Atomic spectrometry serves as the foundation for achieving quantum precision measurement. Controlling the state of the atom through light has significant applications in various fields, especially for measuring external physical parameters, including magnetic fields^[1–3], electric fields^[4], time^[5–7], and angular velocity^[8,9]. In particular, the frequency stabilization system based on the atom spectrum is the guarantee of the stability of the laser frequency in the quantum measurement equipment^[6,10–12]. In this regard, developing the atom–photon interaction devices that accurately capture the spectral response of atoms is crucial for achieving a high-precision laser frequency stabilization system. However, in order to construct an atom–photon interaction device, a large number of optical elements are generally required to control the polarization, amplitude, and propagation of the light field. Currently, the demand for compact, portable, adjustable, and scalable quantum sensors is increasing. Therefore, there is an urgent need for miniaturized and adjustable atom–photon interaction devices.

In recent years, the integration of nano-optical structures with thermal atomic vapor has been proposed and demonstrated, showcasing significant potential. The integration approach can be classified into two types: 1) Designing nano-optical structures that generate evanescent light fields and that then interact with thermal atoms^[13–16], and 2) developing nano-optical structures that convert guided wave light into free-space light that enables interaction with atomic vapor^[3,17–19]. In the case of the interaction between the thermal atoms and the near-field light, the waveguide’s evanescent field enhances atom–photon interaction by tightly confining light on a micrometer scale. Recent studies show that waveguide structures with thermal atomic vapor can stabilize 780 and 1550 nm lasers^[20,21]. However, accurate atomic spectra are challenging due to limited interaction time between near-field photons and atoms, causing significant broadening effects. To enhance the interaction time between photons and atoms, extreme mode converters are proposed to convert guided light into free-space light^[18,22,23]. This type of converter has been successfully employed in a laser frequency stabilization device at 780 nm upon integration with an atomic vapor cell^[24]. Nevertheless, its design is intricate and requires stringent process conditions, and light coupling losses within the mode converter are a concern. To address these challenges, optical transformation structures based on metasurfaces are proposed to optimize multiple optical parameters^[25–30].

Based on these considerations, we have developed an approach that enables metasurfaces to control the atom–photon interaction and demonstrated that it is feasible to a obtain sub-Doppler spectrum^[31]. The demonstration illustrates the feasibility of employing metasurfaces to manipulate atomic spectra and construct integrated quantum measurement devices, providing significant insight. However, the integration process for the metasurface atomic vapor cell remains immature, resulting in poor vacuum performance. As an alternative, the metasurface chip can be independently employed in a standard laser frequency stabilization system. This means the metasurface chip and a conventional glass vapor cell can be separately installed using packaging techniques. The metasurface chip’s multifunctional capabilities allow for a simplified design of traditional atomic frequency stabilizers, offering a more flexible assembly method.

In this Letter, a compact laser frequency stabilization system operating at 780 nm is proposed, utilizing a multi-functional metasurface chip in combination with a rubidium (Rb) atomic vapor cell. In these configurations, the frequency stability of 3×10−11 from 1 to 200 s can be obtained even when the incident light power is below 20 µW. This laser frequency stabilization scheme aligns with the trend of device integration, which is helpful for simplifying the composition of the device. As schemed in Fig. 1(a), the optical components for the laser frequency stabilization device can be packaged in a small volume. In the future, it has the potential to be combined with the micro-mechanical fabrication of atomic vapor cells for the mass production of laser frequency stabilization devices^[32–35].

Sub-wavelength grating displays significant artificial birefringence^[28,29,36], enabling effective manipulation of the light field for precise control of the atomic spectrum^[31]. Utilizing this structure to modulate both the intensity and polarization of reflected light across a broadband spectrum constitutes an effective method for enhancing the tunability of atomic spectra and stabilizing laser frequency. Based on that, we have developed a sub-wavelength grating structure that utilizes silicon nanowires as the grating and borosilicate glass as the substrate, achieving high reflectance and transmittance for TM- and TE-polarized lights, respectively. In this work, the wavelength of 780 nm is considered, which aligns with the atomic spectrum associated with the Rb D2 line transition. Here, the sub-wavelength grating is constructed with a t=290nm thick silicon layer and the period Λ=441nm with the wire width w=285nm, as shown in Fig. 1(b). The refractive index (RI) of silicon is 3.46 and the RI of the borosilicate glass is 1.47. The nanograting structure is patterned on a wafer by electron beam lithography and dry etching process, and then the metasurface chip is diced into a size of 17mm×21mm. As shown in Fig. 1(c), the circular region with a diameter of 1 mm at the center of the chip is the sub-wavelength grating structure. The enlarged part displays the scanning electron microscope (SEM) image of the sub-wavelength grating.

