Nowadays, optical clocks have achieved an instability of ${10}^{-19}$, making significant breakthroughs in fundamental physics tests [1–6]. They have found wide applications in fields such as atomic physics [7,8], quantum optics [9,10], and precision measurements [11–13]. However, the complexity and large size of laboratory-based optical clock systems severely limit their application scenarios and operational efficiency [13–15]. To address this issue, it is crucial to integrate the complex components of optical clock systems into highly integrated units, reducing system complexity, minimizing volume, and enhancing portability. In recent years, significant advancements have been made in transportable laboratory optical clocks, facilitating geodesy experiments [14] and testing general relativity [13]. However, despite achieving transportability, factors such as sensitivity to environment and the need for manual maintenance still impose limitations on their application scenarios and efficiency.

Using thermal atoms or molecules as optical references could significantly simplify the complexity of the system, enhance integration, and improve portability [16–19]. Building upon this approach, employing modulation transfer spectroscopy (MTS) [20–26] offers better frequency instability compared to saturated absorption spectroscopy [27–29] and requires no vacuum system compared to Pound–Drever–Hall (PDH) locking [30–33] to lock lasers to atomic transition lines. This, combined with corresponding mechanical and thermal control designs, enables the entire optical frequency standard system to be enclosed within a compact enclosure [15,24,34,35]. Furthermore, reducing or even eliminating the cost of manual maintenance and achieving a turn-key function are the key issues for improving the efficiency and resistance to environmental changes of transportable optical clocks. One of the primary reasons for manual correction in optical clock systems is the laser source’s free-running frequency drift, after long-term placement, to drift away from the target operating frequency, leading to challenges in subsequent frequency locking. The method of using software to identify absorption lines allows for partial compensation of the drift by adjusting parameters such as diode current, thereby enabling automatic frequency locking [36–38]. However, after prolonged idle periods or exposure to significant vibrations or temperature shocks, the laser output wavelength may deviate substantially from the target transition line. In such cases, manual adjustment of the internal frequency-selective components’ angle is required to restore proper operation. This issue can be resolved by utilizing a newly proposed atomic-filter-based laser [39–42], where the laser frequency is automatically matched to the atomic transition line using an atomic filter as a frequency selection element. This laser is immune to the fluctuation of diode current and temperature. Moreover, throughout long-term operation, it maintains the output frequency within the Doppler width of the atomic transition lines without requiring human intervention, thereby enabling a turn-key optical frequency standard once the laser frequency is stabilized [39].

Atomic-filter-based lasers can be categorized into two types based on different principles of atomic filtering: Faraday lasers [40–42] and Voigt lasers [39], both capable of achieving the turn-key functionality. Considering the potential advantages of Voigt lasers in system integration and miniaturization, Voigt lasers could be prioritized for assembling optical clock systems. However, since the proposal of atomic filters in 1956 [43], there have been few articles reporting on the Voigt anomalous dispersion optical filter (VADOF) [44–48], and it was not until 2023 that the Voigt laser was first realized [39]. Despite their superior resistance to environmental changes, Voigt lasers face challenges in automatically aligning with atomic spectral lines. Since the output wavelength of Voigt lasers always corresponds to the highest transmission peak in the VADOF transmission spectrum, comprehensive research on VADOF is essential to optimize its transmission spectrum and align the highest transmission peak with atomic transition lines.

In this article, we report and design a portable optical frequency standard, the Voigt optical frequency standard, which achieves turn-key functionality. This development greatly expands the application range and efficiency of optical clocks in various research fields. The parameters of the VADOF have been thoroughly investigated, employing sophisticated magnetic field design and precise temperature control to achieve alignment of the transmission spectrum’s peak with atomic transition lines. This advancement could lead to the development of a Voigt laser capable of automatic correspondence with atomic transition lines. Following frequency stabilization using modulation transfer spectroscopy, a turn-key Voigt optical frequency standard is realized. In this case, the Voigt optical frequency standard will autonomously generate the desired frequency laser upon activation, regardless of the prolonged placement or abrupt variations in environmental parameters. Detailed analyses were conducted to optimize factors influencing both short-term and long-term instability. As a result, a Voigt optical frequency standard with a short-term instability of $8.5\times {10}^{-14}/\sqrt{\tau }$ was developed, and a long-term instability was measured as $5.8\times {10}^{-13}$ at an integration time of 10,000 s. Due to its inherent turn-key features, compact size, and portability, the Voigt optical frequency standard can continuously operate in various work environments such as laboratories, factories, and outdoor settings. It offers extensive application scenarios and convenient usability, with potential for operation even in marine or outer space environments.

