## 3 Method  
In this work, we have tuned an ECDL to the \(D_{1}\) line of \({}^{87}Rb:F=2\to F^{\prime}=1\) to create a \(\Lambda\)-type configuration based on the Zeeman sub-levels. This arrangement is chosen to maximize the response and increase the sensitivity of the magnetometer. For example, the choice of \(F_{g}>F_{e}\) such as \(F=2\) and \(F^{\prime}=1\) (where \(g\) and \(e\) are the ground and excited states, respectively ) results in observation of sub-natural linewidth resonance [25], whereas the \(D_{1}\) line of Rb produces narrower linewidth and higher CPT amplitude as compared to the \(D_{2}\) line. It has been reported that the \(D_{1}\) line offers a nearly ten-fold improvement in the performance of a CPT based magnetometer as compared to the \(D_{2}\) line [26], and, finally, \({}^{87}Rb:F=2\) has the highest gyromagnetic ratio [27], thus it has a higher B-field sensitivity as compared to the other states. The experimental setup consists of two main regions, as shown in Figure 1. These are the interaction region (represented by green), where control and manipulation of the atom-light interaction takes place, whereas the property of the laser beam is monitored via the frequency measurement and monitoring region (in blue). The frequency measurement and monitoring region consists of three main parts, as can be seen in Figure 1. The first component is a Fabry-Perot interferometer from Toptica FP100 with a Free Spectral Range of 1 GHz and a finesse of 186. The second component is made up of a Doppler-free saturated absorption spectroscopy (DF-SAS) setup, through which the desired scanning frequency and peak of Rb is chosen for use in subsequent part of the experiment. A wavemeter makes up the last part of this setup, which it is mainly used to measure the actual wavelength of the laser in vacuum and to monitor the locking property of the laser when the ECDL was locked to a given transition of Rb atom. The incident laser beam that is directed toward the interaction region of the experiment is split via a polarizing beam splitter. The s-polarized component, which acts as the coupling beam (\(\omega_{0}\)), is directed towards a reference cell. The atomic ensemble cell contains Rb atoms with 30 Torr Ne buffer gas. The cell is placed in a solenoid, and a small magnetic field of  
Figure 1: Optical setup of the experiment. The setup is divided into two regions: the frequency measurement and monitoring region in blue, and the Interaction region in green, which highlights the main part of the experiment. In the figure, (ECDL) is external cavity diode laser, (DF-SAS) is Doppler free saturated absorption spectroscopy setup for locking purposes, (FPI) is a Fabry–Perot interferometer, (OI) is an optical isolator, (BS) is a beam splitter, (PBS) is a polarizing beam splitter, (\(\frac{\lambda}{2}\)) is a half-wave plate, (\(\frac{\lambda}{2}\)) is a quarter-wave plate, (PCV) is a plano-convex lens, (CM) is a concave mirror, (BCV) is a biconvex lens, (BD) is a beam dump, (PD) is a photodiode, and the AOM is the Bragg cell. The two AOMs are in double pass configuration, where the first AOM shifts the frequency up, whereas the second AOM shifts the frequency down and is used for scanning. 250-450 mG is applied to lift the degeneracy of the Zeeman sub-levels. The whole system is then installed in a three layer \(\mu\)-metal cylinder that has a measured magnetic shielding factor of more than 10\({}^{4}\). The p-polarized component, acting as the probe beam (\(\omega_{\pm}\)), is directed onto the AOM setup. This part of the setup consists of two AOMs, where the first AOM (1 st-AOM in Figure 1) is placed in frequency shift up position (\(+1\)st order diffracted beam is observed), while the second AOM (2 nd-AOM in Figure 1) was set up in frequency shift down configuration (\(-1\)st diffraction order is created).