The grating structure exhibits two eigenmodes, corresponding to polarization along the x-axis (TM polarization) and y-axis (TE polarization), respectively [see Fig. 1(c)]. For a linearly polarized incident light, the electric field ErMS for the reflected light of the metasurface can be expressed as ErMS=E0[rxcosφrysinφ],(1)where E0 and φ represent the initial amplitude and the polarization angle of the incident light, respectively, and rx (ry) is the complex reflectance for the perfect TM (TE) polarized incident lights, where φ=0° for TM polarization and φ=90° for TE polarization. Specifically, the angle difference δ=arg(ry)−arg(rx) represents the phase shift between the TE and TM polarization components of the reflected fields introduced by the metasurface. Further, the ellipticity χ for the polarization state of the reflected light can be deduced by sin(2χ)=1(rx*rx+ry*ry)E02ErMS*[0−ii0]ErMS,(2)where ErMS* is the Hermite matrix of ErMS. By changing the polarization state of the incident light from TM to TE polarization, the reflectivity, transmissivity, and ellipticity of the reflected light induced by the metasurface are adjusted. As shown in Fig. 2(a), when the polarization angle changes from 0° to 90°, the reflectivity and transmissivity vary in the ranges of 0.93 to 0.16 and 0.01 to 0.72, respectively. The transmission results indicate that the polarization extinction ratio is more than 18 dB, which means that the transmitted light is nearly a TE-polarized field. The polarization state of the reflected light is depicted in Fig. 2(b), showcasing the ellipticity variation within an amplitude range from 0° to 30°. With Eqs. (1) and (2), the corresponding parameters of the metasurface can be calculated by fitted rx and ry from the experimental results. Using the measured curves shown in Figs. 2(a) and 2(b), we obtained |rx|=0.93, |ry|=0.16, and δ=65°, and the calculated results also are displayed in Figs. 2(a) and 2(b). These results demonstrate the capability of the all-dielectric metasurface chip to manipulate the reflectivity, transmissivity, and polarization state of the incident light. This metasurface chip can be utilized as a replacement for the cascaded waveplates to achieve control of the light fields. It provides a key component for flexible adjusting and streamlining the laser frequency stabilization system.

When incident light passes through the atomic vapor and hits the metasurface, the interference between the left-hand and right-hand circular polarization σ± components, as well as the interactions of two photons for populations and Zeeman coherences in three-photon mixing, makes the atomic spectrum highly dependent on the polarization state. In particular, sub-Doppler transparent responses can be achieved when the circular polarization component of incident light exists^[31]. Therefore, by adjusting the polarization state of the incident light, a distinct narrow bandwidth transparent peak can be achieved in the atomic transmitted spectrum. Subsequently, the laser frequency can be stabilized by locking this peak response. In laser frequency stabilization systems, the use of the metasurface with an atomic vapor cell not only provides flexible control of the optical field but also reduces the size of the conventional frequency stabilization devices. To optimize the peak for greater frequency stabilization, we will fine-tune the circular polarization component of the incident and reflected lights to modify the spectral shape of the transparency peak. To account for the input and reflected lights with distinct circular polarization components, on the basis of the metasurface intrinsic mode analysis, the incident light is set to be elliptically polarized. Typically, the elliptical polarization light can be generated by a cascade of a polarizer and a quarter-wave (λ/4) plate, where there is an angle difference (θ) between their optical axes, with the polarizer oriented along the x-axis. Thus, the electric field of the incident light can be expressed as Ein=E0[1+icos(2θ)isin(2θ)],(3)and then the electric field for the reflected light of the metasurface can be given by ErMS=E0[rx[1+icos(2θ)]irysin(2θ)].(4)

From Eqs. (3) and (4), it can be found that the ellipticities of both the incident and reflected lights are changed by adjusting θ. As shown in Fig. 3(a), the experimental result demonstrates that the magnitude of ellipticity of the reflected light is varied between 0° and 13° as changing θ from 0° to 90°, which indicates that the polarization states of the reflected lights can be altered with changes in the polarization states of the incident light. A comparison with the calculation result obtained using Eq. (4) is also provided. It is evident that when θ=30°, the ellipticity of polarization attains its maximum value. Meanwhile, Fig. 3(b) shows that the reflectivity ranges from 0.56 to 0.96 as a function of θ, demonstrating the intensity tunability of the reflected light passing through the hybrid vapor cell. With the incident power of about 20 µW for the cell, the atomic spectra of the transmitted light at different θ from 0° to 50° are obtained and depicted in Fig. 3(c). The measured sub-Doppler atomic spectra show that changing θ leads to a transition between the transparent peak and the absorption dip, since the behavior of the atoms is affected by the intensity and polarization of the reflected light. The line width of this peak varies with changes in θ, demonstrating the most defined sharpness at θ=30°. At this point, the ellipticity of the reflected light is at its maximum, and consequently, the circular polarization component is also maximized. This characteristic provides a prominent spectral feature that can be leveraged as a precise targeting point within laser stabilization systems.