The three-dimensional structure of the Voigt optical frequency standard is depicted in Fig. 1(a). Using the modulation transfer spectroscopy technique, the frequency of the Voigt laser is locked to the ${}^{85}\mathrm{Rb}$ D₂ transition lines $5^2{\mathrm{S}}_{1/2},F=3\to 5^2{\mathrm{P}}_{3/2},F=4$, resulting in a precise Voigt optical frequency standard. The detailed MTS experimental scheme is provided in Appendix A. The Voigt optical standard incorporates all optical components within a compact enclosure measuring $36\mathrm{cm}\times 31.4\mathrm{cm}\times 12.5\mathrm{cm}$, while the electrical components are housed in a separate enclosure with dimensions of $42\mathrm{cm}\times 40.5\mathrm{cm}\times 9.5\mathrm{cm}$. With a total mass of 28 kg, this system can be easily carried by a single person without the need for a large truck [13,14], providing exceptional portability. Subsequently, this standard is compared with an optical comb for down-conversion of its frequency into the microwave range and facilitating instability evaluation. The optical comb is capable of generating a broad spectrum spanning from 1450 to 1650 nm. In order to align with the Voigt optical frequency standard and enhance signal output, single-pass frequency doubling is employed to concentrate the emission at a wavelength of 780 nm. When the single-pass frequency doubling technique is applied, wavelengths near a specific wavelength in the broadened spectrum are doubled in frequency. For the optical comb in this experiment, a frequency-doubling crystal is selected for 1560 nm. When the supercontinuum laser enters the crystal, it automatically exhibits frequency-doubling effects exclusively for the 1560 nm wavelength, effectively selecting a specific single wavelength for frequency doubling and outputting a 780 nm laser. The detailed assessment of frequency instability and influencing factors for the Voigt optical frequency standard is presented in Fig. 1(b). Due to limitations on short-term instability associated with the optical comb, which reference the hydrogen clocks, accurate evaluation of frequency stability for the Voigt optical frequency standard necessitates separate discussions on short-term and long-term instability. Short-term instability is obtained through beat measurements between two identical Voigt optical standards, while the long-term instability is achieved through the utilization of a Voigt optical frequency standard incorporating a frequency comb.

For short-term instability, the decisive factor is the frequency noise mainly induced by the residual amplitude noise, with significant contributions from parasitic etalon effects and birefringence [24]. Currently, the achievable short-term instability is $1.38\times {10}^{-13}$, which corresponds to the equivalent frequency instability associated with the measured frequency noise, as shown by the red dots and green squares in Fig. 1(b). Therefore, the short-term instability of the Voigt optical frequency standard is $8.50\times {10}^{-14}/\sqrt{\tau }$ according to the linear fit result, seeing the black dashed line in Fig. 1(b). To further improve this, parasitic etalon effects must be mitigated using wedge-shaped electro-optic modulation (EOM) crystals and wedge-shaped reference cells, thus reducing residual amplitude noise. For the long-term instability test, the short-term instability $3.75\times {10}^{-13}/\sqrt{\tau }$ is primarily limited by the suboptimal short-term instability $3.5\times {10}^{-13}/\sqrt{\tau }$ of the optical comb, seeing the black triangles and cyan pentagrams in Fig. 1(b). When the integration time is less than 100 s, the data obtained using the frequency comb are constrained by its short-term instability. However, for integration times exceeding 100 s, these data can effectively capture the long-term instability of Voigt optical frequency standard, which amounts to $5.8\times {10}^{-13}$ at 10,000 s.

