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arXiv:2507.04911

Dual frequency calibration to build a portable vapor cell optical clock with improved stability and without a frequency comb

Sreeshna Subhash, Greeshma Gopinath, Sankar Davuluri

Published Jul 7, 2025• 0 citations
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Abstract

This article theoretically proposes a new dual interferometer technique to accurately calibrate two laser frequencies simultaneously using four-wave mixing in an alkali metal vapor cell. The two frequency-calibrated lasers are mixed to create a beat signal at radio frequency to build a portable optical atomic clock (OAC) without an optical frequency comb (OFC). Removal of the OFC improves the portability of OAC, while the dual interferometer setup enhances the one second stability to $1.3\times 10^{-15}$, which is better than the current portable OAC. Thermal noise in the OAC is minimized by choosing the double-lambda atomic scheme with co-propagating laser fields. Using D2 transition of Rb-87, the standard quantum limited frequency sensitivity and stability of the OAC are estimated as $3.2\;\sqrt{\mbox{Hz}}$, and $1.3\times10^{-15}\sqrt{\mbox{Hz}^{-1}}$, respectively. After considering broadening effects due to $357\,$K temperature and collisions, the optimum stability of the OAC is reduced to $3.3\times10^{-15}\sqrt{\mbox{Hz}^{-1}}$ for a laser with $1\,$KHz linewidth and $0.54$ mW power at the input of the vapor cell.