Based on the above analysis, a laser frequency stabilization system based on the metasurface atomic vapor cell was established on the optical platform, as shown in Fig. 4(a). The system contains two lasers with a wavelength of 780 nm as the stabilized laser and the reference laser, respectively. The stabilized laser is split into two copies using a fiber-coupled beam splitter with a ratio of 99:1. The lower power splitter light path is used for frequency stabilization, while the higher one is employed for subsequent applications, in this setup, as the measuring light for characterizing the frequency stabilization performance. The stabilization light emitted from the fiber is converted into collimated free-space light, and then the beam spot is shaped by a focusing lens. The elliptically polarized incident light is produced by combining a polarizer with a λ/4 waveplate, which is incident on the metasurface structure after passing through the vapor cell, and the reflected light then reenters the vapor cell, where the photons interact with the atoms once more. The cylinder vapor cell has a diameter of 15 mm, a length of 70 mm, and a vacuum level better than 10−6Pa. Because of the increase in the interaction length between the light and the atoms, the device can operate at room temperature, and then the transmitted light is detected by a photodiode (PD) as a probe. The transparent peak in the transmission spectrum is identified and used to adjust the laser drive current with a servo loop to stabilize the laser frequency. To assess the laser frequency stability performance, a beat frequency measurement system was constructed. The reference laser is interfered with the split light from the stabilized laser using a coupler in the measurement system, which is stabilized using a typical saturated absorption spectroscopy (SAS) setup. The beating signal is generated using a photodiode and sent into a frequency counter, which is used to evaluate the performance of the laser frequency stabilization device.

In this work, the laser frequency stabilization system is designed to stabilize the frequency at the transparent peak of the atomic spectrum. Therefore, the sharpest spectral transparency peak is reached at θ=30° as shown in Fig. 3(c), and then laser frequency stabilization is achieved by locking at this transparent peak. The measured Allan deviations are shown in Fig. 4(b) for both the free running and locked laser. It can be found that the laser frequency is locked at the transparent peak of the transition Rb87:Fg=1→Fe, and the instability of 3×10−11 from 1 to 200 s is realized.

In this Letter, we propose a laser frequency stabilization system using a metasurface chip with an atomic vapor cell. The key to achieving frequency stabilization using this method is obtaining a clearer sub-Doppler peak. The above analyses show that the sub-Doppler spectrum can be obtained and controlled by adjusting the polarization, amplitude, and transmission direction of the incident light. Controlling the optical transmission in traditional systems often involves a series of components like polarizers, waveplates, attenuation plates, and mirrors, resulting in large and complex systems. To address this issue, we design and fabricate a multifunctional metasurface that can adjust the polarization, amplitude, and propagation direction of light to obtain the transparent sub-Doppler peak using only one chip. This greatly reduces the volume of the system and simplifies regulation. However, the current metasurface does not cover the full range of ellipticity in the reflected light. By optimizing the structure to expand the ellipsometric range, sharper sub-Doppler transparent peaks could be achieved, potentially providing effective frequency locking points. Such improvements are expected to enhance the performance of frequency stabilization systems in future work.

Here, we demonstrate laser frequency stabilization using the sub-Doppler transparent peak associated with the Rb87:Fg=1→Fe transition lines. However, this method is not restricted to this specific frequency locking point and can be adapted to other transition lines as needed. For instance, adjusting the polarization state of the incident light can reveal a sub-Doppler transparent peak in the Rb85 transition lines for laser frequency stabilization.

Additionally, compared to integrated hybrid metasurface atomic vapor cells, where the metasurface is integrated with the vapor cell cavity, standalone vapor cells combined with current vapor cell preparation advantages allow for various shapes of atomic vapor cells to be prepared in a high vacuum. In this Letter, we demonstrate the use of a cylindrical vapor cell, which can be made smaller to accommodate more narrow environmental requirements. Above all, this approach provides a more flexible solution for compact laser frequency stabilization systems.

In summary, we present a laser frequency stabilization system that employs tunable sub-Doppler atomic spectra generated by a metasurface with an atomic vapor cell. The metasurface with the atomic vapor cell is able to manipulate the atomic spectrum by controlling the incident light field, including polarization, amplitude, and propagation direction, and generate the sub-Doppler transparent peaks that stabilize the frequency of the laser. The utilization of the metasurface chip can be a substitute for cascaded waveplates, thereby simplifying the structure and reducing the volume of the system. The measurement results indicate that the instability of 3×10−11 from 1 to 200 s is achieved. The metasurface chips with atomic vapor cells provide a feasible approach to achieve miniature frequency stabilization systems.