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Photonics Research

Inverse weak measurement in a SERF magnetometer

Qian Cao, Liang Xu, Ziqian Yue, Jianqi Yang, Yueyang Zhai

Published Oct 27, 2025• 5 citations
Publisher

Abstract

Weak measurement techniques have been extensively applied in the field of quantum precision measurement to detect ultra-small signals due to the amplification effect. In this work, we propose an optical detection system for a spin-exchange relaxation-free (SERF) magnetometer based on the inverse weak measurement (IWM) framework. By using the spatial pattern of a probe laser as the measurement pointer, we successfully detect ultra-weak magnetic fields. In our model, the spatial pattern of the probe laser is weakly coupled to its polarization, which is sensitive to external magnetic fields. Through post-selection on the optical polarization, the ultra-small magnetic field is significantly amplified with the amplification factor inversely proportional to the coupling strength, as reflected in the measured displacement of the final spatial pattern. By analyzing the response curve of the probe laser displacement to the magnetic field, we identify the point of maximum sensitivity, achieving a magnetic field sensitivity of 182.8 fT / Hz 1/2 . Furthermore, in the IWM scheme, the detected signals depend only on the internal degrees of freedom of the probe laser, making the system robust against the fluctuations in laser power. To demonstrate this advantage, we compute the Allan standard deviation of the output signals for both conventional and IWM detection methods. The results indicate that the IWM-based method improves stability of detection by one to two orders of magnitude. This work presents, to our knowledge, a novel detection approach that integrates weak measurement techniques, offering a significant enhancement in the performance of SERF magnetometers.

