The contributions of precise frequency measurements to global communications, satellite navigation, and scientific research can hardly be overestimated, as it enables us to build the most accurate atomic clocks [1–4]. This feature allows atomic clocks to have a broad range of applications in basic physics research through frequency ratio measurements [5], such as the verification of general relativity [6], dark matter detection [7], detection of changes in physical constants over time [8], and definition and revision of a base unit of time in the International System of Units (SI) [9]. Although the measurement precision of the optical-lattice and single-ion clocks has reached the mid-19th digit [2–4], scientists continue to enrich the types of atomic clocks to probe for physics beyond the standard model, such as highly charged ions [10], single molecular ions [11], vibrational molecular lattice [12], hydrogen optical lattice [13], mercury ion [14], thorium-229 nuclear clock [15], and even nature’s clock of millisecond radio pulsars [16].

Despite the fact that there are many types of atomic clocks and that the Consultative Committee for Time and Frequency (CCTF) is committed to updating the roadmap toward the redefinition of the SI second [9,17,18], the current frequency standard realizations are based on the Cs atom. To maintain continuity with the definition based on Cs, an ensemble definition can be created using the weighted geometrical mean of the frequencies of an ensemble of selected transitions, including Cs [19]. Therefore, the combination of Cs microwave clocks and optical clocks is widely applicable with their practical and performance advantages, respectively.

The Cs clock, being the most outstanding of the atomic clocks, is utilized to establish the definition of the SI second. Cs atoms have only one stable isotope ${}^{133}\mathrm{Cs}$ with a low moving speed at room temperature, which results in a narrow Doppler broadening. In addition, its hyperfine energy level is simple, so the Cs atomic clock has been used as the primary frequency standard since 1967. The lifetime [$\tau =30.105(77)\mathrm{ns}$] [20–22] of the $6{\mathrm{P}}_{3/2}$ states provides a natural linewidth of approximately $2\pi \times 5.234(13)\mathrm{MHz}$. This is sufficiently narrow to serve as a frequency reference for sub-Doppler spectroscopy. In addition, Cs has many relevant physical and optical properties to various quantum optics experiments. First, optical clocks based on thermal atoms have a more compact structure and are easier to transport than optical lattice and ion clocks. Second, the frequency comparison among compact optical clocks is convenient and practical, which will enable significant advancements in various applications from laboratory to environmental studies. Third, the Cs optical clock can be used as a high-performance laser source to integrate into an optically pumped cesium beam atomic clock to reduce the laser frequency noise and facilitate a high-performance microwave atomic clock. Thus, atomic clocks that use Cs atoms as quantum references are of great significance.

In this study, we employed a Cs vapor cell for optical atomic clocks and a Cs atomic beam for microwave atomic clocks as our frequency references. Both clocks could be freely switched or simultaneously output. The physics package for the Cs optical clock was divided into optics and electronics boxes with dimensions of $428\mathrm{mm}(W)\times 200\mathrm{mm}(D)\times 57.8\mathrm{mm}(H)$ and $430\mathrm{mm}(W)\times 200\mathrm{mm}(D)\times 32\mathrm{mm}(H)$, respectively. A homemade external-cavity diode laser (ECDL) was frequency-stabilized to the $\mathrm{Cs}6{\mathrm{S}}_{1/2}(F=4)-6{\mathrm{P}}_{3/2}(F^{\prime }=5)$ transition using modulation transfer spectroscopy (MTS) [23–28]. The frequency stability of the Cs optical clock was $4\times {10}^{-13}/\sqrt{\tau }$, as measured by the erbium-doped optical comb, which was frequency referred to the active hydrogen maser. Furthermore, this compact optical frequency standard was used as the pump and probe lasers for the optically pumped Cs beam atomic clock, which had an overall size of $553\mathrm{mm}(W)\times 454\mathrm{mm}(D)\times 177\mathrm{mm}(H)$. The frequency stability of the Cs beam clock was $1.8\times {10}^{-12}/\sqrt{\tau }$ and reached $6\times {10}^{-15}$ at ${10}^5\mathrm{s}$. Since many physical and optical properties of Cs are relevant to various quantum optics experiments, this dual-frequency microwave-optical atomic clock based on thermal Cs atoms is technically ready for field applications. For example, it can serve as a timer for global satellite navigation and a high-performance light source for frequency comparison, which will have an immense impact on society.

