# A High-Sensitivity Cesium Atomic Magnetometer Based on A Cesium Spectral Lamp
## 2 Design and Construction of Cesium Atomic Magnetometer
### Electronic Unit
Similarly, the Cs-Cs spin destruction rate between Cs-Cs collisions can be modeled and characterized as  
\[R_{\rm Cs-Cs}^{SD}=n_{\rm Cs}\sigma_{\rm Cs-Cs}^{SD}\overline{v}_{\rm Cs-Cs}^{ rel} \tag{3}\]  
where \(n_{\rm Cs}\) is the number density of Cs, \(\overline{v}_{\rm Cs-Cs}^{rel}\) is the relative velocity between Cs atoms, and \(\sigma_{\rm Cs-Cs}^{SD}=2.03\times 10^{-16}\) cm\({}^{2}\)[23] is the spin-destruction collision cross-section. The wall collision rate of Cs atoms during the diffusive motion in the He buffer gas is approximately given by  
\[R_{\rm Cs-wall}=\left(\left(\frac{2.405}{r}\right)^{2}+\left(\frac{\pi}{L} \right)^{2}\right)D \tag{4}\]  
where the diffusion coefficient \(D\) is calculated via the same quantity \(D_{0}=0.27\) cm\({}^{2}\)/s [24] at \(P_{0}=1\) atm and \(T_{0}=0\)\({}^{\rm o}\)C,  
\[D=D_{0}\frac{P_{0}}{P}\left(\frac{T}{T_{0}}\right)^{\frac{3}{2}} \tag{5}\]  
\(P\) is the He pressure scaled to \(T_{0}\) and \(T\) is the cell working temperature. The nuclear slowing-down factor \(q\approx 22\) is estimated considering small spin polarizations [21] in typical conditions of the current work. It describes the fact that the Cs-He and Cs-Cs electron randomization collisions don't fully destroy the nuclear spin polarization; thus, the total atomic spins cannot be fully randomized. The wall collisions can destroy the total atomic spins. The intrinsic longitudinal relaxation is shown in the Figure 4.  
The magnetometer is based on the Larmor precession of the transverse component of the total polarization vector of the atomic ensemble. The intrinsic transverse relaxation rate (\(\Gamma_{2}\)) refers to the physical processes that affect the decay of the transverse component of the total polarization vector, taking into account other factors in addition to the intrinsic  
Figure 4: The calculated intrinsic longitudinal relaxation rate. longitudinal relaxation rate. Assuming a homogeneous magnetic field, \(\Gamma_{2}\) is primarily influenced by electron spin-exchange collision relaxations between cesium atoms,  
Figure 3:0  
where \(\frac{1}{q_{SE}}\approx 0.22\) is the estimated spin broadening coefficient under a given external magnetic field when \(\omega_{L}\gg R_{\text{Cs-Cs}}^{SE}\)[21]. The spin exchange collision rate is  
Figure 3:1  
where \(\sigma_{\text{Cs-Cs}}^{SE}=2.18\times 10^{-14}\text{ cm}^{2}\)[25] is the spin-exchange collision cross-section. Note that the maximum spin exchange rate in the given temperature range is approximately \(R_{\text{Cs-Cs}}^{SE}\leq 2\pi\times 247\) Hz, which is much smaller than the Larmor frequency over the whole work. Taking into account all the processes above, the intrinsic transverse relaxation rate was solved for different temperatures and buffer gas pressures, as shown in Figure 5a. To measure the intrinsic transverse relaxation of our cesium vapor cell with 60 Torr buffer gas at \(\sim 46\)\({}^{\circ}\)C cell temperature, we used the free induction decay method (FID) [26] to obtain \(\Gamma_{2}/(2\pi)\) values for various light powers and extrapolate to zero light power (no optical power broadening). The result is shown in Figure 5b. Note that the experiment was performed under \(\text{B}_{0}=1\)\(\upmu\)T; thus, the condition \(\omega_{L}\gg R_{\text{Cs-Cs}}^{SE}\) was well satisfied. From the plot we can see that the fitted \(\Gamma_{2,0}/(2\pi)=13.15\pm 4.8\) Hz, matching the calculated value on the left plot. As for Cs magnetometers operating in the Earth's magnetic field, the quadratic Zeeman effect should be considered [27]. In an external magnetic field of 50 \(\upmu\)T, the cesium atoms in the F4 level exhibit eight equidistant Zeeman sublevels, with a spacing of  
Figure 3:2  
Obviously, within the given parameter range, the intrinsic transverse relaxation rates are comparable with the quadratic Zeeman broadenings (\(8\epsilon B^{2}=53.6\) Hz).