# A High-Sensitivity Cesium Atomic Magnetometer Based on A Cesium Spectral Lamp
## 2 Design and Construction of Cesium Atomic Magnetometer
### Electronic Unit
The Larmor signal from the photodetector is firstly amplified by a preamplifier and then stabilized using automatic gain control (AGC) to maintain a constant amplitude. It is then further amplified in an intermediate stage before being fed into the feedback coil inside the sensor through a 90\({}^{\circ}\) phase shift circuit, generating the feedback magnetic field with the Larmor frequency. Self-oscillation is automatically achieved through a positive feedback process. Simultaneously, the intermediate stage output signal is shaped into a square wave through a comparator and fed into a frequency measurement module, resulting in the corresponding values of the external magnetic field. This self-oscillating technique ensures a rapid response and accurate measurement of the magnetic field while maintaining stability. Evaluation of the Intrinsic Spin Relaxation and Magnetometer's Fundamental Quantum Limit Sensitivity  
The quantum spin projection noise of the involved cesium ensemble ultimately determines the sensitivity of the cesium magnetometer and can be calculated as a function of the atomic number and intrinsic transverse relaxation rate for a specific measurement duration [1]. Even though it has been widely evaluated in some modern magnetometer configurations (for example, spin-exchange-relaxation-free magnetometer and comagnetometer, etc. ), there remains a lack of effort on this topic for conventional Mx magnetometers working in geomagnetic applications. Moreover, to properly analyze and quantify various intrinsic spin relaxation processes is always the first step for the implementation of an atomic magnetometer. Because the working conditions of each sensor and the specific application characteristics of magnetometers are different, the intrinsic spin relaxation process needs to be specifically analyzed [19; 20]. In this work, Helium-4 (He) is used as the buffer gas to localize the cesium atoms, and the dimension of the cylindrical cell is \(\Phi\)25 mm \(\times\) L 25 mm (\(\Phi\) is the diameter of the bottom surface and L is the length). We briefly calculate the total intrinsic relaxation rate of the cesium vapor over a practical parameter space (cell heating temperature range: 30-70 \({}^{\circ}\)C; He pressure range: 20 Torr to 200 Torr), considering all types of spin relaxation processes. A separate experimental measurement is performed to verify the calculation. Moreover, for Earth magnetic field measurement, the quadratic Zeeman effect of cesium vapor is found to be the main broadening mechanism over the current cell parameter range and used to estimate the quantum limit sensitivity. First of all, the intrinsic spin depolarization rate (longitudinal relaxation rate) can be described as follows [21],  
\[\Gamma_{1}=\frac{1}{\mathrm{T}_{1}}=\frac{1}{q}\Big{(}R_{\mathrm{Cs-He}}^{SD}+ R_{\mathrm{Cs-Cs}}^{SD}\Big{)}+R_{\mathrm{Cs-wall}} \tag{1}\]  
where \(R_{\mathrm{Cs-He}}^{SD}\), \(R_{\mathrm{Cs-Cs}}^{SD}\), and \(R_{\mathrm{Cs-wall}}\) are electron spin-destruction rates due to collisions between Cs and He, between Cs atoms and the wall collisions, and \(q\) is the nuclear slowing-down factor, accounting for the remaining nuclear spin polarizations after collisions [21]. The Cs-He electron spin-destruction rate (or electron randomization rate) is typically much smaller than the normal collision rate between Cs and He. Thus, the spins of the cesium can be preserved during the multiple normal collisions with He and the movement of cesium atoms towards cell walls slows down dramatically. The very few electron randomization collisions can be characterized by an electron spin-destruction collision cross-section \(\sigma_{\rm Cs-He}^{SD}=2.43\times 10^{-23}\) cm\({}^{2}\)[22] and calculated as  
\[R_{\rm Cs-He}^{SD}=n_{\rm He}\sigma_{\rm Cs-He}^{SD}\overline{v}_{\rm Cs-He}^{ rel} \tag{2}\]  
where \(n_{\rm He}\) is the number density of He and \(\overline{v}_{\rm Cs-He}^{rel}\) is the relative velocity between Cs and He.