Consequently, our work offers three main advantages. (i) Our dual-frequency optical-microwave atomic clocks are referenced to the microwave and optical transitions of Cs atoms, which define the SI second. This broad applicability stems from their practical and performance-based benefits. (ii) The 852 nm optical atomic clock and the Cs beam microwave atomic clock exhibit favorable short- and long-term frequency stabilities, respectively, enabling satisfactory performance across averaging times ranging from 1 to ${10}^5\mathrm{s}$. (iii) The dual-frequency microwave-optical atomic clock we propose not only demonstrates outstanding performance, but also boasts a highly compact design. By carefully dividing the 852 nm optical frequency standard into separate physical and electrical modules for optics, we seamlessly integrate them into the microwave clock. These innovative dual-wavelength optical-microwave atomic clocks, which utilize Cs atoms, are compact and easily portable, significantly expanding the potential applications and capabilities of atomic clocks.

Here, we report an experimental demonstration of the dual-frequency optical-microwave atomic clocks. Figures 1(a) and 1(b) show the energy level scheme and general setup, respectively. The transitions of Cs atoms at optical and microwave frequencies were used as reference standards of the optical and microwave clocks. For the optical clock, an ECDL working at a wavelength of 852 nm was used as the local oscillator, whose frequency was stabilized to the $6{\mathrm{S}}_{1/2}(F=4)-6{\mathrm{P}}_{3/2}(F^{\prime }=5)$ transition of thermal Cs atoms inside a vapor cell using the MTS technique, as shown in Fig. 1(b). Then, the frequency stability of the 852 nm optical frequency standard was estimated by optical heterodyne between the 852 nm laser and one tooth of the optical frequency comb, whose wavelength was nearly 852 nm. The initial frequency and repetition frequency of the optical comb were stabilized to a hydrogen maser. This stabilized low-noise 852 nm laser was also used as a light source of the optically pumped Cs beam clock. The 852 nm laser was divided into two parts: one part was frequency-shifted at approximately 251 MHz to the transition of $\mathrm{Cs}6{\mathrm{S}}_{1/2}(F=4)-6{\mathrm{P}}_{3/2}(F^{\prime }=4)$ as the pumping laser; the other part was the detection laser of the microwave clock. By reducing the frequency noise of the laser source, we optimized the frequency stability of the Cs beam clock. In summary, we obtained a high-performance dual-wavelength microwave-optical atomic clock.

With the MTS technique [29], i.e., transfer of modulation from the phase-modulated pump laser to the unmodulated probe laser, the modulated hole burning occurred in a sufficiently nonlinear resonant atomic medium in a vapor cell. Compared with saturation absorption spectroscopy (SAS), MTS reduces the direct feed-through of the laser amplitude noise while retaining most of the signal. In addition, MTS utilizes the advantage of high modulation frequencies and four-wave mixing to enhance the signal-to-noise ratio (SNR) performance above polarization spectroscopy. As an optically heterodyned saturation spectroscopy technique, MTS has the advantages of high resolution, high sensitivity, and being Doppler-free. Further, vapor-cell-based optical frequency standards feature a small size and low cost compared to optical frequency standards based on single ions and cold atoms, which promise a potential stability of ${10}^{-19}$ [2,3], so vapor-cell-based optical frequency standards are expected to realize a transportable optical clock.