DOI
10.1364/prj.573309

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Weak measurement techniques have been extensively applied in the field of quantum precision measurement to detect ultra-small signals due to the amplification effect. In this work, we propose an optical detection system for a spin-exchange relaxation-free (SERF) magnetometer based on the inverse weak measurement (IWM) framework. By using the spatial pattern of a probe laser as the measurement pointer, we successfully detect ultra-weak magnetic fields. In our model, the spatial pattern of the probe laser is weakly coupled to its polarization, which is sensitive to external magnetic fields. Through post-selection on the optical polarization, the ultra-small magnetic field is significantly amplified with the amplification factor inversely proportional to the coupling strength, as reflected in the measured displacement of the final spatial pattern. By analyzing the response curve of the probe laser displacement to the magnetic field, we identify the point of maximum sensitivity, achieving a magnetic field sensitivity of 182.8 fT / Hz 1/2 . Furthermore, in the IWM scheme, the detected signals depend only on the internal degrees of freedom of the probe laser, making the system robust against the fluctuations in laser power. To demonstrate this advantage, we compute the Allan standard deviation of the output signals for both conventional and IWM detection methods. The results indicate that the IWM-based method improves stability of detection by one to two orders of magnitude. This work presents, to our knowledge, a novel detection approach that integrates weak measurement techniques, offering a significant enhancement in the performance of SERF magnetometers.
Weak measurement techniques have been extensively applied in the field of quantum precision measurement to detect ultra-small signals due to the amplification effect. In this work, we propose an optical detection system for a spin-exchange relaxation-free (SERF) magnetometer based on the inverse weak measurement (IWM) framework. By using the spatial pattern of a probe laser as the measurement pointer, we successfully detect ultra-weak magnetic fields. In our model, the spatial pattern of the probe laser is weakly coupled to its polarization, which is sensitive to external magnetic fields. Through post-selection on the optical polarization, the ultra-small magnetic field is significantly amplified with the amplification factor inversely proportional to the coupling strength, as reflected in the measured displacement of the final spatial pattern. By analysing the response curve of the probe laser displacement to the magnetic field, we identify the point of maximum sensitivity, achieving a magnetic field sensitivity of 182.8 fT/Hz1/2. Furthermore, in the IWM scheme, the detected signals depend only on the internal degrees of freedom of the probe laser, making the system robust against the fluctuations in laser power. To demonstrate this advantage, we compute the Allan standard deviation of the output signals for both conventional and IWM detection methods. The results indicate that the IWM-based method improves stability of detection by one to two orders of magnitude. This work presents a novel detection approach that integrates weak measurement techniques, offering a significant enhancement in the performance of SERF magnetometers.
In quantum metrology researching, weak measurement has been widely applied in many aspects, providing weak-value amplification and noise suppressing ability. Recently, several modified schemes of weak measurement have been proposed, such as inverse, almost-balanced, and biased weak measurement. In this study, we enhance a spin-exchange relaxation-free (SERF) magnetometer using the biased weak measurement metrology technique. We establish and simulate a biased weak measurement (BWM)-enhanced SERF magnetometer model. By adjusting the pre-coupling process and analysing the Fisher information, higher sensitivity to magnetic fields is verified in this study. 0.003 fT can be achieved through adjusting pre-coupling process and extinction ratio, which is higher than the best sensitivity of SERF magnetometer in existence. Our work paves the way for embedding weak measurement techniques into atomic magnetometer sensors and greatly improving their sensitivity.
The spin-exchange relaxation-free (SERF) atomic magnetometer (AM) has vital importance in advanced research and has been widely applied in different fields. To improve the sensitivity and robustness of SERF magnetometers, understanding the relaxation mechanism is a significant approach. By controlling the amplitude and direction of external magnetic fields, and switching statuses of the pump and probe laser beam, we measured both the transverse and longitudinal relaxation rate in two experimental methods, respectively, and obtained the Larmor precession frequency, the spin-exchange relaxation rate, the spin-destruction relaxation rate, and the relaxation rate due to collisions between atoms and vapor cell walls. All experimental results are verified with the theoretical calculations. The final longitudinal relaxation rate of our magnetometer is 53 Hz. Furthermore, we measured the sensitivity of our SERF magnetometer reaching 5 fT/Hz1/2 from 5 to 70 Hz after differential measurement with the 3-dB bandwidth of 70 Hz. Our work helps to improve the detection capability of SERF magnetometers, providing performance assurance for searching for exotic spin-dependent interactions and applications, including magnetoencephalograms and magnetocardiograms.
Ultra-sensitive measurement of the magneto-optical rotation, due to interaction of linearly-polarized light passing through room-temperature Rb85 atoms, in response to change in longitudinal magnetic field (δBz) is demonstrated using the weak measurement method. The polarization rotation angle measurement sensitivity (δϕ) of 16 μrad and hence of the magnetometer of 1 nT, achieved using the weak measurement method is better than the balanced optical polarimetry results by a factor of three. The improvement in the measurement sensitivity is realized via optical amplification of the polarization rotation angle via spin-orbit coupled light beam-field. The method is devoid of external rf(/ac) modulation, allows for optimal tunability of sensitivity depending on the dynamic range of the applied magnetic field and the sensitivity can be further enhanced by operating in the spin exchange relaxation free regime of alkali spin polarization.
Spin-exchange relaxation-free (SERF) atomic magnetometers have emerged as highly promising candidates for ultra-weak magnetic field detection, particularly in biomagnetic imaging, owing to their exceptional sensitivity, amenability to miniaturization, and near-room-temperature operation. While current miniaturized magnetometers typically employ laser chips with fixed optical power, the quantitative impact of laser power on critical performance metrics remains to be fully elucidated. This study systematically investigates the influence of laser power on sensitivity, bandwidth, and dynamic range by incorporating considerations of power broadening, saturation absorption, and noise constraints. A miniaturized probe, integrated with an actively controlled vertical-cavity surface-emitting laser (VCSEL), was developed for experimental validation. Theoretical and experimental results consistently demonstrate that as optical power increases, sensitivity exhibits a non-monotonic dependence, whereas both bandwidth and dynamic range manifest a monotonic upward trend, aligning well with theoretical simulations. The optimized sensor achieved a peak sensitivity of 16 fT/√Hz at 300 μW, while the bandwidth and dynamic range reached 230 Hz and ±5.4 nT at 500 μW, respectively. This work establishes a robust theoretical and experimental framework for the comprehensive performance optimization of laser-integrated miniaturized atomic magnetometers.
We demonstrate that atomic spin trajectories on the Bloch sphere can be manipulated through direct feedback, achieving spin amplification. This method is applied to Spin-Exchange Relaxation-Free (SERF) magnetometers where a feedback loop introduces a magnetic field positively proportional to the transverse spin polarization, which significantly amplifies the low-frequency response signal by an order of magnitude. Experimental results show that the feedback mechanism improves the signal-to-noise ratio and effectively strengthens the system’s ability to suppress technical noise. In addition, this feedback-enabled magnetometer exhibits superior sensitivity at lower spin polarization, reducing reliance on optical power and thereby facilitating scalability in multi-channel systems. This approach can be extended to various physical systems utilizing atomic spins, such as quantum memory and quantum metrology.