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This article theoretically proposes a new dual interferometer technique to accurately calibrate two laser frequencies simultaneously using four-wave mixing in an alkali metal vapor cell. The two frequency-calibrated lasers are mixed to create a beat signal at radio frequency to build a portable optical atomic clock (OAC) without an optical frequency comb (OFC). Removal of the OFC improves the portability of OAC, while the dual interferometer setup enhances the one second stability to 1.3×10−151.3\times 10^{-15}1.3×10−15, which is better than the current portable OAC. Thermal noise in the OAC is minimized by choosing the double-lambda atomic scheme with co-propagating laser fields. Using D2 transition of Rb-87, the standard quantum limited frequency sensitivity and stability of the OAC are estimated as 3.2  \mboxHz3.2\;\sqrt{\mbox{Hz}}3.2\mboxHz​, and 1.3×10−15\mboxHz−11.3\times10^{-15}\sqrt{\mbox{Hz}^{-1}}1.3×10−15\mboxHz−1​, respectively. After considering broadening effects due to 357 357\,357K temperature and collisions, the optimum stability of the OAC is reduced to 3.3×10−15\mboxHz−13.3\times10^{-15}\sqrt{\mbox{Hz}^{-1}}3.3×10−15\mboxHz−1​ for a laser with 1 1\,1KHz linewidth and 0.540.540.54 mW power at the input of the vapor cell.
Optical frequency standards surpass their microwave counterparts in both stability and accuracy, yet they are often bulky, power-hungry, and unable to operate outside of a well-controlled laboratory environment. Leveraging a two-photon transition in 87{}^{87}87Rb vapor and recent advances in fiber frequency combs, the authors build an optical clock to beat the current portable standards, with an architecture that can be made compact and low-power. These results point the way to a real-world optical frequency standard of even higher stability, for applications such as satellite navigation.
We demonstrated a compact 780 nm rubidium optical clock, which includes an optical frequency standard and an optical frequency comb, with an optical volume of 11.6 liters. Unlike the 778 nm rubidium atomic clocks based on two-photon transition, here, the laser frequency is stabilized to the Rb D2 transition, using modulation transfer spectroscopy. This approach effectively eliminates Doppler background and provides a high signal to noise ratio and high sensitivity. A nearly 300 MHz microwave signal, whose phase exactly tracks that of the optical frequency standard, is generated via the optical frequency comb, yielding a frequency instability of 1.91 E-13 @1 s and 5.29 E-14 @1000 s in the electronic domain. To the best of our knowledge, this is the most precise frequency stabilization result for the first-excited-state transition of alkali metal atoms to date and represents the first optical clock based on this transition. These results offer a promising approach for the development of portable optical clocks.
Portable atomic clocks are essential in a wide variety of applications, most notably in the operation of global navigation satellite systems. Existing portable atomic clocks utilizing microwave-based interrogation schemes are now routinely eclipsed by the next generation of atomic frequency standards based on optical interrogation. While optical frequency standards demonstrate greatly improved frequency stability, they have only recently reached a level of technical maturity required to demonstrate this improved performance outside of well curated laboratory environments. Here, we demonstrate a fully autonomous and portable optical frequency standard based on an efficient dual-color excitation of the 5S1/2→5D5/25S_{1/2}\rightarrow5D_{5/2}5S1/2​→5D5/2​ two-photon transition in 87^{87}87Rb. The standard utilizes a combination of robust, highly developed commercial-off-the-shelf telecommunications technologies and a fully integrated portable optical frequency comb, providing the optical and microwave outputs vital for interfacing with existing electronic systems and infrastructure. The system demonstrates a fractional frequency stability of 1.9×10−131.9\times10^{-13}1.9×10−13 at 1s of integration time, reaching 3.5×10−153.5\times10^{-15}3.5×10−15 at 8000s of integration time without the need for drift removal. This portable demonstrator unit marks a significant achievement in the development of Rb optical atomic frequency standards, and for the deployment of optical atomic frequency standards outside of the laboratory.
Optical clocks represent the hallmark of precise timekeeping. The most precise atomic clocks are laboratory-based ones that utilize transitions in the microwave/optical domain of neutral atoms or trapped ions. These clocks define an international time scales, confirm the consistency of physical constants and stimulate the search for new physics outside the Standard Model. The other area is the regime of portable atomic clocks based on warm atomic vapor, which is small, power-efficient and deployable in the field with a variety of civilian applications, including sensing, communication and navigation. Two-photon resonance and optical transition based field deployable clocks present a viable alternative that may outperform current commercial chip scale clocks by at least a factor of 10 in terms of both long-term and short-term stability. For portable clocks, two-photon transitions in alkaline earth metals are of special interest. One of the systematic inaccuracies in the optical reference is eliminated by using counter-propagating laser beams to create Doppler-free spectroscopy. At IIT Tirupati, we are engaged in developing the next generation of atomic vapor based portable frequency standard using two-photon transition in Rubidium (Rb) for atomic sensing and quantum positioning applications. This article discusses the physics behind the two-photon transition in Rubidium atoms suitable for a clock reference. Briefly, it discusses the experimental methodology for realizing an optical clock using warm rubidium vapor.
Optical wavelength standards, based on the optical transitions of atoms or molecules, provide ultra-high precision frequency references and are the core technology of next-generation optical clocks. Their stability far exceeds that of the microwave frequency range, laying the foundation for precision metrology and cutting-edge scientific research. The wavelength standard device based on the 5S1/2-5D3/2 hyperfine level two-photon transition of 87Rb atoms exhibits significant advantages such as no Doppler broadening, high signal-to-noise ratio (SNR), and potential for miniaturization and chip integration, showing important application potential in precision measurement fields like rubidium atomic clocks and optical communication. In this paper, an experimental setup for two-photon transition was constructed using an external cavity diode laser (ECDL), achieving stable locking of the 778 nm wavelength by modulating the laser current. The effects of the temperature and length of the atomic vapor cell on the blue fluorescence linewidth, SNR, and frequency stability were systematically studied, further optimizing the system. By using an atomic vapor cell designed at Brewster's angle, optical reflection loss was effectively reduced, compensating for the impact of shortened optical path on frequency stability in miniaturized atomic vapor cells. This provides new research directions and performance enhancement solutions for the miniaturization and chip integration of two-photon transition systems. In the improved system, a Brewster-angle glass vapor cell with a length of 30 mm was used and heated to 110°C, achieving a linewidth of 1.69 MHz full width at half maximum (FWHM) and a SNR of 20 dB. The system demonstrated a instability of 9.86×10-11 over a 1-second averaging time and a minimum instability of 5.79×10-11 over a 5.7-second averaging time. This achievement provides key technological support for the practical application of the next generation of miniaturized optical atomic clocks, with the potential for widespread use in portable metrology equipment and space science through integrated design and noise suppression optimization in the future.
High precision portable and deployable frequency standards are required for modern navigation and communication technologies. Optical frequency standards are attractive for their improved stability over their microwave counterparts; however, increased complexities have anchored them in the laboratory. Sacrificing sensitivity of the most stable optical clocks has led to the recent development of deployable and portable optical frequency standards, leveraging hot atomic or molecular vapor. The short term limit for a majority of previous reports on two-photon rubidium standards is either the shot-noise or intermodulation limit hindering the one second fractional frequency stability to around 1×10−13/τ1\times10^{-13}/\sqrtτ1×10−13/τ​. The answer for the shot-noise limit is to increase optical power and collected fluorescence, while the intermodulation limit solution requires improvements in laser linewidth, stimulated Brillouin scattering (SBS) lasers are known to reduce frequency noise, suppressing noise of the pump laser at high offset frequencies. We investigate an optical frequency standard based on the two-photon transition in 87^{87}87Rb probed with a narrow linewidth photonic integrated circuit SBS laser with a quality factor over 130 million and instantaneous linewidth <<< 10 Hz. The use of a narrow linewidth clock laser coupled with operating at higher optical intensities yields clock instabilities of 2×10−142\times10^{-14}2×10−14 at one second, currently the best reported short-term stability for a two-photon rubidium optical frequency standard.