Therefore, we demonstrate a simple optical clock frequency stabilized to the $6{\mathrm{S}}_{1/2}(F=4)-6{\mathrm{P}}_{3/2}(F^{\prime }=5)$ optical transition of Cs thermal atoms using the MTS technique. Cs atoms have a low melting point of only 28.5°C, which can greatly reduce the power consumption. Moreover, the manufacture of a laser diode with an operation wavelength of 852 nm is mature. As shown in Fig. 2(a), a homemade ECDL frequency selected by an interference filter was used as the local oscillator; its laser power could reach 45 mW, which is sufficient for frequency stabilization and application. The laser worked in the TEM00 mode and was wavelength-tunable with the voltage of piezoelectric ceramic (PZT) to adjust the cavity length, and a current was applied on the laser diode, as depicted in Fig. 2(b). To improve the environmental adaptability of the laser system, we designed the secondary temperature control for the laser diode with an accuracy of 0.01°C. Next, the laser frequency was locked to the transition frequency of thermal Cs atoms. The double-layer Ni-Fe alloy and multi-layer Teflon were designed outside the vapor cell for magnetic shielding and heat retaining. Then, we locked the laser mode output from the 852 nm ECDL to the quantum reference using MTS. Through optimization, the power ratio between pumping laser and probe laser was 6:1, the vapor temperature was 35°C to adapt to the high-temperature Cs oven inside a sealed atomic beam clock, the modulation frequency applied on the EOM was 4.97 MHz, and the slope of the MTS error signal was optimized to 0.07 V/MHz [Fig. 2(c)]. The full width at half maximum of the beating power spectroscopy was $39.95\pm 1.91\mathrm{kHz}$ as measured by the optical heterodyne between two identical stabilized ECDLs [Fig. 2(d)]. The in-loop frequency stability reached $4.3\times {10}^{-14}/\sqrt{\tau }$ [Fig. 2(e)]. This was measured by recording fluctuations in the amplitude of the residual error signal after frequency locking, then converting the amplitude values into frequency values, and calculating the in-loop frequency stability; this method shares many similarities with that proposed in Ref. [30]. The in-loop locking accuracy can only reflect the tracking accuracy between local oscillator and frequency reference. The deterioration of frequency stability is mainly caused by mechanical vibration, temperature changes of the vapor cell and the EOM, and electrical locking noise. Moreover, we designed a function to automatically scan the atomic spectroscopy and relock again after losing lock to improve the reliability and increase the continuous locking time of the frequency-stabilized laser.

Here, we used an optical comb to estimate the frequency stability of the compact cell-based optical frequency standard. As shown in Fig. 1(b), the frequency-stabilized 852 nm laser was beam-combined with the $N\mathrm{th}$ tooth of the erbium-doped optical comb to measure its frequency stability. The initial frequency $f_0$ and repetition frequency $f_r$ ($\sim 200\mathrm{MHz}$) were both locked to a hydrogen maser, so the phase-tracking stability and frequency instability of the optical comb were better than $5\times {10}^{-16}/\sqrt{\tau }$ and $1\times {10}^{-13}/\sqrt{\tau }$, respectively. Next, the frequency of the beating signal $f_b=f_N-f_{\mathrm{cw}}$ was recorded by a frequency counter using the hydrogen maser as the frequency reference. The frequency stability of the hydrogen maser was better than $1\times {10}^{-13}/\sqrt{\tau }$.

After 28 h of measurement, the frequency fluctuation of the stabilized laser was smaller than 8 kHz, as shown in Fig. 3(a). Therefore, the Allan deviation of the 852 nm optical frequency standard was $3.9\times {10}^{-13}$ at 1 s, $2.2\times {10}^{-13}$ at 32 s, and $3.3\times {10}^{-12}$ at ${10}^4\mathrm{s}$, as shown in Fig. 3(b). The large frequency change within 10 h resulted in a temperature drift of the atomic vapor cell that was used as the frequency reference. After a period of operation, the atomic temperature, i.e., the atomic number density, gradually stabilized, and the collision and Doppler shifts caused by atomic number fluctuation decreased. However, the frequency stability decreased to the best value of $2.2\times {10}^{-13}$ at 32 s and worsened afterward because the long-term temperature drift of the reference atoms and electro-optic modulation crystal induced a frequency drift of the locking point and residual amplitude modulation (RAM) noise, respectively. Moreover, the power fluctuations of the pumping and probe lasers in MTS induced a light shift, which also worsened the long-term results. The frequency of the local oscillator is stabilized to the atomic reference. Consequently, the laser frequency is affected by fluctuations in the reference frequency. We thus examined the primary technical noises [24,25,27,28] that impact the frequency stability of the 852 nm optical frequency standard.

