## 2 The Experiment Setup  
The experimental setup is shown in Figure 1 and is a typical laser pumped \({}^{4}\)He magnetometer under the conventional MODR configuration. The laser emitted from a fiber laser (FL) has a wavelength of about 1083 nm. A beam expander (BE) is inserted into the path to expand the waist diameter to 12 mm (\(1/e^{2}\)) in order to increase the signal amplitude. A half-wave plate (HWP) and a polarizer (P) are used to adjust the pumping light intensity and then a quarter-wave plate is used to convert the linear polarization to the circular polarization. The circularly polarized pumping light passes a 70 mm \({}^{4}\)He atomic cell with diameter being 50 mm and  
Figure 1: Schematic diagram of the experiment setup. FL, fiber laser; BE, beam expander; HWP, half-wave plate; P, polarizer; QWP, quarter-wave plate; L, lens; HC, Helmholtz coils; PD, photodiode; LIA, lock-in amplifier; PID, Proportion-Integration-Differentiation controller; FS, frequency synthesizer; MS, magnetic shield. with low-pressure being 0.3 Torr. The cell is discharged by power source with 33 MHz to produce the metastable-state \({}^{4}\)He atoms. The MODR signal is driven by a weak oscillating magnetic field \(B_{1}\), which is perpendicular to the propagation direction of the pumping light. The weak oscillating magnetic field \(B_{1}\) is generated by a pair of Helmholtz coils (HC). To suppress the fluctuations of the external magnetic field, both the cell and the coils are located in a five-layer magnetic shield. A bias magnetic field \(B_{0}\), parallel to the propagation direction of the pumping light, is generated by another coil inside the magnetic shield (not shown). The strength of the bias magnetic field \(B_{0}\) is about 11,320 nT in our experiment. For MODR configuration magnetometer of \(M_{z}\) type, the circularly polarized resonant light passes through the \({}^{4}\)He gas and polarizes the metastable \({}^{4}\)He atoms. The polarized \({}^{4}\)He atoms form a macroscopic magnetic moment parallel to the direction of the bias magnetic field \(B_{0}\). Scanning the frequency \(\omega\) in the Helmholtz coils, an absorption signal is detected with the photodiode. When the frequency \(\omega\) is equal to the magnetic resonance frequency (Larmor frequency) \(\omega_{0}\), the light absorption is at its maximum. A small sinusoidal signal with a frequency of 1.3 kHz is applied to modulate the frequency \(\omega\) and the absorption signal is demodulated with a lock-in amplifier (LIA). The LIA acts as a narrow band-pass filter around the reference signal frequency. For each frequency component of the magnetic resonance signal, the LIA generates two output components, respectively in-phase and in-quadrature. The in-phase component is referred to as \(X=R\cdot\cos\theta\), while the quadrature component is referred to as \(Y=R\cdot\sin\theta\), where \(R\) is the amplitude of the (demodulated) magnetic resonance signal and \(\theta\) is the phase difference between the detection signal and the reference signal. According to this experimental setup, the power of the pumping light is set to 3 mW. The wavelength of the laser is about 1083.205 nm and it can be adjusted through the piezoelectric transducer (PZT). By scanning the frequency \(\omega\) of the frequency synthesizer (FS), the demodulated signal amplitude \(R\) is shown in Figure 2a. It can be seen that, when the laser frequency is resonant, the line shape of the magnetic resonance signal is symmetric and the maximum absorption is zero. When the laser frequency is detuned, the line shape becomes asymmetric and the value of \(R\) is not zero. Since the quadrature component \(Y\) is a dispersive function of the scanning frequency \(\omega\), we use this quadrature component to lock the Larmor frequency with the help of Helmholtz coils and measure the bias magnetic field \(B_{0}\) along the z direction. The in-phase component vanishes if the laser frequency is resonant.