lett. 127 , 193601 ( 2021 ) PRLTAO 0031-9007 10.1103/PhysRevLett.127.193601 ].