The compact optical frequency standard, with its turn-key operation and portability, has the potential to broaden application scenarios and improve resistance to environmental changes, making it a valuable tool for advancing the use of optical frequency standards in both civilian applications and challenging environment testing. While the portability of the Voigt optical frequency standard has been previously discussed, its unique feature lies in its turn-key ability, which stems from the inherent capability of the Voigt laser to automatically align with atomic transition lines. Specifically, upon activation, the laser frequency remains aligned with atomic transition lines without requiring any manual adjustment, achieving instant frequency locking. However, as previously mentioned in Section 1, achieving turn-key capability for the Voigt optical frequency standard also necessitates precise alignment between the VADOF transmission spectrum and atomic transition lines. This constitutes our primary challenge that needs to be addressed.

It is worth mentioning that previous theoretical models of the transmission spectrum of atomic filters were based on the two-level approximation, neglecting the Rabi frequency term, i.e., the laser intensity term, and only applicable to weak laser intensity conditions, which is close to saturation intensity [49,50]. To calculate the transmission spectrum of atomic filters under high laser intensity, the laser intensity term needs to be incorporated into the theoretical framework to build a new model. Currently, for lasers several orders of magnitude above saturation intensity, there is a significant discrepancy between the atomic filter’s transmission spectrum and theoretical calculations, requiring detailed experimental research. To ensure the reliability of the experimental results, the laser intensity used to detect the transmission spectrum is $350\mathrm{mW}/{\mathrm{mm}}^2$, which is of the same order of magnitude as the intracavity laser intensity of the Voigt laser. Specific calculations of the intracavity laser intensity of the laser are detailed in Appendix B. Through studying VADOFs at different magnetic fields and temperatures, we have found the optimal parameters suitable for Voigt lasers: a magnetic field strength of 3700 G and a working vapor-cell temperature of 81.5°C. It is noteworthy that in the presence of a weak magnetic field ($<1000\mathrm{G}$), the transmission spectrum readily aligns with atomic transition lines. However, as the detection power increases, the transmittance of the VADOF decreases, rendering this parameter unsuitable for constructing a Voigt laser [39]. Detailed studies on the vapor-cell temperature and laser intensity of the atomic filter are provided in Appendix C.

Assembling the VADOF with the above parameters into the Voigt laser results in a laser that automatically corresponds to the atomic transition line, as shown by the inset in Fig. 2. The light, stimulated by the diode, is collimated using a collimating lens to form a Gaussian beam with a diameter of 1 mm. Subsequently, the collimated light passes through the first polarizing beam splitter (PBS), selectively transmitting only P-polarized light. Upon traversing an ${}^{87}\mathrm{Rb}$ atomic cell measuring 30 mm in length, the polarization direction of the light, whose frequency is near the cyclic transition line, undergoes a rotation of 90 deg and becomes S-polarized. This S-polarized light is then reflected by the second PBS and enters a high-reflectivity laser mirror mounted on a piezoelectric ceramic and finally returns along the original path to achieve laser oscillation. It should be noted that a Peltier element is placed beneath the laser diode for temperature control, while a heating film is used to regulate the temperature of the atomic gas cell in the VADOF. Both achieve a temperature control precision of 1 mK. Under the frequency selection effect of VADOF, the output laser only fluctuates within 750 MHz around the highest transmission point of the transmission spectrum. As shown in Figs. 3(b) and 3(c), the laser wavelength remains within the range of 780.2430 nm to 780.2444 nm (1.4 pm) when the diode current and diode temperature change, demonstrating the Voigt laser’s excellent robustness to temperature and current fluctuations. Additionally, as shown in the saturated absorption spectrum in Fig. 3(a), the wavelength corresponding to the cyclic transition line of ${}^{85}\mathrm{Rb}$ is 780.2437 nm, which is exactly at the center of the laser wavelength fluctuation range. The Voigt optical frequency standard in this case can be immediately locked upon startup, enabling turn-key operation. As depicted in Fig. 3(d), even after a significant and rapid change in the laser diode temperature, the Voigt optical frequency standard promptly locks to the corresponding cyclic transition line without requiring any manual adjustment of the frequency-selecting element. In contrast, optical frequency standards based on other semiconductor lasers will drift from the reference when parameters such as diode temperature vary, leading to failure in locking. Then, high-precision wavelength meters and manual intervention are necessary to compensate for this drift, posing a major obstacle to achieving long-term automatic operation of atomic systems.

