Optimization and vectorization of a Mz-type optically-pumped Rubidium magnetometer

Abstract

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.

Figures (10)

• Figure 1: Schematic diagram of the working principle of the $^{87}$Rb Mz atomic magnetometer. (a) Energy level transition diagram of the $^{87}$Rb D1 line. The thick red arrow on the left indicates the D1 transition ($5^2S_{1/2} - 5^2P_{1/2}$) at 795 nm. Solid blue arrows represent the stimulated transitions caused by the absorption of $\sigma^+$ pump light, while dashed black arrows represent the spontaneous emission processes from the excited state back to the ground state. The fractions labeled on the dashed lines indicate the relative transition probabilities (Clebsch-Gordan coefficients) for each path. The curved green arrows ($\Omega_{\text{rf}}$) at the bottom represent the magnetic resonance transitions induced by the radio-frequency field between adjacent Zeeman sublevels. (b) Schematic of the polarization model. The yellow sphere illustrates the atomic ensemble accumulating in the $m_F=+2$ state under the action of optical pumping, resulting in macroscopic spin polarization.
• Figure 2: Schematic diagram of the experimental setup for the Mz-type Rb atomic magnetometer. Cell: Paraffin-coated $^{87}$Rb vapor cell; PD: Photodetector; NDF: Neutral density filter; HR: High-reflectivity mirror; PID: Proportional-integral-derivative controller; Lock-in: Digital lock-in amplifier. The vapor cell is placed inside a four-layer permalloy magnetic shield, where tri-axial Helmholtz coils provide the static magnetic field ($B_0$), the radio-frequency field ($B_{\text{rf}}$), and the modulation magnetic fields required for vector measurement.
• Figure 3: Impact of radio-frequency (RF) field intensity on the characteristics of the magnetic resonance signal. Different colored curves correspond to different pump laser powers ranging from 100 $\mu$W to 600 $\mu$W. (a) Dependence of magnetic resonance linewidth on RF magnetic field. (b) Dependence of signal amplitude on RF magnetic field. (c) Dependence of the Linewidth-Amplitude Ratio (LAR) on RF magnetic field. The inset displays the fine-scan results around the minimum (125--175 nT), used to precisely locate the optimal RF magnetic field ($\sim$165 nT).
• Figure 4: Impact of pump laser power on the characteristics of the magnetic resonance signal. Different colored curves correspond to different radio-frequency (RF) field intensities ranging from 37.03 nT to 296.28 nT. (a) Dependence of magnetic resonance linewidth on pump laser power. (b) Dependence of signal amplitude on pump laser power. (c) Dependence of the Linewidth-Amplitude Ratio (LAR) on pump laser power. The inset displays the fine-scan results under the optimal RF field, identifying the optimal pump laser power at approximately 250 $\mu$W.
• Figure 5: Power spectral density of magnetic noise of the magnetometer in open-loop mode. A sinusoidal calibration magnetic field with a frequency of 63 Hz and an amplitude of 1.84 nT was applied. The sharp peak represents the response to the calibration signal, while the blue dashed line indicates the average noise floor of the system. Based on the signal-to-noise ratio calculation from the calibration signal, the open-loop sensitivity at this operating point is 30.8 pT/Hz$^{1/2}$.