Fig. 1. Fabrication process of the wafer-level MEMS vapor cell. (a) Borosilicate glass wafer. (b) Si–glass two-layer wafer bonded by anodic bonding. (c) Photograph of (b). (d) Filling Rb dispensers into the reactive chambers. (e) Formation of Si–glass–Si three-layer wafer. (f) Photograph of (e). (g) Wafer dicing to form individual cells. (h) Vapor cell after activation with a 980 nm laser. (i) Photograph of the final vapor cell (14mm×14mm×4.3mm).

Fig. 2. Compact optical frequency standard with wafer-level MEMS vapor cells. (a) Photograph of the vapor cell. (b) Design of the vapor cell structure. (c) Clock transition line: Rb87 D2 transition. (d) Photograph of the compact optical frequency standard with dimensions of 28.5cm×28.5cm×14cm. (e) Schematic diagram of experimental setup, the compact optical standard based on modulation transfer spectroscopy.

Fig. 3. Spectra obtained using the MEMS vapor cell. The red curve shows the saturated absorption spectroscopy (SAS), and the black curve shows the modulation transfer spectroscopy (MTS). The strongest MTS signal corresponds to the Rb87D2 transition from Rb8752S1/2F=2 to 52P3/2F′=3, which is used for laser frequency locking.

Fig. 4. Temperature optimization of the wafer-level MEMS vapor cell. (a) Slope of the MTS signal at the zero-crossing point versus cell temperature. (b) Short-term frequency stability as a function of temperature. The optimal operating temperature is determined to be 80°C. The MTS slope increases with temperature, peaks near 80°C, and then decreases. The self-evaluated frequency stability follows a similar trend. In contrast, beat frequency stability shows a different trend because only one system was optimized for slope, while the beat measurement depends on both systems.

Fig. 5. Frequency stability comparison of thermal atomic optical frequency standards based on miniature vapor cells. The black solid line with squares represents this work, using modulation transfer spectroscopy (MTS) on rubidium atoms. Other curves show previously reported results using saturated absorption spectroscopy (SAS), two-photon spectroscopy (TPS), and dual-frequency sub-Doppler spectroscopy (DFSDS) with either rubidium or cesium atoms. The comparison highlights that, despite employing different techniques, the frequency stabilities achieved by state-of-the-art optical references based on miniature vapor cells have become increasingly comparable in recent years.

Fig. 6. (a) Frequency noise spectra of free-running and locked laser beatnotes. (b) Corresponding phase noise spectra. Under locked conditions, the estimated instantaneous linewidth is approximately 6 kHz, corresponding to a single-laser linewidth of 4.24 kHz.

Fig. 7. Analysis of limiting factors affecting the frequency stability of the optical frequency standard. Panel (a) shows the time-domain frequency fluctuations of the locked laser. Panel (b) presents the frequency shifts induced by temperature variations in the EOM. Panel (c) compares the Allan deviation obtained via beat frequency and self-evaluation methods. The short-term frequency stability of a single system reaches 2.6×10−13 at 1 s, and improves to 5.1×10−14 at 200 s for mid-to-long-term averaging times. The estimated contributions from key noise sources are also plotted: laser FM-AM noise (orange dashed line), photon shot noise (yellow dashed line), EOM temperature fluctuations (red solid line), MEMS vapor cell temperature fluctuations (blue solid line), laser power drift (green solid line), and electrical noise (purple solid line). The measured stability (black solid line) reflects the combined influence of these effects. Laser FM-AM noise and EOM thermal fluctuations dominate the short-term instability, while vapor cell temperature drift becomes the main limitation at longer timescales.

Fig. 8. The typical Lorentzian-fitted beat frequency linewidth of 5.5 kHz, with a single laser linewidth of 3.9 kHz. Inset: typical beating data with one laser free-running; the fitted FWHM is 60.4 kHz.