When atoms collide within a vapor cell, they can disturb the wave function of ground and excited states, leading to frequency shifts correlated with atomic density. In this study, a cloud of Cs atoms is confined in a vapor cell and heated to 35°C, resulting in a high atomic density of approximately $1.3\times {10}^{13}{\mathrm{cm}}^{-3}$ [31]. Even a minor temperature fluctuation of 0.1°C can cause a density change on the order of ${10}^{11}{\mathrm{cm}}^{-3}$. The vapor cell’s temperature is controlled by its cold finger, so any temperature fluctuation in the cold finger’s temperatures affects the atomic density, thereby inducing frequency drift in the atomic reference. Furthermore, fluctuations in the vapor-cell temperature not only contribute to collision-induced frequency shifts but also introduce variations in the SNR of the MTS, which in turn affects the Allan deviation of the 852 nm optical frequency standard.

To assess the impact of temperature fluctuations, we monitored the temperature variations of the cold finger in the vapor cell over an 18-hour period. The short-term temperature stability was measured at approximately $1.0\times {10}^{-6}$ per second averaging time. Concurrently, we determined the collision frequency shift coefficient to be around 5 kHz/°C at a vapor-cell temperature of approximately 35°C. This coefficient was obtained by observing changes in beat-note frequency between a tested laser and a reference laser, where the reference laser was frequency-locked using the MTS.

As a result of temperature fluctuation (and consequent atomic density fluctuations), the frequency stability was calculated to be $5.3\times {10}^{-16}$ per second. The frequency drift over the 18-hour period is depicted by the light blue line in Fig. 4(a). Analyzed through Allan deviation [Fig. 4(b)], the frequency stability induced by vapor-cell temperature fluctuations shows the impact on the overall system performance in the short term. However, to mitigate potential effects on long-term frequency stability, we plan to introduce an insulating functional layer to mitigate the influence of temperature fluctuations.

The transition frequency of atoms is inevitably affected by external electromagnetic fields, resulting in Stark and Zeeman shifts. In this study, the DC Stark shift was negligible, and the AC Stark shift arising from the interaction between electric fields of light and atoms predominated. Ideally, to evaluate the frequency shift caused by variations in light power, another light beam interacting with the atoms would be required. However, this approach is challenging, as it would affect the frequency locking of the 852 nm laser. Therefore, our method involves adjusting the total power used for laser locking and recording the resulting frequency shift of the 852 nm optical frequency standard. Similar to collision-induced shifts, fluctuations in laser power not only cause AC Stark shift, but also induce SNR variations in the error signal, thereby impacting the Allan deviation of the 852 nm optical frequency standard.

To assess the impact of power fluctuations on the 852 nm optical frequency standard, we monitored the laser power over two hours. The short-term power stability was approximately $1.0\times {10}^{-5}$ at 1 s. Additionally, we determined the AC Stark shift coefficient to be about 30 kHz/mW under a probe laser power of 0.1 mW, which was measured by comparing beat-note frequency changes between the test and reference lasers, akin to evaluating the influence of vapor-cell temperature. Consequently, the frequency stability resulting from the power fluctuation was approximately $1\times {10}^{-16}$ at 1 s. The drift in frequency over two hours is illustrated by the light red line in Fig. 5(a). Allan deviation calculations indicated minimal frequency stability caused by laser power fluctuations, as depicted in Fig. 5(b), suggesting that power fluctuation was not the primary factor affecting system performance. Nevertheless, we intend to enhance the stability of the 852 nm ECDL power to minimize its impact on frequency stability.

