Enhancing the precision of detecting weak magnetic fields based on weak-value amplification

Jing-Hui Huang; Jing-Hui Huang; Xue-Ying Duan; Xue-Ying Duan; Xue-Ying Duan; Guang-Jun Wang; Guang-Jun Wang; Guang-Jun Wang; Xiang-Yun Hu; Xiang-Yun Hu

doi:10.1364/JOSAB.447515

Journal of the Optical Society of America B
Vol. 39,
Issue 4,
pp. 1289-1296
(2022)
•https://doi.org/10.1364/JOSAB.447515

Enhancing the precision of detecting weak magnetic fields based on weak-value amplification

Jing-Hui Huang, Xue-Ying Duan, Guang-Jun Wang, and Xiang-Yun Hu

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Jing-Hui Huang, Xue-Ying Duan, Guang-Jun Wang, and Xiang-Yun Hu, "Enhancing the precision of detecting weak magnetic fields based on weak-value amplification," J. Opt. Soc. Am. B 39, 1289-1296 (2022)

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Abstract

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 ${10^{- 13}}\;{\rm T}$ level.

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Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Equations (18)

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$β$ [rad]	$φ_{M O M}$ [rad]	$I m A_{w}$	$Δ λ_{0}$ [nm]	$\| ⟨ ϕ_{f} \| ϕ_{i} ⟩ \|^{2}$	k nm/T
0.002	$3.42 \times 10^{- 9}$	$7.99 \times 10^{- 4}$	$3.01 \times 10^{- 2}$	$3.9 \times 10^{- 6}$	$3.01 \times 10^{11}$
0.013	$3.42 \times 10^{- 9}$	$1.89 \times 10^{- 5}$	$7.13 \times 10^{- 4}$	$1.6 \times 10^{- 4}$	$7.13 \times 10^{9}$
0.150	$3.42 \times 10^{- 9}$	$1.36 \times 10^{- 7}$	$5.16 \times 10^{- 6}$	$2.2 \times 10^{- 2}$	$5.16 \times 10^{7}$

$β$ [rad]	$B_{d}$ [MHz]	$λ_{0}$ [nm]	$S (λ_{0})$ [nm]
0.002	1	833.01	0.01
0.002	10	833.01	0.14
0.002	100	832.74	1.46

$β$ [rad]	$φ_{M O M}$ [rad]	$I m A_{w}$	$Δ λ_{0}$ [nm]	$\| ⟨ ϕ_{f} \| ϕ_{i} ⟩ \|^{2}$	k nm/T
0.002	$3.42 \times 10^{- 9}$	$7.99 \times 10^{- 4}$	$3.01 \times 10^{- 2}$	$3.9 \times 10^{- 6}$	$3.01 \times 10^{11}$
0.013	$3.42 \times 10^{- 9}$	$1.89 \times 10^{- 5}$	$7.13 \times 10^{- 4}$	$1.6 \times 10^{- 4}$	$7.13 \times 10^{9}$
0.150	$3.42 \times 10^{- 9}$	$1.36 \times 10^{- 7}$	$5.16 \times 10^{- 6}$	$2.2 \times 10^{- 2}$	$5.16 \times 10^{7}$

$β$ [rad]	$B_{d}$ [MHz]	$λ_{0}$ [nm]	$S (λ_{0})$ [nm]
0.002	1	833.01	0.01
0.002	10	833.01	0.14
0.002	100	832.74	1.46

Abstract

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Tables (2)

Equations (18)

Journal of the Optical Society of America B