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共振线偏振光激发原子张量磁矩，本文理论研究在矢量磁场和射频场的共同作用下，张量磁矩进动的模型，求解刘维尔方程获得透射光时域完整解析解，包括直流、一次和二次谐波分量.研究发现：当进动的拉比频率Ω > 1/（2√2）时，两谐波间的干涉效应使直流分量和一次谐波对称成分的单吸收峰劈裂成双峰，裂距√3√Ω2+Ω4-Ω2-1，一次谐波反对称成分在共振处产生干涉条纹.研究结果显示，谐波间的干涉也可导致直流分量和二次谐波线宽仅为一次谐波线宽的38%，且存在磁场取向临界点，在不同的取向区间分别利用直流及两谐波共振信号辨析磁场变化，可获得最佳测磁灵敏度；同时还可通过共振时直流分量及两谐波对称成分振幅来确定磁场与激光极化方向的夹角，利用两谐波反对称成分相移的差值来确定待测磁场在垂直光极化方向投影与射频场方向的夹角，进而实现结构简单的张量磁矩进动型矢量磁力仪.这种磁力仪适合构成磁力仪阵列，可用于磁定位、水下磁异常源的检测和地磁导航等领域.As is well known a linearly polarized resonant laser will cause atoms to generate a magnetic tensor moment (MTM) by polarizing them. When there exists an external magnetic field, it is possible that the moment will precess around the field. In the presence of a radio frequency (RF) exciting source, we investigate theoretically the dependence of time-independent (direct current, DC), the first and second harmonic signal of the MTM precession on magnetic vector field, and obtain its analytical solution by solving the Liouville equation. The results show that the interference of both harmonic components will result in the precession spectrum evidently varying. A detailed explanation is described in the following. For the DC signal, Rabi frequency Ω of 1/(2√2) is a spectral splitting threshold. When it is greater than the threshold, the interference will cause single resonant absorption dip characterized usually to split into two dips, which has not been reported before to the best of our knowledge, and the separation between both the dips may be expressed as √3√Ω2+Ω4 -Ω2-1. For the first harmonic signal including symmetric and antisymmetric component, an interference fringe will appear near the center of antisymmetric part when Ω >1/(2√2), simultaneously its symmetric part behaves like the above dc component, such as splitting threshold and separation between both dips. With regard to the second harmonic signal, it is found that the interference can also lead to the width of the second harmonic decreasing to 38% compared with the case of the first harmonic signal. At the optimum RF Rabi frequency, on the assumption that noise spectral density is constant, it is theoretically shown that the most sensitive magnetometer, realized by the DC component or the first or second harmonic signal of the precession, depends only on the angle between the light polarization and the measured magnetic field.In fact, we are able to obtain the modules of the measured magnetic vector by RF resonant frequency. The angle between the magnetic field and the laser polarization is determined just by the ratio of the intensity of the DC component to the intensity of the second harmonic signal and the ratio between the intensities of the symmetric parts of two harmonic signals in resonance, and another orientation angle between the measured field projection at the plane perpendicular to the light polarization and the direction of RF source depends on the phase difference between the antisymmetric components of both harmonic signals. Consequently, we demonstrate a vectorial atomic magnetometer that is realized by using the RF source and the linearly polarized resonant laser without rotating laser polarization. This kind of atomic magnetometer with simple sensor structure is easy to integrate vector magnetometer array which will be suitable for solving the inverse problem and geomagnetic navigation.
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Keywords:
- magnetic tensor moment /
- vector magnetometer /
- precession spectrum
[1] Budker D, Romalis M 2007 Nat. Phys. 3 227
[2] Dang H B, Maloof A C, Romalis M V 2010 Appl. Phys. Lett. 97 151110
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[4] Savukov I, Karaulanov T, Boshier M G 2014 Appl. Phys. Lett. 104 023504
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[6] Xia H, Baranga B A, Hoffman D, Romalis M V 2006 Appl. Phys. Lett. 89 211104
[7] Zou S, Zhang H, Chen X Y, Chen Y, Lu J X, Hu Z H, Shan G C, Quan W, Fang J C 2016 J. Appl. Phys. 119 143901
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[10] Huang H C, Dong H F, Hu X Y, Chen L, Gao Y 2015 Appl. Phys. Lett. 107 182403
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[14] Sun W M, Huang Q, Huang Z J, Wang P W, Zhang J H 2017 Chin. Phys. Lett. 34 058501