The Zeeman shift can be considered negligible in this study. A double-layer mu-metal magnetic shielding was utilized around the vapor cell, maintaining the magnetic field at approximately 1 mG, with relative magnetic field fluctuations not exceeding 0.1 mG. According to the Breit–Rabi equation [31], the estimated second-order effect of the Zeeman shift is less than $560\mathrm{kHz}/{\mathrm{G}}^2$. Therefore, the frequency stability induced by the Zeeman effect is at a magnitude of ${10}^{-16}$.

In this study, the frequency of the pumping laser is phase modulated using an EOM crystal, leading to unavoidable RAM noise in the 852 nm optical frequency standard due to the variable birefringence of the EOM crystal and etalon effects [32]. The RAM noise can impact both short- and long-term frequency stability. To mitigate this effect, precise control over the temperature and bias voltage of the EOM crystal is necessary, which typically requires a wide feedback bandwidth.

Efforts have been made to minimize RAM impact. First, a half-wave plate was positioned in front of the EOM crystal to align the laser’s polarization with the principal axis of the EOM crystal. Second, the temperature of the EOM crystal was stabilized with fluctuations within tens of millikelvins at 1 s intervals. According to Ref. [33], temperature variations in the EOM crystal typically induce frequency shifts in the laser of several kilohertz per kelvin. Consequently, the frequency instability caused by RAM is maintained at ${10}^{-13}$, which is consistent with the findings depicted in Fig. 3(b). Moving forward, further efforts are required to suppress RAM noise to enhance short- and long-term frequency stability.

In addition to the technical noises mentioned before that degrade frequency stability, other factors affect the performance of the 852 nm optical frequency standard, including vibrations and electrical noises. Our next steps involve optimizing the temperature stability of the atomic vapor cell and EOM crystal, the laser power stability, the bandwidth of the servo feedback loop, and vibration isolation. These efforts aim to enhance the frequency stability of the 852 nm optical frequency standard.

The optical signal stabilized by MTS is a frequency standard but not strictly an optical atomic clock. Nevertheless, this scheme reflects the performance of an optical signal and provides better frequency stability than most RF sources. In our next work, using a femtosecond-laser-based optical comb to provide the phase-coherent clock mechanism that links the optical and microwave frequencies, we will derive an RF clock signal of comparable stability over an extended wavelength range. The frequency stability of $4\times {10}^{-13}$ at 1 s of a single optical oscillator at 852 nm will transfer to every comb tooth from 400 to 1600 nm. Facilitating the optical frequency metrology using a compact and transportable clock in fundamental physics experiments and practical devices is of great significance, such as in optical communication [34,35]. This compact 852 nm optical frequency standard can serve as a reference for frequency locking in microresonator frequency combs, enhancing the performance of coherent light detection in coherent optical communication systems.

Using such a stable optical frequency standard as the pumping and repumping lasers for the Cs beam clock, the laser frequency noise was greatly reduced and the performance of the Cs microwave atomic clock improved. (i) Compared with the distributed feedback Bragg (DFB) diode laser with SAS-stabilized frequency, the laser source obtained in this work has low frequency noise, and this reduces the noise to improve the SNR of the Ramsey signal. (ii) Although ECDL has lower frequency noise and a narrower laser linewidth [36], it is more sensitive to mechanical vibration and easier to lose locking. Therefore, we designed the automatic lock electrical module. After locking has been lost, the auto-lock module will finely scan the voltage applied on the PZT that controls the external cavity length or finely tune the control current applied on the laser diode to scan the MTS of the $\mathrm{Cs}6{\mathrm{S}}_{1/2}(F=4)-6{\mathrm{P}}_{3/2}(F^{\prime }=5)$ transition and lock the laser frequency to this reference again. The relock time is less than 10 s. Therefore, the laser sources in this work simultaneously combine the advantages of low frequency noise and high reliability to optimize the frequency stability and continuous operation capability of Cs microwave clocks.

