# A High-Sensitivity Cesium Atomic Magnetometer Based on A Cesium Spectral Lamp
## 4 Optimization Processes for Improving the Magnetometer's Sensitivity  
### Factors Affecting Magnetometer's Sensitivity  
Practically speaking, the magnetometer's sensitivity is defined as the minimum change in the magnetic field that can be measured by the magnetometer system. For an open-loop M\({}_{\text{x}}\)-type atomic magnetometers, the sensitivity \(\delta B\) can be estimated using the following expression [28]:  
\[\delta B=\frac{2\pi}{\gamma_{Cs}}\frac{\Delta\
u}{S/N} \tag{11}\]  
where \(\Delta\
u\) represents the magnetic resonance linewidth (half width at half maximum), \(S\) denotes the amplitude of the oscillating signal, and \(N\) represents the noise spectral density. It can be seen from Formula (11) that there are three routines to improve atomic sensitivity:  
(1) Reducing the magnetic resonance linewidth (\(\Delta\
u\)): The magnetic resonance linewidth is fundamentally determined by the intrinsic transverse relaxation rate that was discussed in the last section (\(\Gamma_{2}^{tot}\)), which increases with the temperature due to the spin-exchange collision effect. During the operation of the M\({}_{\text{x}}\)-type magnetometer, the operating linewidth is additionally broadened by the finite optical power and feedback magnetic field amplitude. The former can be understood in terms of the pumping process due to the continuous-wave (cw) pump/probe beam, which acts like a decay term on both longitudinal and transverse atomic polarization, thus leading to a larger relaxation rate until saturation. The latter is considered as the feedback magnetic field broadening effect for a typical radio-optical spectroscopy experiment [6]. Since these two factors are inevitable and monotonically increase  
Figure 6: (**a**) Total intrinsic transverse relaxation rate considering the quadratic Zeeman effect; (**b**) fundamental quantum limit sensitivity based on \(\Gamma_{2}^{tot}\).  
the linewidth, one should consider other processes to determine the optimal parameters for the light power and feedback magnetic field.  
(2) Increasing the amplitude of the Larmor signal: The signal amplitude at the Larmor frequency is perhaps the most complicated variable that depends on nearly all of the factors involved, including (a) cell temperature: a higher temperature results in more vapor phase atoms and a stronger signal, but also larger spin-exchange broadening, which reduces the signal amplitude; (b) buffer gas pressure: a larger buffer gas pressure results in larger collisional broadening, which decreases the initial on-resonant optical depth, thereby reducing the signal amplitude, and also introduces more buffer gas collisional relaxation (although in the current range it is not significant, see Figure 5), whereas a smaller buffer gas pressure causes the atomic vapor to experience more wall collisions, thereby also reducing the signal; (c) light power: larger light power generally produces a larger optical depth change, leading to a large signal amplitude until saturation occurs, while the entire pumping process is also not trivial to model [29]; (d) feedback magnetic field: a larger feedback magnetic field initially increases the signal amplitude, while feedback magnetic field saturation happens later [30].  
(3) Reducing system noise: There are two sources of system noise: the first type is the photon shot noise of the optical source, and the other type comprises all kinds of technical noise, including fluctuations of the light power/frequency from the lamp, photodetector dark current noise, feedback resistor thermal noise, amplifier voltage-current noise, etc. The photon shot noise of the cesium spectral lamp is proportional to the amplitude of the DC optical current, which increases monotonically with the input light power until saturation. The other factors mentioned in (2) above generally do not influence the noise floor, except for technical imperfections like the fluctuations in the feedback magnetic field amplitude, as well as thermal noise when increasing the environmental temperature.