After achieving the portability and turn-key functionality of the Voigt optical frequency standard, further assessment and optimization of its instability are conducted. The short-term frequency instability is assessed by examining the frequency noise spectrum of the Voigt optical frequency standard. The frequency noise mainly comes from the baseline noise $S_{\mathrm{b}}(f)$. As depicted in Fig. 4, in the far-off resonance region of the MTS error signal, the phase noise analyzer (Rohde & Schwarz, FSWP) is utilized to measure the baseline noise. This noise encompasses residual amplitude noise introduced by the etalon effect and birefringence effect from the EOM crystal, as well as the birefringence effect of the reference cavity. Additionally, it incorporates electrical noise originating from the feedback servo circuit and other relevant sources. This baseline noise demonstrates the background noise level of the optical frequency standard system during operation, reflecting the system’s achievable performance limits. The baseline noise measured by the phase noise analyzer can be converted to frequency noise $S_{\mathrm{y}}$ using Eq. (1) and further transformed into equivalent frequency instability using Eq. (2) for intuitive evaluation, where the lower-frequency and the higher-frequency regions are connected to the shorter-term and longer-term instabilities, respectively [51]: $$S_{\mathrm{y}}(f)=\frac{{10}^{(S_{\mathrm{b}}(f)-13)/10}}{k^2},$$(1)$${\sigma }_{\mathrm{y}}^2(\tau )=2\int S_{\mathrm{y}}(f)\frac{{\sin }^4(\pi \tau f)}{{(\pi \tau f)}^2}\frac{1}{{\nu }^2}\mathrm{d}f,$$(2)where $k$ is the MTS signal slope, $f$ is the frequency of the frequency noise spectrum, $\tau$ is the integration time, $\nu$ is the frequency of the optical carrier (384.229 THz), and ${\sigma }_{\mathrm{y}}$ is the equivalent frequency instability. However, due to the minimum sampling frequency limitations of the phase noise analyzer, this approach is restricted to evaluating short-term instability in this study.

The methodology for determining the optimal parameters is as follows: while altering the parameters, monitor the changes in the MTS slope and the baseline noise spectrum to achieve optimal equivalent short-term instability. As shown in Fig. 5(a), when the temperature of the reference cell is increased from 32°C to 44°C, the MTS slope rises from 1.66 to 2.52 V/MHz; therefore, the equivalent short-term instability decreases from $1.7\times {10}^{-13}/\sqrt{\tau }$ to $1.1\times {10}^{-14}/\sqrt{\tau }$. When the temperature reaches 44°C, the increase in MTS slope nearly saturates. Further temperature increases would introduce higher atomic collision noise and higher system power consumption, leading to a rise in equivalent instability. Therefore, the optimal temperature for the reference cell is 44°C.

