Fig. 1. Working principle of the dual-frequency optical-microwave atomic clocks based on cesium atoms. (a) Level scheme for the Cs133 atom, which shows the 852 nm optical transition that was used to pump 6S1/2(F=4)−6P3/2(F′=4) and detect 6S1/2(F=4)−6P3/2(F′=5) for the Cs beam atomic clock. The 9.12 GHz microwave (MW) was used as the microwave clock signal. (b) Sketch of the optical-microwave atomic clock generation, which consists of three modules: (I) the optical atomic clock generating module; (II) the optical atomic clock evaluating module; and (III) the microwave atomic clock generating module. An external-cavity diode laser (ECDL) was frequency-stabilized using the modulation transfer spectroscopy (MTS) technique. This laser source was divided into two parts. One beam beat with the Nth tooth of an erbium-doped optical comb to estimate the frequency stability of the optical frequency standard with beat-note signal fb, which was compared with a hydrogen maser. The initial frequency f0 and repetition frequency frep were locked to a hydrogen maser whose frequency stability was 1×10−13 at 1 s. Then, the other beam was divided into two beams to pump and detect the lasers of the optically pumped Cs beam clock. Notations in the image: ISO, optical isolator; HWP, halfwave plate; PBS, polarized beam splitter; EOM, electro-optic modulation crystal; PD photodetector; AOM, acousto-optic modulation crystal; MW, microwave; EC, electronic control module; M, high-reflectivity mirror. (c) Physical image of the dual-frequency optical-microwave atomic clocks. From left to right, there are the optics physical module, optics electrical module, and Cs microwave clocks. The optics physical and electrical modules were integrated into the microwave clock. The size of each module is indicated in the picture.

Fig. 2. Primary laser characteristics. (a) Output laser power P (purple dotted line) as a function of the current applied to the laser diode. The maximum laser power was 45 mW. Inset: light spot profile output from the ECDL approximately L=30  cm away from the external cavity feedback mirror. It worked at the TEM00 mode for the next frequency stabilization. (b) Wavelengths of the ECDL with the change in injected current to the laser diode (blue dotted line) and voltage applied on the PZT (black dots). (c) Saturation absorption spectrum (red line) and the corresponding modulation transfer spectrum (green line) of the Cs6S1/2(F=4)−6P3/2(F′=3,4,5) transition. (d) Beat-note spectra (grey dots) between two identical 852 nm ECDLs. The resolution bandwidth was 5.1 kHz with a sweep time of 10 ms and a span of 10 MHz. Using Lorentz fitting, the fitted beat-note linewidth was 39.95±1.91  kHz, which indicates that the linewidth of each ECDL was 28.25 kHz because the two ECDLs contributed equally to the laser noise. (e) Allan deviation of the MTS error signal after locking. It reflects the stability of the in-loop locking, i.e., the tracking accuracy between ECDL and transition frequency of the reference atoms. The data were measured by recording the amplitude fluctuation of the error signal and transfer to the frequency fluctuation of the locking frequency point. The frequency stability of the in-loop locking (light blue line) was 9.3×10−14 at 0.1 s and decreased to 2.2×10−14 at 26 s. The dark blue dotted line represents the linear fitting of experimental data, and the result was 4.3×10−14/τ.

Fig. 3. Frequency stability characteristic of the 852 nm optical frequency standard. (a) Frequency fluctuation of the beat-note signal between the 852 nm optical laser and the Nth laser mode of the optical comb frequency near the Cs6S1/2(F=4)−6P3/2(F′=5) transition. (b) Allan deviation of the beating frequency recorded in (a). Frequency compared with a hydrogen maser; the frequency stability of the 852 nm optical frequency standard was 3.9×10−13 at 1 s and 2.2×10−13 at 32 s. After 100 s, the Allan deviation worsened because of the temperature drift of the atomic vapor temperature and power fluctuation of the pumping and probe lasers. Finally, the frequency stability was 5×10−12 over 104  s.

Fig. 4. (a) Vapor-cell temperature Tcell fluctuation-induced frequency drift of the 852 nm optical frequency standard with the change of measurement time. The frequency shift was measured by recording the Tcell fluctuation and combining the collision frequency shift coefficient. The coefficient is 5 kHz/°C under the vapor-cell temperature of around 35°C. (b) The frequency stability induced by vapor-cell temperature fluctuations is calculated by Allan deviation, which reflects the limited Allan deviation caused by vapor-cell temperature fluctuation.

Fig. 5. (a) Power-fluctuation-induced frequency drift of the 852 nm optical frequency standard with the change of measurement time. The drift was assessed by monitoring fluctuations in the local oscillator’s power and considering the AC Stark frequency shift coefficient. This coefficient is measured at 30 kHz/mW when the probe laser operates at approximately 0.1 mW. (b) The frequency stability induced by power fluctuations using Allan deviation reveals the resultant limitations caused by these fluctuations.

Fig. 6. Frequency stability characteristic of a Cs microwave clock. (a) Ramsey fringes of the Cs microwave clock transition (green line) corresponding to the frequency stability depicted by black dots in the bottom image. (b) Frequency stability of the Cs microwave clock. The 10 MHz frequency signal output from the optically pumped Cs beam clock was recorded by a frequency counter, which was referenced by the hydrogen maser. The black square dots and blue circle dots represent the frequency stability calculated by Hadamard and Allan deviations, respectively. They both use ECDL, whose frequency is stabilized by MTS, as the pumping and probe lights. The pink triangular points represent the result of Allan deviation using DFB laser, whose frequency is stabilized by SAS, as the pumping and probe lights. The Hadamard deviation (black squares) of the frequency was 1.8×10−12 at 1 s and 6×10−15 at 105  s. It was linearly fitted to 1.8×10−12/τ, as shown by the red dotted line.