Figure 6(a) shows the Ramsey fringes of the Cs microwave clock transition, whose linewidth is 431.7 Hz. The scanning range was 2 kHz, where the central frequency corresponded to the transition of ground state $|F=3,m_F=0⟩-|F^{\prime }=4,m_F=0⟩$. Using the hydrogen maser as a frequency reference, we measured the frequency stability of the compact Cs beam clock to be $1.8\times {10}^{-12}$ at 1 s, $2.2\times {10}^{-13}$ at 100 s, and $6\times {10}^{-15}$ at ${10}^5\mathrm{s}$. These values are better than those of the magnetic selection state Cs beam clock and optically pumped Cs beam clock using a DFB laser [37] as the light source, as depicted in Fig. 6(b). The frequency stability was calculated using Hadamard deviation because the frequency shift of the reference hydrogen clock was on the order of $5\times {10}^{-16}$ per day. During a testing time of more than 15 days, the magnitude of the reference clock’s drift was similar to that of the long-term stability of the tested Cs microwave clock. Therefore, using Hadamard deviation for stability calculation is more reliable. For comparison, the frequency stability calculated using the Allan deviation is represented by the blue circular points in Fig. 6(b). The results show that the frequency stabilities determined by the Allan deviation and the Hadamard deviation agree well when $\tau$ is less than ${10}^4\mathrm{s}$, but there is a slight discrepancy when $\tau$ exceeds ${10}^4\mathrm{s}$, likely due to frequency shifts in the reference. Moreover, the temperature of the Cs oven was 100°C, which is similar to other experiments. Therefore, the frequency stability was optimized due to the noise suppression of the laser sources. We integrated the frequency-stabilized 852 nm laser, including optical and electrical modules, into the Cs beam clock, and Fig. 1(c) shows the Cs clock product with the size of $553\mathrm{mm}(W)\times 454\mathrm{mm}(D)\times 177\mathrm{mm}(H)$. This miniaturized atomic clock combines the advantages of excellent frequency stability and frequency accuracy, and is used for communication, traffic, and national power as the primary frequency standard. Inside the sealed environment, the temperature of the 852 nm laser diode was seriously affected by the high-temperature oven, microwave generation module, and power supply, causing the internal temperature to be more than 30°C above room temperature. The temperature fluctuation of the laser diode affected the laser wavelength, so we designed the double temperature control to improve the environmental adaptability of the laser. In the future, we will further optimize the immunity to mechanical vibration of the laser for a longer continuous locking time.

In this section, we examine the connection between the frequency stability of the optically pumped Cs beam clock and the performance of the laser source.

First, compared to the Cs beam clock with magnetic state selection, the optically pumped method can significantly enhance the SNR of the Ramsey signal by preparing all atoms in the state $6{\mathrm{S}}_{1/2}|F=3,m_F=0⟩$ [38]. Additionally, since the laser beam is perpendicular to the atomic beam, this excitation method is not velocity-selective, thereby increasing the number of atoms in the beam. Moreover, optical state preparation helps avoid the frequency shift induced by Majorana transitions. In summary, the primary advantage of the optically pumped method over magnetic state selection is the improvement in the SNR. For the clock operation, the short-term frequency stability ${\sigma }_y(\tau )$ is highly dependent on the SNR and can be expressed as ${\sigma }_y(\tau )\propto \frac{{\tau }^{-1/2}}{\mathrm{SNR}}$, where $\tau$ is the sampling time. Therefore, the optically pumped method can significantly enhance short-term frequency stability.

However, this method can also introduce additional laser frequency noise. To substantially improve the frequency stability of the Cs clock, the laser frequency noise must be lower than the atomic shot noise, which is the fundamental noise source. Suppressing laser frequency noise or narrowing the laser linewidth can effectively enhance the SNR of Ramsey fringes [39,40]. For instance, Dimarcq et al. demonstrated that reducing the lase linewidth from 5 MHz to 100 kHz increased the SNR by an order of magnitude [39]. Therefore, it is crucial to narrow the laser linewidth or reduce laser frequency noise. Simultaneously, it is important to ensure that this high-performance laser source remains as compact as possible for integration into the microwave clock. Balancing performance and size is critical to the practical implementation of the system.