In the MTS optical path, the power levels of the pump laser and the probe laser significantly affect the phase detector slope and baseline noise, necessitating a detailed discussion. The photodetector approaches saturation at a probe light power of 0.2 mW. To ensure that the saturated absorption spectrum signal and error signal remain undistorted, the maximum probe power is set to 0.2 mW. Additionally, the pump power is gradually increased from 0.2 to 2 mW. As shown by the black curve in Fig. 5(b), at a pump power of 0.2 mW, the equivalent short-term instability decreases from $5.7\times {10}^{-13}/\sqrt{\tau }$ to $9.5\times {10}^{-14}/\sqrt{\tau }$ as the probe light power increases from 0.02 to 0.2 mW, reaching minimum at 0.2 mW. In this case, the increase in MTS slope is greater than the increase in baseline noise, resulting in a decrease in equivalent instability. However, if the probe power continues to increase, the increase in MTS slope will become comparatively smaller than the increase of baseline noise, leading to a subsequent rebound in equivalent instability. Increasing the pump power leads to a more rapid attainment of the minimum equivalent instability, and the value of this minimum will vary. By increasing the pump power to 2 mW, the system achieved the minimum equivalent instability of $9.26\times {10}^{-14}/\sqrt{\tau }$ when the probe power was set at 0.1 mW. Based on our experimental findings, a pump power of 0.6 mW and a probe power around 0.16 mW yield a minimum equivalent short-term instability of $8.77\times {10}^{-14}/\sqrt{\tau }$. In this case, the beat instability of two optimized Voigt lasers is shown in Fig. 5(c), with a short-term instability of $8.5\times {10}^{-14}/\sqrt{\tau }$ after linear fitting. This represents the best short-term instability under the current structure of the Voigt optical frequency standard, consistent with the equivalent short-term instability $8.77\times {10}^{-14}/\sqrt{\tau }$ derived from the frequency noise. The state-of-the-art Rb-locked frequency standards based on MTS technology currently achieve short-term stability of $4.5\times {10}^{-14}/\sqrt{\tau }$ [24], utilizing a wedged EOM and a reference cell to mitigate residual amplitude noise caused by the etalon effect. By optimizing our system following this approach, we expect to improve the short-term frequency instability of the Voigt optical frequency standard to the same level.

When assessing factors influencing long-term instability, it is imperative to modify the parameters of the optical frequency standard within a short timeframe, record the resulting frequency fluctuations, and evaluate their impact on various factors. However, it is essential that the frequency fluctuations caused by these short-term parameter changes are significantly greater than those observed during normal free-running operation of the optical frequency standard in order for this approach to yield reliable test data. Therefore, testing in a stable environment is essential to accurately evaluate the impact of various parameters on frequency drift and to obtain better long-term frequency instability data. To facilitate subsequent experiments, a Voigt optical frequency standard was moved to the underground laboratory of the National Institute of Metrology in China, where the daily temperature fluctuation is less than 0.6°C. Additionally, it is monitored by an optical frequency comb locked to a commercial hydrogen maser. As derived from Eq. (2), the low-frequency portion of frequency noise is a critical factor influencing the long-term frequency instability of the Voigt optical frequency standard. The low-frequency portion of the frequency noise partly originates from the long-term temperature fluctuations of the EOM and the long-term power fluctuations of the Voigt laser. Therefore, a thorough investigation of the impact of these two parameters is required. The EOM temperature and the laser power entering the MTS optical path were systematically varied within a short timeframe, while monitoring the frequency changes of the beat note between the optical frequency standard and the optical comb; the results are illustrated in Figs. 6(a) and 6(b). During the process of increasing the EOM temperature from 22°C to 27.4°C, the beat frequency exhibited a periodic variation with an interval of 0.8°C, while the EOM temperature frequency shift coefficient $k_{\mathrm{EOM}}$ underwent a cycle of large-small-large changes, with its minimum value observed around 25.5°C at 35 kHz/°C. Consequently, it can be concluded that maintaining an optimal EOM operation temperature at 25.5°C is crucial as lower values of $k_{\mathrm{EOM}}$ result in reduced frequency drift. The instability of the Voigt optical frequency standard with EOM temperature control is depicted as black squares in Fig. 6(b). In comparison to the red squares representing the curve without EOM temperature control, a noticeable divergence between the two curves occurs after 10 s. Notably, the frequency stability of the experimental system using EOM temperature control scheme improves with longer averaging time. After 10,000 s, the instability of the Voigt optical frequency standard with EOM temperature control is only one-quarter of that without temperature control.

