## 2 Principle of Mx Optically Pumped Cesium Magnetometer  
Magnetometers based on magnetic resonance phenomena are divided into Mx and Mx types, classified according to the signals used for the resonance detection. Mx and Mx signals are distinguished according to the projections of the magnetic moment [29]. Mx signals are associated with the transverse component of the magnetic moment and Mx signals are associated with the longitudinal component of the magnetic moment. The sketched view of a single-beam M\({}_{\rm x}\) Cs-OPM is shown in Figure 1. A cesium lamp provides pump-light and probe-light sources for the gas-cell. The light passes through the gas-cell and the lens, where the photo detector converts the light signal into the current. Subsequently, the current is converted into a measurable voltage by the amplifier. The feedback network consists of a phase shifter and an automatic gain control (AGC) circuit. The former distinguishes the Larmor frequency and outputs a control signal to make the AGC driving the RF coil in order to establish a self-resonant condition. Following References [2; 10], the sensitivity \(\delta B\) (in T/VHz) is expressed as  
\[\delta B=\frac{1}{\gamma}\frac{\Gamma}{S/N}, \tag{1}\]  
where \(\gamma\) is the gyromagnetic ratio, here, \(\gamma\cong\) 3.5 Hz/nT for the Cs-OPM, S/N is the SNR of the system with the noise expressed per unit bandwidth, and \(\Gamma\) is the relaxation rate. For the single-beam M\({}_{\rm x}\) magnetometer, the magnetic field provided by the RF coil is parallel to the optical path. The transmitted power \(P(t)\) injected to the photo detector can be expressed as [28]  
\[P(t)=P_{DC}+P_{IP}\sin\omega_{rf}t+P_{QU}\cos\omega_{rf}t=P_{DC}+P_{R}\sin \Bigl{(}\omega_{rf}t+\phi\Bigr{)}, \tag{2}\]  
\[P_{DC}=P_{0}(1-\kappa_{0}L+\kappa_{0}L\alpha S_{DC}), \tag{3}\]  
\[P_{IP}=-P_{0}S_{0}\kappa_{0}L\alpha\frac{\Bigl{(}\omega_{rf}-\omega_{L} \Bigr{)}\Omega\sin\theta_{B}}{\Bigl{(}\omega_{rf}-\omega_{L}\Bigr{)}^{2}+ \Gamma^{2}+\Omega^{2}\sin^{2}\theta_{B}}\cos\theta_{B}\sin\theta_{B}, \tag{4}\]  
\[P_{QU}=P_{0}S_{0}\kappa_{0}L\alpha\frac{\Gamma\Omega\sin\theta_{B}}{\Bigl{(} \omega_{rf}-\omega_{L}\Bigr{)}^{2}+\Gamma^{2}+\Omega^{2}\sin^{2}\theta_{B}} \cos\theta_{B}\sin\theta_{B}, \tag{5}\]  
\[P_{R}=\sqrt{P_{IP}{}^{2}+P_{QU}{}^{2}}=P_{0}S_{0}\kappa_{0}L\alpha\frac{ \Omega\sin\theta_{B}\sqrt{\Bigl{(}\omega_{rf}-\omega_{L}\Bigr{)}^{2}+\Gamma^{ 2}}}{\Bigl{(}\omega_{rf}-\omega_{L}\Bigr{)}^{2}+\Gamma^{2}+\Omega^{2}\sin^{2} \theta_{B}}|\cos\theta_{B}\sin\theta_{B}|, \tag{6}\]  
\[\tan\phi=\frac{P_{QU}}{P_{IP}}=-\frac{\Gamma}{\omega_{rf}-\omega_{L}}, \tag{7}\]  
where, \(P_{DC}\) is the DC component, \(P_{IP}\) is the in-phase component, \(P_{QU}\) is the quadratic component, \(P_{0}\) is the power of the incident light, \(\kappa_{0}\) is the peak absorption cross section, \(L\) is the length of the gas cell, \(\alpha\) is the multipole analyzing power that depends on the atomic transition with which the light is resonant, \(S_{0}\) is the equilibrium spin polarization, \(S_{DC}\) is the DC component of the polarization, \(\omega_{rf}\) is the radio frequency, \(\omega_{L}\) is the Larmor frequency, \(\Omega\) is the Rabi frequency, and \(\theta_{B}\) is the angle between the incident light and the measured magnetic field. Figure 2 shows measured line shapes under conditions optimized for maximal sensitivity (see Section 4.4 for details). The measured magnetic field is 53 \(\mu\)T and the Larmor frequency is 185.5 kHz. It can be seen that in the case of self-resonance (\(\omega_{rf}\) = \(\omega_{L}\)), the in-phase component crosses  
Figure 1: Sketched view of an optically pumped cesium magnetometer with (**1**) lamp, (**2**) lens, (**3**) filter, (**4**) polarizer, (**5**) radio frequency (RF) coil, (**6**) gas cell, (**7**) lens, (**8**) photo detector. the zero point, the quadrature component can reach the maximum amplitude. Thus, the phase difference between the in-phase component and the quadrature component is 90 degrees.