1.State Key Laboratory of Quantum Optics and Quantum Optics Devices, Collaborative Innovation Center of Extreme Optics, Institute of Opto-Electronics, Shanxi University, Taiyuan 030006, China 2.College of Physics and Electronic Engineering, Shanxi University, Taiyuan 030006, China
Fund Project:Project supported by the National Key Research and Development Program of China (Grant No. 2017YFA0304502) and the National Natural Science Foundation of China (Grants Nos. 11634008, 11674203, 11574187, 61227902).
Received Date:06 January 2019
Accepted Date:25 February 2019
Available Online:01 May 2019
Published Online:05 May 2019
Abstract:Magnetometry has already been widely used in mineral exploration, medical exploration and precision measurement physics. One is trying to improve the sensitivity of the magnetometer. One of the most widely used magnetometers is based on the Bell-Bloom structure, which can be realized by modulating the pump light. The sensitivity of the Bell-Bloom magnetometer is determined by the magnetic resonance linewidth (MRL) and the signal-to-noise under the condition of magnetic resonance (SNR). Both are affected by the pump intensity and the relaxation rate of the atoms. In order to achieve a higher sensitivity, how these factors affect the magnetic field measurement should be analyzed. In this paper, the influence of the pump light on the sensitivity of the linearly polarized Bell-Bloom magnetometer is investigated based on the Bloch equation with amplitude modulated pump beam and the rate equations with spin relaxation. The rate equations are obtained from the Liouville equation, and the theoretical analysis is based on the cesium. The pump beam is linearly polarized and is resonant to D1 transition of cesium. Both the direct pump (pump frequency is resonant to ${6^2}{{\rm{S}}_{1/2}}\;F = 4$?${6^2}{{\rm{P}}_{1/2}}\;F' = 3$ transition) and the indirect pump (pump frequency is resonant to ${6^2}{{\rm{S}}_{1/2}}\;F = 3 $?${6^2}{{\rm{P}}_{1/2}}\;F' = 4$ transition) are analyzed. The experiment is performed based on a 20-mm cube cesium vapour cell with 20-Torr helium as buffer gas. The linearly polarized probe beam is tuned to resonance to cesium D2 transition ${6^2}{{\rm{S}}_{1/2}}\;F = 4$?$ {6^2}{{\rm{P}}_{3/2}}\;F' = 5$, and the intensity of the probe is 0.2 W/m2. The spectra of magnetic resonance are measured by using the lock-in detection with a scanning of the modulation frequency. Then the sensitivity can be obtained by measuring MRL and SNR. The experimental results show that the sensitivity and the pump intensity are related nonlinearly, which is coincident with theoretical result. Higher sensitivity can be obtained under the condition of indirect pump. In addition, the effect of atomic spin relaxation on sensitivity is also analyzed with the indirect pump beam. This work clarifies the dynamics of the Bell-Bloom magnetometer to some extent. The highest sensitivity obtained is $31.7\;{\rm{pT}}/\sqrt {{\rm{Hz}}} $ in our experiment, which can be optimized by using other kinds of vapour cells and different measuring methods. Keywords:magnetic field measurement/ magnetic resonance/ spin relaxation/ atomic polarization
抽运光与原子相互作用, 导致原子在基态各个磁子能级上分布不均匀, 由此可以实现原子的极化. 这一过程可以用速率方程[25]来描述. 如图2(a)所示, 铯原子D1线基态与激发态之间的拉比振荡频率为ΩR, $\left| a \right\rangle $和$\left| c \right\rangle $表示基态的两个磁子能级, $\left| b \right\rangle $为激发态的一个磁子能级. 抽运光与原子共振, 频率为${\omega _0}$, 即$\left| a \right\rangle $与$\left| b \right\rangle $之间的频率差. 在抽运光的作用下, 原子由$\left| a \right\rangle $跃迁至$\left| b \right\rangle $. 若$\left| b \right\rangle $的自发辐射率为${\varGamma _0}$, $\left| a \right\rangle $与$\left| b \right\rangle $之间的偶极矩阵元为$\eta $, $\left| c \right\rangle $与$\left| b \right\rangle $之间的偶极矩阵元为$\theta $, 则原子由$\left| b \right\rangle $自发辐射至$\left| a \right\rangle $和$\left| c \right\rangle $的速率分别为${\eta ^2}{\varGamma _0}$和${\theta ^2}{\varGamma _0}$. 原子密度矩阵$\hat \rho $随时间t的演化可以用刘维尔方程[23]描述:
(7)式右侧第一项表示光与原子之间的相互作用, 第二项和第三项分别表示由于$\left| b \right\rangle $的自发辐射和基态的自旋弛豫引起的各个磁子能级布局数的减小和增加. 其中
$ \hat H = \hbar {\omega _0}\left| b \right\rangle \left\langle b \right| + \hbar \left( {\eta {\varOmega _{\rm{R}}}} \right)\cos \left( {{\omega _0}t} \right)\left( {\left| a \right\rangle \left\langle b \right| + \left| b \right\rangle \left\langle a \right|} \right), \tag{8a} $
$\hat \varGamma = {r_0}\left| a \right\rangle \left\langle a \right| + { \varGamma _0}\left| b \right\rangle \left\langle b \right|{\rm{ + }}{r_0}\left| c \right\rangle \left\langle c \right|, \tag{8b} $
$ \hat \varLambda \!=\! \left( {{\eta ^2}{\varGamma _0}{\rho _{bb}} \!+\! {r_0}/n} \right)\left| a \right\rangle \left\langle a \right| \!+\! \left( {{\theta ^2}{\varGamma _0}{\rho _{bb}} \!+\! {r_0}/n} \right)\left| c \right\rangle \left\langle c \right|,\tag{8c} $
图 1 线极化的Bell-Bloom测磁系统基本原理图
图 2 抽运光与铯原子相互作用 (a)光与铯原子相互作用; (b)线偏振的抽运光与铯原子相互作用
图 3 铯原子基态
图 4 磁共振时, 信号幅度
图 5 实验装置图(SAS, 饱和吸收谱; VNDF, 连续可变衰减片; HWP, 半波片; PBS, 偏振分束器; HR, 高反镜; GTP, 格兰泰勒棱镜; WP, 渥拉斯顿棱镜; EO-AM, 电光振幅调制器; BPD, 平衡探测器; LIA, 锁相放大器; AC, 交流电源; DC, 直流电源; HC, 亥姆霍兹线圈; OSC, 示波器; SA, 频谱分析仪; P, 光的偏振方向)
图 6 直接抽运与间接抽运的磁共振谱线
图 7 磁共振线宽
图 8 磁共振时, 信噪比SNR与磁场灵敏度
图 9 在自旋弛豫率
