## 4 Results and Discussion  
To create the dark state, the frequency of \(\omega_{\pm}\) beam is modulated via the application of a triangular waveform to the 2 nd-AOM driver using a National Instrument (NI) software and hardware (myDAQ) (a standard laboratory function generator could also be used, however the former method is chosen for reasons related to flexibility in controlling of the applied signal). This triangular waveform produces the desired modulation required for CPT, however, it creates a problem that is critical for the observation of CPT. This problem is related to the dependency of the diffraction angle and therefore the separation between the zeroth and the first order diffracted beam on the applied RF signal. Figure 2: Double pass configuration optical setup. The incident and retroreflected beams, using a mirror (M), are orthogonally circularly polarized due to the presence of the quarter-wave plate \(\frac{\lambda}{4}\), and they are separated through the polarizing beam splitter (PBS). In both the incident and retroreflected beam, the zeroth order beams are blocked using a beam stop (S). The root of the problem can be explained as follows. When a triangular waveform is applied to the AOM driver, the diffraction angle also follows this triangular signal, as it is well known there exists a direct relationship between the diffraction angle and the applied RF signal, as can be seen from Equation (1). \[\Theta=\frac{\lambda\ f_{RF}}{2\,n\,V_{A}} \tag{1}\]  
Here, \(\Theta\) is the diffraction angle, \(\lambda\) is the optical wavelength, \(f_{RF}\) is the RF frequency that depends on the voltage applied to the AOM driver, \(n\) is the refractive index of the AOM crystal (which is tellurium dioxide \(TeO_{2}\) for the AOM used), and \(V_{A}\) is the acoustic velocity. Due to the above dependency, a variable beam steering for the first order diffracted beam is created. As a result, a periodical change in the degree of overlap between \(\omega_{0}\) and \(\omega_{\pm}\) forms. Critically, previous studies have shown broadening of the linewidth due to decreased overlap between the two beams [21; 28; 29]. Consequently, application of a triangular waveform creates a periodical change in the broadening of the dark resonance, which introduces artifacts to the CPT signal and ultimately a reduction in sensitivity of the magnetometer. These problems clearly defeat the purpose of creating a sensitive magnetometer based on this method and, therefore, one must avoid them. There has been some efforts to reduce the above beam steering effect, namely in the form of a double pass configuration [30] as well as the use of fiber-optic cable [31], where the two beams are coupled together to eliminate the change in overlapping between the two beams. Although these methods reduce the beam steering effect, they introduce further complications in the form of intensity fluctuation in the modulated beam. This is because, as a result of the applied triangular signal, the coupling efficiency of the fiber cable changes periodically, as the modulated beam moves in and out of focus of the lens that is used to couple the light with the optical cable. This fluctuation in intensity creates a periodical power difference between \(\omega_{0}\) and \(\omega_{\pm}\) and, as a result, the interaction frequency between the two beams shifts due to a light shift phenomenon [20]. The periodical variation in intensity shifts the position of the CPT resonance and, as a result, a magnetometer based on this method is impractical unless these technical difficulties are overcome. This is because it cannot be determined if the shift in the resonance position is due to the intensity fluctuation or due to changes in the B-field in the vicinity of the detector. To reduce and eliminate this change in the intensity fluctuation and the change in overlapping degree between \(\omega_{0}\) and \(\omega_{\pm}\), an optical setup was used as shown in Figures 1 and 2.