Next, we evaluate the impact of the Voigt laser output power on the frequency of the optical frequency standard. In order to replicate the laser power fluctuations in the normal operation of the Voigt optical frequency standard, we intentionally manipulate the laser power entering the MTS optical path, where both pump and probe powers are adjusted proportionally. The measured frequency fluctuations of the Voigt optical frequency standard output are shown in Fig. 6(b). When the power is low, with probe power below 0.1 mW, variations in input power lead to significant frequency fluctuations of the optical frequency standard, indicating a high power frequency shift coefficient $k_{\mathrm{power}}$. Conversely, when the probe power approaches saturation at approximately 0.2 mW and beyond, the system poses a risk of losing lock due to probe power saturation during operation of the optical frequency standard, rendering it equally unsuitable. After comprehensive consideration, a probe power of 0.15 mW is chosen. The inflection point of the power frequency drift curve is precisely located at this position, exhibiting a minimal power frequency shift coefficient of only 50 kHz/mW on both sides and eliminating any risk of probe power saturation. The green squares in Fig. 6(c) represent the optimal Allan deviation of the Voigt optical frequency standard at this specific power point. In comparison to data obtained solely with EOM temperature control, the instability is further decreased.

After optimizing the adjustable parameters mentioned above to their optimal values, we conducted a comprehensive evaluation of the contribution of different parameters to the final frequency instability. This involved simultaneous monitoring of fluctuations in error signals, variations in reference cell temperature, changes in EOM temperature, and fluctuations in laser power over an extended period. The equivalent Allan deviation was then calculated based on the respective frequency drift coefficients, as illustrated in Fig. 7. The frequency instability below an averaging time of 100 s was mainly limited by the comb instability, shown as the black dot in Fig. 7. Otherwise, the short-term frequency instability should be consistent with the curve in Fig. 5(c). In the average time range of 100–10,000 s, the temperature fluctuations in the reference cell have a significant impact on system instability. Additionally, power fluctuations of the Voigt laser and the optical comb also contribute to system instability. As the average time is extended to 10,000 s, the influence of laser power fluctuations becomes dominant. The residual error noise refers to the remaining fluctuation of MTS error signal after frequency locking and reflects the feedback circuit’s ability to track atomic transition lines. It can be observed that it generally remains at a level of ${10}^{-14}$, with minimal impact on the final frequency stability.

Notably, the current long-term instability results still exceed the combined value of all contributing factors. This is mainly because our current evaluation method underestimates the impact of EOM temperature fluctuations on long-term frequency drift. When actively controlling the temperature of the EOM, we only regulate the temperature of the EOM’s metal shell, with temperature fluctuations less than 1 mK over 24 h. This results in a low estimated impact of EOM temperature fluctuations. However, there are multiple layers of air and low thermal conductivity materials between the EOM shell and the internal crystal, meaning the crystal’s temperature fluctuations could be significantly larger than the test results. Given the EOM’s large temperature frequency drift coefficient, the contribution of EOM temperature fluctuations to long-term frequency drift may far exceed the current calculation results. To address this issue, a customized system that directly controls the temperature of the EOM crystal is imperative. Once the above mentioned issues are resolved, it is expected that the short-term and long-term frequency instabilities of the Voigt optical frequency standard can be maintained at the ${10}^{-14}$ level. Furthermore, enhancing the power stability of Voigt lasers and optimizing the temperature control methodology for the reference cell can yield further advancements in the frequency instability of Voigt optical frequency standards.

In this study, we have developed a Voigt laser-based optical frequency standard and successfully demonstrated its turn-key functionality, which remains robust even in the face of severe temperature fluctuation in the laser diode without requiring any human intervention. The integration of modular optical and electrical components enables easy transport and operation by a single person. Through comprehensive frequency noise analysis, we conducted an extensive investigation into system parameters that affect the short-term and long-term instabilities of the Voigt optical frequency standard. By iteratively optimizing key influencing factors such as reference cell temperature, pump and probe laser power, and EOM temperature, we achieved optimal short-term stability of $8.5\times {10}^{-14}/\sqrt{\tau }$ and long-term stability of $5.8\times {10}^{-13}$ at an averaging time of 10,000 s, respectively. Furthermore, we reported the contributions of various parameters to the frequency instability of the Voigt optical frequency standard for future optimization purposes. Importantly, future integration of both optical and electrical components in the optical comb could lead to a truly compact turn-key Voigt optical clock with high portability and efficiency. Such advancements will be crucial in applications such as global navigation positioning, geodesy, and fundamental physical quantity measurements involving atomic clocks deployed on satellites, maritime vessels, transportation vehicles, or even individuals.