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arXiv:2105.13638

Weak-value technique for detecting weak magnetic field based on Faraday magneto-optic effect

Jing-Hui Huang, Xue-Ying Duan, Guangjun Wang, Xiangyun Hu

Published May 28, 2021• 1 citation
arXivHTMLPDF

Abstract

We study the amplification of weak magnetic field with Weak-value technique based on Faraday magneto-optic effect. By using a different scheme to perform the Sagnac interferometer with the probe in momentum space, we have demonstrated the new weak measure protocol to detect the small weak magnetic field by amplifying the phase shift of Faraday magneto-optic effect. At the given the maximum incident intensity of the initial spectrum, the detection limit of the intensity of the spectrometer and the accuracy of detecting weak magnetic field, we can theoretically give the appropriate pre-selection, post-selection and others optical structure before experiment. Our numerical results show our scheme with Weak-value technique is effective and feasible to detect weak magnetic field with magnetic field intensity lower than $10^{-10}$ T.

DOI
10.48550/arxiv.2105.13638

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We study the amplification of weak magnetic field with Weak-value technique based on Faraday magneto-optic effect. By using a different scheme to perform the Sagnac interferometer with the probe in momentum space, we have demonstrated the new weak measure protocol to detect the small weak magnetic field by amplifying the phase shift of Faraday magneto-optic effect. At the given the maximum incident intensity of the initial spectrum, the detection limit of the intensity of the spectrometer and the accuracy of detecting weak magnetic field, we can theoretically give the appropriate pre-selection, post-selection and others optical structure before experiment. Our numerical results show our scheme with Weak-value technique is effective and feasible to detect weak magnetic field with magnetic field intensity lower than 10−1010^{-10}10−10 T.
We study the amplification of a weak magnetic field with the weak-value amplification (WVA) technique based on the Faraday magneto-optic effect. By using a different scheme to perform the Mach–Zehnder interferometer with the probe in momentum space, we have demonstrated a new, to the best of our knowledge, weak measure protocol to detect the small weak magnetic field by amplifying the phase shift of the Faraday magneto-optic effect. Our numerical results show that our scheme with the WVA technique has a higher signal-to-noise ratio than the traditional optical fiber scheme with the open-loop modulation technique. Besides, considering the instrument limitations of our scheme, we have demonstrated the magnetic field resolution at the 10 − 13 T level.
We propose a modified difference weak measurement scheme that permits precise measurements of the magneto-optical Faraday effect. By making normalized difference processing for a set of post-selected light intensity, a linear-response regime with a significant weak-value amplification effect is established. In the proof-of-principle experiment, we measure the magnetic intensity using the polarization system and achieve precision at the order of ∼10−7 T. Our scheme can be applied to measure other magneto-optical effects, providing a method for future ultra-sensitive sensing and metrology in magnetic physics.
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.
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.
The extraordinary concept of weak value amplification and a number of other seemingly counter-intuitive wave phenomena are manifestations of fine interference effects. In this report, we show that weak value amplification naturally arises in the cases of nearly destructive interference between the two orthogonal states of the observable which mimics the corresponding near destructive interference between the eigenstates of the measuring observable as a consequence of nearly mutually orthogonal pre and post selections of the system states. In order to elucidate this, we first experimentally demonstrate a weak measurement concept that uses near destructive interference of two paths of an interferometer having slightly rotated linear polarization states of light. By generating nearly destructive interference between the two paths with small amplitude and phase offsets of the waves, we observe both real and imaginary (respectively) weak value amplification of the small polarization rotation leading to large rotation of the polarization vector orientation and dramatic changes in the circular polarization descriptor fourth Stokes vector element of light, respectively. We go on to demonstrate that the giant enhancement of magneto-optical Kerr rotation, by which we can claim that we have found a non-modulation based and cost-effective magneto-optical Kerr effect (MOKE) measurement. At the end, we show successful weak value amplification of spin Hall shift in magneto-optical sample in both longitudinal and polar MOKE. Our ongoing work is to find out the relation between magneto-optical Kerr rotation and spin Hall shift of light in magnetic material.