To compare the impact of laser frequency noise on the frequency stability of the Cs beam clock, we also evaluated the performance of a Cs clock using a DFB laser with a linewidth of approximately 1 MHz. The DFB laser’s frequency was stabilized by SAS and used for both pumping and probing. The frequency stability achieved with the DFB laser was on the order of ${10}^{-11}$ in magnitude, which is significantly inferior to that achieved with the ECDL frequency stabilized by the MTS.

As illustrated in Fig. 6(b), the black squares represent the frequency stability of the optically pumped Cs beam clock using an ECDL stabilized by MTS as the pumping and probe light source. The frequency stability was evaluated using Hadamard deviation due to frequency shifts in the hydrogen maser reference. In contrast, the pink triangular points represent the results obtained using the DFB laser, stabilized by SAS, as the pumping and probe light. This was assessed using the Allan deviation, as its long-term frequency stability was far from the limitations of the hydrogen maser. The comparison indicates that by improving the performance of the laser, the frequency stability of the Cs beam clock is enhanced by at least fivefold.

Although the results of this work surpass those of most compact and miniaturized optically pumped Cs beam clocks, there is still potential for further optimization by reducing the laser frequency noise. A detailed analysis of the influence of technical noises on the 852 nm optical frequency standard, along with strategies for further optimization, is provided in Section 2.C. Additionally, we plan to implement a two-laser pumping scheme [41] to enhance the SNR of fluorescence, aiming to further improve the frequency stability of the Cs beam clock to the ${10}^{-13}$ level at 1 s.

In this work, we experimentally demonstrated a dual-frequency optical-microwave atomic clock based on thermal Cs atoms. Two simple and reliable atomic clocks were simultaneously built with convenient operation, which could arbitrarily switch or simultaneously output microwave and optical signals. In other words, they expanded the application range of practical microwave atomic clocks and miniaturized high-performance optical atomic clocks.

First, using an ECDL as a local oscillator, after optimizing the experimental parameters, we achieved a highly stable Cs 852 nm optical frequency standard, with frequency stability being better than $7\times {10}^{-13}$ between 1 and 1000 s. When compared with other compact optical clocks, such as the two-photon-transition-based Rb clock achieving fractional-frequency instabilities better than $1\times {10}^{-14}$ for $\tau$ from 10 to 10,000 s [42], the ${\mathrm{I}}_2$ optical clock demonstrating short-term instability of $3.3\times {10}^{-15}$ for space-based gravity missions [43], the ${\mathrm{I}}_2$ optical clock with a frequency instability of $6\times {10}^{-15}$ at 1 s integration time for future space applications [24], and the integrated ${\mathrm{I}}_2$ optical clock achieving short-term instabilities of $5\times {10}^{-14}/\sqrt{\tau }$ at sea level [44], the performance achieved in our work indicates a need for further enhancement. Moving forward, we aim to enhance the temperature control accuracy of the atomic vapor cell, improve the power stability of the ECDL, suppress electronic servo noise, and reduce RAM noise. These efforts are crucial to optimizing the frequency stability of the 852 nm optical frequency standard. Nonetheless, our research extends the wavelength coverage of compact optical clocks and improves the frequency stability of optically pumped Cs beam clocks by mitigating laser frequency noise. Consequently, the development of 852 nm optical frequency standards holds promise for portable compact optical atomic clocks suitable for applications in gravitational wave detection, geodesy, and measurements of the time variation of fundamental constants. Second, by applying this optical frequency standard as the laser source in the Cs microwave atomic clock, we optimized the frequency stability of the Cs microwave clock to be $6\times {10}^{-15}$ at ${10}^5\mathrm{s}$, better than the values of most miniaturized microwave clocks.

In the future, we will derive an RF clock signal of comparable frequency stability to the 852 nm optical frequency standard over an extended wavelength from 400 to 1600 nm. This result will make Cs atoms the next length standard, include them in the CIPM, and facilitate the application of frequency metrology to precision experiments for fundamental physics and practical devices for communication.