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[16] Cox K, Yudin V I, Taichenachev A V, Novikova I, Mikhailov E E 2011 Phys. Rev. A 83 015801
[17] Fu J Q, Du P C, Zhou Q, Wang R Q 2016 Chin. Phys. B 25 010302
[18] Gu Y, Shi R Y, Wang Y H 2014 Acta Phys. Sin. 63 110701 (in Chinese) [顾源, 石荣晔, 王延辉 2014 物理学报 63 110701]
[19] Lin Z S, Peng X, Li W H, Wang H D, Guo H 2017 Opt. Express 25 7668
[20] Bevilacqua G, Breschi E 2014 Phys. Rev. A 89 062507
[21] Gawlik W, Krzenmień L, Pustelny S, Sangla D, Zachorowski J 2006 Appl. Phys. Lett. 88 131108
[22] Weis A, Bison G, Pazgalev A S 2006 Phys. Rev. A 74 033401
[23] Domenico G D, Bison G, Groeger S, Knowles P, Pazgalev A S, Rebetez M, Saudan H, Weis A 2006 Phys. Rev. A 74 063415
[24] Breschi E, Weis A 2012 Phys. Rev. A 86 053427
[25] Budker D, Kimball D F, DeMille D P 2012 Atomic Physics (2nd Ed.) (England: Oxford University Press) pp110-112
[26] Li N, Huang K K, Lu X H 2013 Acta Phys. Sin. 62 133201 (in Chinese) [李楠, 黄凯凯, 陆璇辉 2013 物理学报 62 133201]
[27] Ding Z C, Yuang J, Luo H, Long X W 2017 Chin. Phys. B 26 093301
[28] Grewal R S, Pattabiraman M 2016 Eur. Phys. J. D 70 219
[29] Weis A, Shi Y Q, Grujić Z D 2017 Eur. Phys. J. D 71 80
[30] Grosz A, Haji-Sheikh M J, Mukhopadhyay S C 2017 High Sensitivity Magnetometers (Switzerland: Springer) pp380-387
[31] Ben-Kish A, Romalis M V 2010 Phys. Rev. Lett. 105 193601
[32] Zhang F, Tian Y, Zhang Y, Gu S H 2016 Chin. Phys. B 25 094206
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[1] Budker D, Romalis M 2007 Nat. Phys. 3 227
[2] Dang H B, Maloof A C, Romalis M V 2010 Appl. Phys. Lett. 97 151110
[3] Shah V, Knappe S, Schwindt P D D, Kitching J 2007 Nat. Photon. 1 649
[4] Savukov I, Karaulanov T, Boshier M G 2014 Appl. Phys. Lett. 104 023504
[5] Lee H J, Shim J H, Moon H S, Kim K 2014 Opt. Express 22 19887
[6] Xia H, Baranga B A, Hoffman D, Romalis M V 2006 Appl. Phys. Lett. 89 211104
[7] Zou S, Zhang H, Chen X Y, Chen Y, Lu J X, Hu Z H, Shan G C, Quan W, Fang J C 2016 J. Appl. Phys. 119 143901
[8] Allmendinger F, Heil W, Karpuk S, Kilian W, Scharth A, Schmidt U, Schnabel A, Sobolev Y, Tullney K 2014 Phys. Rev. Lett. 112 110801
[9] Goldenberg F 2006 IEEE/ION Position, Location and Navigation Symposium-PLANS San Diego, California of USA, April 25-27 2006 p684
[10] Huang H C, Dong H F, Hu X Y, Chen L, Gao Y 2015 Appl. Phys. Lett. 107 182403
[11] Patton B, Zhivun E, Hovde D C, Budker D 2014 Phys. Rev. Lett. 113 013001
[12] Seltzer S J, Romalis M V 2004 Appl. Phys. Lett. 85 4804
[13] Vershovskii A K 2011 Tech. Phys. Lett. 37 140
[14] Sun W M, Huang Q, Huang Z J, Wang P W, Zhang J H 2017 Chin. Phys. Lett. 34 058501
[15] Yudin V I, Taichenachev A V, Dudin Y O, Velichansky V L, Zibrov A S, Zibrov S A 2010 Phys. Rev. A 82 033807
[16] Cox K, Yudin V I, Taichenachev A V, Novikova I, Mikhailov E E 2011 Phys. Rev. A 83 015801
[17] Fu J Q, Du P C, Zhou Q, Wang R Q 2016 Chin. Phys. B 25 010302
[18] Gu Y, Shi R Y, Wang Y H 2014 Acta Phys. Sin. 63 110701 (in Chinese) [顾源, 石荣晔, 王延辉 2014 物理学报 63 110701]
[19] Lin Z S, Peng X, Li W H, Wang H D, Guo H 2017 Opt. Express 25 7668
[20] Bevilacqua G, Breschi E 2014 Phys. Rev. A 89 062507
[21] Gawlik W, Krzenmień L, Pustelny S, Sangla D, Zachorowski J 2006 Appl. Phys. Lett. 88 131108
[22] Weis A, Bison G, Pazgalev A S 2006 Phys. Rev. A 74 033401
[23] Domenico G D, Bison G, Groeger S, Knowles P, Pazgalev A S, Rebetez M, Saudan H, Weis A 2006 Phys. Rev. A 74 063415
[24] Breschi E, Weis A 2012 Phys. Rev. A 86 053427
[25] Budker D, Kimball D F, DeMille D P 2012 Atomic Physics (2nd Ed.) (England: Oxford University Press) pp110-112
[26] Li N, Huang K K, Lu X H 2013 Acta Phys. Sin. 62 133201 (in Chinese) [李楠, 黄凯凯, 陆璇辉 2013 物理学报 62 133201]
[27] Ding Z C, Yuang J, Luo H, Long X W 2017 Chin. Phys. B 26 093301
[28] Grewal R S, Pattabiraman M 2016 Eur. Phys. J. D 70 219
[29] Weis A, Shi Y Q, Grujić Z D 2017 Eur. Phys. J. D 71 80
[30] Grosz A, Haji-Sheikh M J, Mukhopadhyay S C 2017 High Sensitivity Magnetometers (Switzerland: Springer) pp380-387
[31] Ben-Kish A, Romalis M V 2010 Phys. Rev. Lett. 105 193601
[32] Zhang F, Tian Y, Zhang Y, Gu S H 2016 Chin. Phys. B 25 094206
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