# The Microfabricated Alkali Vapor Cell with High Hermeticity for Chip-Scale Atomic Clock
## 3 Results and Discussion  
The optical absorption spectroscopy of the microfabricated cell was characterized using a 795 nm ECDL laser resonant with a Rb D1 line to verify the presence the Rb vapor and buffer gas. As Figure 6 shows, a saturated absorption line in a cm-scale pure Rb cell was used as the reference to compare it with the microfabricated cell. The microfabricated cell containing Rb and 70 torr nitrogen was heated to 90 \({}^{\circ}\)C to ensure the sufficient density of the atoms, and the absorption spectroscopy of the reference cell was measured at ambient temperature. Although the microcell was heated to 90 \({}^{\circ}\)C, the intensity of the absorption peaks was still relatively weak compared to the reference cell due to the only 1 mm optical path in the microfabricated cell. Without buffer gas, two optical absorption peaks (87 Rb: Fg = 1 \(\rightarrow\) Fe = 2, Fg = 2 \(\rightarrow\) Fe = 2) of the reference Rb cell were separated by the Rb hyperfine transition frequency and were broadened by the Doppler effect. For the microfabricated cell, the absorption peaks were broadened and shifted by the addition of the buffer gas. The absorption peaks were also broadened by the increasing laser power. Figure 7 exhibits the typical result of a CPT resonance in a Rb-N2 MEMS cell heated at 90 \({}^{\circ}\)C. The laser beam has a diameter of 1 mm and a power of 120 \(\upmu\)W. The 0-0 CPT resonance is well fitted by a Lorentzian function with a linewidth of 28 kHz. The linewidth was about an order of magnitude broader than the typical CPT linewidth based microfabricated cell as the content of N2 was decreased by the absorption of Zr-Al getter in the SAES dispenser [20]. The wall collision decoherence contributed to the abnormal broadening of the CPT linewidth in our results. The contrast of the resonance, which was identified as the ratio between the height and the DC background, was measured to be 1.1%. It did not clamp the expected short-term frequency stability (1 \(\times\) 10\({}^{-10}\)) of the chip scale atomic clock [21]. Figure 5: Schematic of the table-top CPT system with MEMS cell. EOM: electro-optic modulator. PD: photodiode. A CPT resonance line shape can be fitted by Lorentzian, and its full width at half maximum FWHM is given by the following [22]:  
\[FWHM=\frac{1}{\pi}\Bigg{(}\gamma_{2}+\frac{\omega_{\rm R}^{2}}{\Gamma^{*}} \Bigg{)} \tag{1}\]  
where \(\gamma_{2}\) is the hyperfine coherence relaxation rate, \(\Gamma^{*}\) is the linewidth of the optical resonance, and \(\omega_{\rm R}\) is the optical Rabi oscillation frequency related to the laser intensity I (\(\omega_{\rm R}^{2}\propto l^{2}\) laser power). So, as shown in the Figure 8, the CPT linewidth increases linearly with the laser power. The slope of linear fitting in Figure 8 decreases as the buffer gas pressure increases due to the pressure broadening of the optical resonance (\(\Gamma^{*}=\Gamma+kP\)). This means that in our anodic bonding system, the buffer gases of different pressure were filled in the microfabricated cells. The CPT linewidth was dominated by collisions of the atoms with the cell walls, and the N\({}_{2}\) was utilized to prevent the diffusion and decoherence of atoms. Therefore, under the same optical power, the linewidth of the CPT signal was gradually narrowed as the buffer gas pressure increased (50-90 torr). This is shown in Figure 8. The linewidth is related to the different relaxation rates, as shown in the following Equation (2) [23]:  
Figure 6: Optical absorption lines obtained in a cm-scale pure Rb reference cell (Pink dot) compared to a Rb-N\({}_{2}\) microfabricated cell heated at 90 \({}^{\circ}\)C with laser power from 40 \(\mu\)W to 110 \(\mu\)W.  
Figure 7: Typical CPT resonance obtained in a Rb-N\({}_{2}\) cell (inset: simplified schematic of three-level system involved in Rb cells CPT resonances, \(\Gamma^{*}\): linewidth of the optical resonance). The red line is a Lorentzian fit to the experimental data (black dot).